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2026-05-31T23:30:05Z
User contributions
MediaWiki 1.23.15
https://www.hexwiki.net/index.php/Board_size
Board size
2024-05-21T20:39:12Z
<p>HappyHippo: </p>
<hr />
<div>The '''board size''' in [[Hex]] varies, and no size is considered standard. 10 &times; 10 is considered by many a lower bound for interesting games.<br />
<br />
See also the article [[Small boards]].<br />
<br />
; 10 &times; 10<br />
: Used to be offered on [[Kurnik]] until 2008.<br />
; 11 &times; 11<br />
: The size [[Piet Hein]] used.<br />
: Offered on [[Kurnik]] as default.<br />
: The standard size on Richard Rognlie's [http://www.gamerz.net/pbmserv/ Play-By-eMail] server.<br />
: Offered on [[Board Game Arena]] as default.<br />
: Offered on [[Little Golem]].<br />
; 12 &times; 12<br />
: Offered on [http://en.boardgamearena.com Board Game Arena].<br />
: The size used for Con-tac-tix boards produced in the 60s.<br />
; 13 &times; 13<br />
: The original size on [[Little Golem]]. (Games with this size are still called "hex" by the site engine, while 19 &times; 19 Hex games are named "hex19".)<br />
: Offered on [[Board Game Arena]].<br />
: Offered on [[Kurnik]].<br />
; 14 &times; 14<br />
: The size [[John Nash]] used.<br />
: Offered on [[Board Game Arena]].<br />
; 15 &times; 15<br />
: Offered on [[Board Game Arena]].<br />
: Offered on [[Little Golem]].<br />
; 18 &times; 18<br />
: Used to be offered on [[Playsite]] and Lycos but they no longer offer Hex.<br />
; 19 &times; 19<br />
: Offered on [[Board Game Arena]].<br />
: Offered on [[Little Golem]].<br />
: Offered on [[Kurnik]].<br />
<br />
In addition, [[PlayHex]] offers all sizes from 1 &times; 1 to 42 &times; 42.<br />
<br />
<br />
Printable boards of size up to 14 &times; 14 here: [[Printable boards]].<br />
<br />
[[category: Rules and Conventions]]<br />
[[category: Online play]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Six
Six
2023-02-11T17:29:22Z
<p>HappyHippo: /* External links */ Add archive link</p>
<hr />
<div>Six is a free [[Hex]] playing program running on Unix written by Gábor Melis. The currently offered version is 0.5.3. It has won [[ICGA]] Hex tournament in 2003, 2004 and 2006. Six is quite good against human beings too.<br />
<br />
==Features==<br />
<br />
*It allows playing on boards of [[board size|size]] 4 to 15.<br />
*It offers 4 different skill levels (Beginner, Intermediate, Advanced, Expert).<br />
*Games as well as positions can be saved.<br />
<br />
==Windows Port==<br />
Six has been adapted to Windows by [http://www.littlegolem.net/jsp/info/player.jsp?plid=6603 ab]. The project came out of [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=301 a thread] in the [[Little Golem]] forum. "ab" separated the GUI from the Six engine, thus creating [[HexGui]], inspired by GoGui.<br />
<br />
To play the AI:<br />
*Put HexGui.jar and six_gtp_engine.exe in one directory<br />
*Double-click on HexGui.jar (or use "java -jar HexGui.jar")<br />
*File menu / attach / "six_gtp_engine.exe --level=0"<br />
*F5 to make a computer move, or<br />
*Game menu / Computer plays / "Black" or "White" or "Both"<br />
<br />
While the computer is thinking about its move, which can take a while at expert level, you cannot access all the program functions.<br />
The two zip files full of source code are unnecessary to play.<br />
<br />
==See also==<br />
<br />
[[Hexy]] is another Hex playing program. Hexy runs on Microsoft Windows.<br />
<br />
[[Roland Illig vs. Six 0.5.3, 2007-09-28]].<br />
<br />
==External links==<br />
<br />
[http://six.retes.hu/ Six on Gábor Melis page].<br />
<br />
[http://mgame99.mg.funpic.de/havannah.php Download Windows version] ([https://web.archive.org/web/20120322042711/http://mgame99.mg.funpic.de/havannah.php web archive link]).<br />
<br />
[http://www.grappa.univ-lille3.fr/icga/round.php?tournament=100&round=1 8 games between Six and Mongoose] in the 8th Computer Olympiad in Graz (2003).<br />
<br />
==References==<br />
<br />
[http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=294 Six is pretty darn strong on a fast machine] a forum topic by David J Bush (top hex rating > 2150 on [[Little Golem]]).<br />
<br />
[[category:Computer Hex]]<br />
[[category:Hex playing program]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Typesetting_Hex
Typesetting Hex
2023-01-22T15:24:20Z
<p>HappyHippo: </p>
<hr />
<div>When creating [[Hex]] diagrams for printed media, you can use raster graphics (if their resolution is high enough) or use a vector graphics application. Some tools specific to Hex have been created:<br />
<br />
* Meron Brouwer's [http://www.ctan.org/tex-archive/macros/latex/contrib/hexgame/ hexgame] is a package for [[Wikipedia:LaTeX|LaTeX]]<br />
* Tom Ace's [http://www.minortriad.com/golem2eps.html golem2eps] is an excellent still-improving EPS creator from a [[Smart Game Format|SGF]] file.<br />
* [[Cameron Browne]] has a tool for setting Hex diagrams, which he used in his [[Hex Strategy Making the Right Connections|book]].<br />
* It is possible to type Hex boards directly into text by using one of the [[Unicode and ASCII boards]]<br />
* A website for drawing diagrams and exporting them in SVG format: [http://www.mseymour.ca/hex_draw/hexdraw.html]<br />
* Some LaTeX code for drawing diagrams with tikz: [https://github.com/matthewseymour/hex_latex]<br />
<br />
For information on creating Hex diagrams on this wiki, see [[New board diagrams]].<br />
<br />
[[Category: Computer Hex]]<br />
[[Category: Resources]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Online_playing
Online playing
2022-05-09T14:11:27Z
<p>HappyHippo: </p>
<hr />
<div>Hex can be played online either using a web-based format or via e-mail. <br />
<br />
=Web-based games=<br />
<br />
Web-based games can be played either in ''real-time'', where moves are made within minutes (or even seconds), or ''turn-based'', where a player has days for one move.<br />
<br />
==Realtime playing sites==<br />
<br />
The most popular sites (approximatively ordered by the number of hex games played on them daily) are:<br />
* [[Kurnik|PlayOK (Kurnik)]] for real-time play with rankings, game records, tournaments<br />
* [[igGameCenter]] for real-time play, with time settings, and ranking (it has many connection games).<br />
* [http://en.boardgamearena.com Board Game Arena] supports real-time as well as turn-based play<br />
* [[boardspace]] for real-time play<br />
* http://www.ludoteka.com/ for real-time play<br />
* http://games.wtanaka.com/hex for real-time or turn-based play<br />
* [https://hex.plus Hex+] for high speed real-time play<br />
<br />
==Turn-based playing sites==<br />
<br />
* [[Little Golem]] for turn-based play (also has other games).<br />
* [http://en.boardgamearena.com Board Game Arena]<br />
* See also [http://www.gamerz.net/pbmserv Richard's server]. One can play completely by e-mail, but it also has a [http://www.gamerz.net/pbmserv/List.php?Hex graphical interface] now. Furthermore any sized board is supported.<br />
* Hex may also be played over e-mail, in a turn-based fashion, with [[Unicode and ASCII boards]].<br />
<br />
==Services for game analysis==<br />
<br />
There are some services in the net, which help one play out different variations, analyze the games and share game records.<br />
<br />
* [https://hexworld.org/board HexWorld] has an interactive board that can be shared as a link. It has all board sizes up to 30.<br />
<br />
* [https://www.trmph.com/hex/board TRMPH] has 3 board sizes: 11, 13 and 19. It can import games from [[Little Golem]].<br />
<br />
* [http://www.hexmaster.net/ Hex master] is a service for analyzing and commenting games from [[Little Golem]].<br />
<br />
* [https://minortriad.com/ahex.html AHex] is a service for analyzing games, including variations. See the extensive help page for more info. [[Little Golem]] provides a link to analyze games using this service.<br />
<br />
<br />
[[category: Hex community]]<br />
[[category: online play]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Swap_rule
Swap rule
2021-10-20T14:14:02Z
<p>HappyHippo: /* Size 13 */ Adding leela_bot's swap map</p>
<hr />
<div>The '''swap rule''' states that after Red plays the first move, Blue decides whether to swap colours or not. If Blue swaps colours, Blue becomes Red and Red becomes Blue. Whichever player ends up being Blue makes the second move and then the game continues as usual.<br />
<br />
== Reason for the swap rule ==<br />
<br />
When playing Hex without the swap rule, the [[first player]] has a considerable advantage. The swap rule was devised to make the game more even. Namely, if the first player plays a move that is too strong, the second player will swap and be in a strong position. And if the first player plays a move that is too weak, the second player will not swap (and therefore also be in a strong position). Therefore, the swap rule creates an incentive for the first player to play a move that is as fair as possible.<br />
<br />
The swap rule is sometimes also called the "pie rule", since it resembles the well-known "you cut, I choose" method for fairly dividing a pie between two people. Namely, one person cuts the pie in two, and the other person chooses which piece to eat. Here, the incentive for the first person is to make the two pieces as equal as possible.<br />
<br />
Since each opening move is theoretically either winning or losing, there exists no opening move that is exactly fair. For this reason, the second player theoretically has a forced win when playing with the swap rule. However, the second player's advantage is very small, and certainly much smaller than the first player's advantage would be when playing without the swap rule.<br />
<br />
== Implementations of the swap rule ==<br />
<br />
Swapping can be implemented in two ways, as follows. As usual, we assume that the players are Red and Blue, with Red going first.<br />
<br />
# '''"Swap sides":''' The players perform the swap by switching colours: Red becomes Blue and Blue becomes Red. After the swap, it is Blue's turn.<br />
# '''"Swap pieces":''' The players perform the swap by switching pieces. This means the initial red piece is replaced by a blue piece in the mirror image position, where the mirroring takes place with respect to the board's long diagonal. For example, a red piece at a3 becomes a blue piece at c1. The players do not switch colours: Red stays Red and Blue stays Blue. After the swap, it is Red's turn.<br />
<br />
In face-to-face play, the "swap sides" method is most practical, since it is easier for the players to switch colours than to remove and add pieces on the board. This is especially true when playing with pencil and paper. It is also less error-prone. On [[Online playing|online game sites]], the "swap pieces" method is more common, presumably because the colours are determined at the start of the game, and it is easier to change the board position than the colour designation. This also makes the game record more readable, since it is always clear which player was "Red" and which was "Blue".<br />
<br />
== When to swap ==<br />
<br />
The decision whether to swap is an important one. Accidentally swapping a weak move, or accidentally failing to swap a strong move, is bad for the second player. <br />
<br />
Different players have different preferences for which moves to swap. It is generally agreed that moves near the center of the board are far too strong and should be swapped, whereas moves on the first player's own edge (except in the obtuse corner) are too weak and should not be swapped. a1 and b1 are provably losing and should never be swapped. a3&ndash;a8, a10, a11, c2, and c10 (on an 11 &times; 11 board) are relatively balanced, and whether or not to swap them depends on the player's preferences. a9 is fairly weak and should probably not be swapped. Of course, the same applies to the corresponding cells on the opposite side of the board.<br />
<br />
To get an idea of which opening moves are winning, it is useful to study the situation for [[small boards]]. For boards up to size 9 &times; 9, the winning opening moves are known. While the winning opening moves have not been solved for boards of size 10 &times; 10 or greater, it is reasonable to extrapolate from the smaller board sizes. On the [[small boards]], the red hexes should be swapped, and the blue hexes should not be swapped. Fair opening moves are probably the ones that are near the boundary of red and blue. <br />
<br />
Some strong players have suggested that when a position is roughly balanced, having an extra stone on the board usually makes the game easier to play. This means that whenever there is doubt about a move, it might be a good idea to swap it. However, the first player can take advantage of this behaviour by playing a first move that is probably losing under perfect play. This idea has been popularized by "lazplayer" at littlegolem/igg.<br />
<br />
Another consideration is not to use the same opening move all the time. Some players may be very familiar with particular openings. Playing an unfamiliar opening can confuse the opponent.<br />
<br />
In the following diagrams, it is suggested that an opening move played in a red cell is probably winning and should be swapped; those in a blue cell are probably losing and should not be swapped; and those marked "*", which are near the boundary of red and blue, are probably relatively fair opening moves. It must be kept in mind, however, that these diagrams reflect somebody's sugjective guess. The opening on 11 &times; 11 boards has not been solved, so nobody really knows for sure which moves are winning or losing. Many players have different opinions on when to swap.<br />
<br />
=== Size 11 ===<br />
<hexboard size="11x11"<br />
coords="show"<br />
contents="S red:all blue:(a1--j1 g2--i2 k3 a9 c10--e10 b11--k11)<br />
blue:(a2--c2 a3) blue:(i10--k10 k9)<br />
E *:(a3--a8 a11 c2 c10)<br />
E *:(k1 k4--k9 i2 i10)"<br />
/> <br />
<br />
=== Size 13 ===<br />
<br />
Based on [http://www.mseymour.ca/hex_book/hexstrat.html Hex: A Strategy Guide] by Matthew Seymour.<br />
<br />
<hexboard size="13x13"<br />
coords="show"<br />
contents="S red:all <br />
blue:(a1--l1 a2--k2 a3 f3--i3 m3)<br />
blue:(a11 e11--h11 m11 c12--m12 b13--m13)<br />
E *:(a3--a10 a13 c2 c12)<br />
E *:(m1 m4--m11 k2 k12)"<br />
/><br />
<br />
<br />
Based on the [https://littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=739 swap map] of leela_bot, a very strong computer player on LG. Moves have been marked as "close" when the odds of winning are within 10% of even (40-60%). <br />
<br />
<hexboard size="13x13"<br />
coords="show"<br />
contents="S red:all <br />
blue:(a1--l1 a2--k2 a3 m3)<br />
blue:(a11 m11 c12--m12 b13--m13)<br />
E *:(m1 a2 b2 c2 d2 k2 a3 f3 g3 h3 j3 m3 m4)<br />
E *:(a10 a11 d11 f11 g11 h11 m11 c12 j12 k12 l12 m12 a13)"<br />
/><br />
<br />
=== Size 14 ===<br />
TODO<br />
<br />
== A more general swap rule ==<br />
<br />
It has been suggested that one could use a more general swap rule. Under this proposal, instead of placing just one piece, the first player places any number of red and blue pieces, and state which color has the next move. Let's assume that the first player has placed N stones in the board. The second player then can start playing Hex with one color of his choice or, if he fears that the other player has an excessive advantage due to home preparation, he can swap roles with the first player, remove all stones from the board and place at most N-1 stones as he wants. This rule has been first proposed by "lazplyayer" at littlegolem/igg. However, it is not widely used, nor implemented by any [[online playing|game sites]].<br />
<br />
==See also==<br />
<br />
[[Basic (strategy guide)#10_.C3.97_10_swap_rules|Guideline for 10x10 board size]], in the basic strategy guide.<br />
<br />
==External links==<br />
<br />
[http://www.cs.cmu.edu/People/hde/hex/hexfaq/ A FAQ about Hex]<br />
<br />
[http://www.cs.ualberta.ca/~queenbee/openings.html A more complete site] with solutions to size 7. Beware, the colours are inverted, vertical is blue there.<br />
<br />
[[category: Opening]]<br />
[[category: Basic Strategy]]<br />
[[Category: Rules and Conventions]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Talk:Switchback
Talk:Switchback
2021-06-28T18:36:07Z
<p>HappyHippo: Created page with "For the situation depicted with the C4 switchback, wouldn't this be the stronger move, connecting directly? <hexboard size="6x9" coords="hide" edges="bottom right" conte..."</p>
<hr />
<div>For the situation depicted with the C4 switchback, wouldn't this be the stronger move, connecting directly?<br />
<hexboard size="6x9"<br />
coords="hide"<br />
edges="bottom right"<br />
contents="R g3 e1 d2 B b4 c4 e2 R 1:d3 B 2:d4 R 3:f2"<br />
/></div>
HappyHippo
https://www.hexwiki.net/index.php/Talk:Flank
Talk:Flank
2021-03-29T19:40:18Z
<p>HappyHippo: Created page with "Great article! If you're looking for a real world example of method 2 of the interior templates, there's a good one here https://littlegolem.net/jsp/game/game.jsp?gid=1900840"</p>
<hr />
<div>Great article!<br />
<br />
If you're looking for a real world example of method 2 of the interior templates, there's a good one here https://littlegolem.net/jsp/game/game.jsp?gid=1900840</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2021-02-28T18:58:13Z
<p>HappyHippo: After checking with benezene, the template was not minimal. I've replaced it with the minimal version, and updated one of the lines to use the reduced space.</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hexboard size="6x9" edges="bottom" coords="bottom right" contents="R ↑:g1 h1" visible="area(a6,f1,i1,i6)"/><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C9 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C9 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C9 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexes.<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bf4 Rd4 B1e3 R2f3 B3e4 R4g4 B5g3 R6i2 B7h3 R8i3 B9h5 R10h4</hex><br />
<br />
And now Red can escape the ladder:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bf4 Rd4 Be3 Rf3 Be4 Rg4 Bg3 Ri2 Bh3 Ri3 Bh5 Rh4 B1f6 R2f5 B3e6 R4e5 B5d6 R6d5</hex><br />
<br />
And now Red has connected.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5 B9g6 R10g5</hex><br />
<br />
And Red is connected. This method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
== Intrusion at C6 or G6 ==<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
=== Block at G2 ===<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Irrelevant_move
Irrelevant move
2021-01-04T18:53:28Z
<p>HappyHippo: Adding note that irrelevant moves can be used to manage the game clock.</p>
<hr />
<div>An '''irrelevant move''' or '''wasted move''' is a move that does not improve the position of the player who makes the move. It is considered as a waste of time and should be avoided. <br />
<br />
Any move in a [[dead cell]] is irrelevant. An example of this is the [[useless triangle]]. If a player plays in a dead cell, the opponent does not have to respond, i.e., the situation is as if the player had passed. <br />
<br />
Another example of an irrelevant move is a move in a cell that is already [[captured cell|captured]] by the same player. Such moves can also be ignored by the opponent, i.e., they are equivalent to passing.<br />
<br />
A move in a cell that is [[captured cell|captured]] by the opponent is also an irrelevant move, but sometimes the opponent is forced to respond to maintain the capture. While such a move does not improve the position of the player who makes it, it can sometimes happen that it does not improve the opponent's position either. Thus, the effect of such a move is in the best case neutral for the player who makes it. However, if the opponent has a better response available, such a move can still hurt the player who makes it.<br />
<br />
Any move that the opponent can [[dead cell|kill]] with the next move is also irrelevant, as it only helps the opponent and doesn't help the player.<br />
<br />
A move that does not interfere with any of the opponent's threats is also irrelevant.<br />
<br />
An irrelevant move that is also a forcing move can sometimes be used to manage the game clock. If the time controls include an increment (for example 10 minutes/+30 seconds per move), then a player who is low on time could make an irrelevant move that forces a response in order to get more time on their clock without changing the game situation. This is risky, though, as the opponent could potentially find a better response.<br />
<br />
== Examples ==<br />
<br />
Red to move.<br />
<hexboard size="6x6"<br />
coords="top left"<br />
contents="B b2 c1 d1 d2 R f1 E *:c2 *:e1 R e5 E *:d6 R c4 B e4 E *:f3 *:b5"<br />
/><br />
A red move at c2 would be irrelevant because it is in a [[useless triangle]] (therefore [[dead cell|dead]]).<br />
A red move at e1 would be irrelevant because e1 is also dead.<br />
A red move at d6 would be irrelevant because d6 is already [[captured cell|captured]] by Red.<br />
A red move at f3 would be irrelevant because f3 is already captured by Blue. Blue could in principle respond at f4 to [[dead cell|kill]] f3, showing that f3 had no possible benefit for Red. (However, it is much better for Blue to instead respond at e3, which is winning for Blue, unlike f4, which is losing).<br />
A red move at b5 would be irrelevant because it is not in the path of any of Blue's threatened connections. <br />
<br />
[[Category:Definition]]<br />
[[Category:Intermediate Strategy]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Board_size
Board size
2020-10-29T21:02:48Z
<p>HappyHippo: </p>
<hr />
<div>The '''board size''' in [[Hex]] varies, and no size is considered standard. 10 &times; 10 is considered by many a lower bound for interesting games.<br />
<br />
See also the article [[Small boards]].<br />
<br />
; 10 &times; 10<br />
: Used to be offered on [[Kurnik]] until 2008.<br />
; 11 &times; 11<br />
: The size [[Piet Hein]] used.<br />
: Offered on [http://games.wtanaka.com/hex games.wtanaka.com].<br />
: Offered on [[Kurnik]] as default.<br />
: The standard size on [[pbmserv]].<br />
: Offered on [http://en.boardgamearena.com Board Game Arena].<br />
: Offered on [[Little Golem]].<br />
; 13 &times; 13<br />
: The original size on [[Little Golem]]. (Games with this size are still called "hex" by the site engine, while 19 &times; 19 Hex games are named "hex19".)<br />
: Offered on [[Kurnik]].<br />
; 14 &times; 14<br />
: The size [[John Nash]] used.<br />
: Offered on [http://games.wtanaka.com/hex games.wtanaka.com].<br />
: Offered on [http://en.boardgamearena.com Board Game Arena].<br />
; 15 &times; 15<br />
: Offered on [http://en.boardgamearena.com Board Game Arena].<br />
: Offered on [[Little Golem]].<br />
; 18 &times; 18<br />
: Used to be offered on [[Playsite]] and Lycos but they no longer offer Hex.<br />
; 19 &times; 19<br />
: Offered on [http://games.wtanaka.com/hex games.wtanaka.com].<br />
: Offered on [[Little Golem]].<br />
: Offered on [[Kurnik]].<br />
<br />
<br />
Printable boards of size up to 14 &times; 14 here: [[Printable boards]].</div>
HappyHippo
https://www.hexwiki.net/index.php/Puzzles
Puzzles
2020-10-10T17:56:59Z
<p>HappyHippo: /* See also */</p>
<hr />
<div>Solving puzzles is a very good way of becoming a stronger player. Solve as many as possible! And feel free to post your own puzzles here.<br />
<br />
== [[Piet Hein]]'s puzzles ==<br />
<br />
See article [[Piet Hein's puzzles]]<br />
<br />
== [[Claude Berge]]'s puzzles ==<br />
<br />
See article [[Claude Berge's puzzles]]<br />
<br />
== Bert Enderton ==<br />
<br />
=== Puzzle 1 ===<br />
<br />
Red to play and win.<br />
<br />
<hex>R7 C7 Q1<br />
Hc3 Hf3<br />
Vc4 Hd4 <br />
Hc5 Ve5<br />
Va6</hex><br />
<br />
=== Puzzle 2 ===<br />
<br />
Red to play and win.<br />
<br />
<hex>R7 C7 Q1<br />
Hc3<br />
Hf5<br />
Vb6</hex><br />
<br />
=== Puzzle 3 ===<br />
<br />
Red (Vertical) to play and win.<br />
<br />
This is a very difficult puzzle whose complete solution is extremely complex.<br />
<br />
<hexboard size="6x6"<br />
contents="B c2 R f4"<br />
/><br />
<br />
== Other authors ==<br />
<br />
=== Puzzle 1 ===<br />
By [[John Tromp]]<br />
<br />
Blue to play and win.<br />
<br />
<br />
<hex> R10 C10<br />
Ri1 <br />
Bg4 Rh4 <br />
Bf5 Rg5<br />
Be6 Rf6 <br />
Bd7 <br />
Rc8 <br />
Rd9 </hex><br />
<br />
=== Puzzle 2 ===<br />
By ''lazyplayer''. Blue to play and win.<br />
<br />
<hex> R7 C7<br />
Vb2<br />
He3<br />
Vb5<br />
</hex><br />
<br />
=== Puzzle 3 ===<br />
By [[David J Bush]]. Taken from a game on [[Playsite]] in 2003. Red to play and win.<br />
<br />
<hex> R10 C10 Q1<br />
He2 Hf2 Hg2 Hh2 Hi2<br />
Va3 Hb3 Hd3 Ve3 Vf3 Vg3<br />
Va4 Vb4 Vc4 Hd4 Ve4 Hf4 Vg4 Vh4<br />
Hb5 Vc5 Vd5 He5 Vf5<br />
Hd6 Ve6<br />
Ve7<br />
Hg8<br />
Hc9 Hd9<br />
</hex><br />
<br />
Source: this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=14 thread].<br />
<br />
=== Puzzle 4 ===<br />
Designed by ''Door1'', helped by ''David J Bush''. Inspired by a game on [[Kurnik]] in May 2005. Blue to play and win.<br />
<br />
<hex> R10 C10 Q1<br />
Hb2 Hg2<br />
Hf3 Vg3<br />
Vb4 Ve4 Hf4<br />
He5<br />
Vc6<br />
Vd7<br />
Vd8<br />
</hex><br />
<br />
Source: this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=212 thread].<br />
<br />
=== Puzzle 5 ===<br />
Designed by ''Arek Kulczycki''. Game where both players play very close to perfect. Move 7.b9 was the first mistake, however it was very hard to refute it.<br/><br />
Blue to move and win (there is just 1 winning sequence).<br />
<br />
<hexboard size="11x11"<br />
coords="hide"<br />
contents="B 4:h2 R 1:a4 R 5:b5 R 3:c6 B 6:e7 B 2:g8 R 7:b9"<br />
/><br />
<br />
=== Puzzle 6 ===<br />
From Ryan B. Hayward, "A puzzling Hex primer". Red to play and win.<br />
<br />
<hexboard size="6x6"<br />
coords="hide"<br />
contents="R d1 B e1 R f1 B e2"<br />
/><br />
<br />
== See also ==<br />
<br />
* [[Solutions to puzzles]]<br />
* [[Ladder puzzles]]<br />
* [[Puzzle server]]<br />
<br />
[[Cameron Browne]] offers a lot of original puzzles in his book [[Hex Strategy Making the Right Connections]]<br />
<br />
[[Matthew Seymour]] has created a website with 500 interactive Hex puzzles at http://www.mseymour.ca/hex_puzzle/hexpuzzle.html<br />
<br />
[[Ryan Hayward]] and [[Bjarne Toft]] include several sets of puzzles in their book [[Hex: The Full Story]], including 49 puzzles originally published in Politiken, 28 unpublished puzzles by Jens Lindhard, and 99 puzzles by Henderson.<br />
<br />
[[category:Puzzle]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV2j
Edge template IV2j
2018-05-24T23:33:58Z
<p>HappyHippo: </p>
<hr />
<div>The template:<br />
<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 R c2 E *:a3 E *:a4"<br />
/><br />
<br />
(From: [http://www.drking.org.uk/hexagons/hex/templates.html www.drking.org.uk])<br />
<br />
Red has two threats:<br />
<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 E +:d1 R e1 E *:a2 E *:b2 R c2 E +:d2 E *:a3 E +:b3 E +:c3 E *:a4 R 1:b4"<br />
/><br />
<br />
and<br />
<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 R c2 E +:d2 E +:e2 E *:a3 R 1:d3 E *:a4 E +:c4 E +:d4"<br />
/><br />
<br />
For a blocking attempt Blue has to play on the overlap field:<br />
<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 E +:d1 R e1 E *:a2 E *:b2 R c2 B 1:d2 R 2:e2 E *:a3 R 4:c3 E +:d3 E *:a4 B 3:d4"<br />
/><br />
<br />
Red 4 is connected to the bottom and also to the top by one of the two fields marked with +.<br />
<br />
This template has an extraneous hex. The correct template is:<br />
<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 R c2 E *:a3 E *: b3 E *:a4"<br />
/><br />
<br />
The first threat needs to be modified to:<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 E +:d1 R e1 E *:a2 E *:b2 R c2 E +:d2 E *:a3 E *: b3 E +:c3 E *:a4 R 1:c3 E +:b4 E +:c4 "<br />
/><br />
<br />
There are now two overlap points. The response to the first is the same as above. The response to the second is:<br />
<hexboard size="4x5"<br />
coords="hide"<br />
contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 R c2 E *:a3 E *: b3 E *:a4 B 1:c4 R 2:c3 B 3:b4 R 4:e3"<br />
/><br />
<br />
== See also ==<br />
<br />
[[Multiple threats]]<br />
<br />
[[category:edge templates]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T01:03:13Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.<br />
<br />
The situation prior to a switchback generally looks like this (assume the piece on D1 is in some way connected to the top):<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4</hex><br />
<br />
Red makes a switchback as follows:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3</hex><br />
<br />
Now the ladder continues back to the left:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3 Vg3 N:on Vg1, Hf2, Vf1, He2, Ve1</hex><br />
<br />
Note here how red was able to connect back to the D1 piece. This is not always possible, but even if it isn't the switchback can be used to create a long line connected to the edge and four rows back from it, a distinct advantage.<br />
<br />
<br />
== A Different Situation ==<br />
<br />
A different kind of switchback can occur on the third row:<br />
<br />
<hex>R5 C8 Q1 Vd1, Vc2, Vh2, Hb2, Hd2, Hb4</hex><br />
<br />
If Blue yields the ladder to the second row, then Red can create a switchback as shown above which would continue back and reconnect. If the ladder stays on the third row then Red creates a switchback as follows: <br />
<br />
<hex>R5 C8 Q1 Vd1, Vc2, Vh2, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3</hex><br />
<br />
Red's piece on G3 is connected to the bottom. Play continues: <br />
<br />
<hex>R5 C8 Q1 Vd1, Vc2, Vh2, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3 N:on Hf3, Vg1, Hf2, Vf1, He2, Ve1</hex></div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T00:50:13Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.<br />
<br />
The situation prior to a switchback looks like this (assume the piece on D3 is in some way connected to the top):<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4</hex><br />
<br />
Red makes a switchback as follows:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3</hex><br />
<br />
Now the ladder continues back to the left:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3 Vg3 N:on Vg1, Hf2, Vf1, He2, Ve1</hex><br />
<br />
Note here how red was able to connect back to the D3 piece. This is not always possible, but even if it isn't the switchback can be used to create a long line connected to the edge and four rows back from it, a distinct advantage.</div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T00:31:21Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.<br />
<br />
The situation prior two a switchback looks like this (assume the piece on D3 is in some way connected to the top):<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4</hex><br />
<br />
Red makes a switchback as follows:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3</hex><br />
<br />
Now the ladder continues back to the left:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3 Vg3 N:on Vg1, Hf2, Vf1, He2, Ve1</hex><br />
<br />
Note here how red was able to connect back to the D3 piece. This is not always possible, but even if it isn't the switchback can be used to create a long line connected to the edge and four rows back from it, a distinct advantage.</div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T00:30:46Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.<br />
<br />
The situation prior two a switchback looks like this (assume the piece on D3 is in some way connected to the top):<br />
<br />
<hex>R4 C8 Q1 Vc1, Vc2, Vh1, Hb2, Hd2, Hb4</hex><br />
<br />
Red makes a switchback as follows:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3</hex><br />
<br />
Now the ladder continues back to the left:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3 Vg3 N:on Vg1, Hf2, Vf1, He2, Ve1</hex><br />
<br />
Note here how red was able to connect back to the D3 piece. This is not always possible, but even if it isn't the switchback can be used to create a long line connected to the edge and four rows back from it, a distinct advantage.</div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T00:27:52Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.<br />
<br />
The situation prior two a switchback looks like this (assume the piece on D3 is in some way connected to the top):<br />
<br />
<hex>R4 C8 Q1 Vc1, Vc2, Vh1, Hb2, Hd2, Hb4</hex><br />
<br />
Red makes a switchback as follows:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3</hex><br />
<br />
Now the ladder continues back to the left:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3 Vg3 N:on Vg1, Hf2, Vf1, He2, Ve1</hex><br />
<br />
Note here how red was able to connect back to the D3 piece.</div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T00:25:50Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.<br />
<br />
The situation prior two a switchback looks like this:<br />
<br />
<hex>R4 C8 Q1 Vc1, Vc2, Vh1, Hb2, Hd2, Hb4</hex><br />
<br />
Red makes a switchback as follows:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4 N:on Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3</hex><br />
<br />
Now the ladder continues back to the left:<br />
<br />
<hex>R4 C8 Q1 Vd1, Vc2, Vh1, Hb2, Hd2, Hb4, Vc3, Hc4, Vd3, Hd4, Ve3, He4, Vg3, Hf3 N:on Vg3, Hf2, Vf3, He2</hex></div>
HappyHippo
https://www.hexwiki.net/index.php/Switchback
Switchback
2009-11-03T00:19:55Z
<p>HappyHippo: </p>
<hr />
<div>A '''switchback''' is a situation in which a [[ladder]] moves back two rows and changes direction. The attacker is still in control after the switchback. Although it is not always ladder escape, it often can be and is usually a strong play.</div>
HappyHippo
https://www.hexwiki.net/index.php/Strategy
Strategy
2009-11-03T00:17:17Z
<p>HappyHippo: </p>
<hr />
<div>== General advice ==<br />
* One important advice for novice players to remember: "In [[Hex]], the best attacking move is often to defend." Instead of trying to connect your [[Edge|sides]], do your best to [[Blocking|impede]] your [[opponent]].<br />
* If you play with a strong player and you lose, try to repeat the opponent's moves and observe the responses. This can be a fast way to learn new bit of strategy.<br />
* Another good way to learn strategy is to analyse games &mdash; preferably in your head and not with a program. Talking to senior players is also a good idea.<br />
<br />
== General strategy guide ==<br />
<br />
These three pages originate from Glenn C. Rhoads' excellent strategy guide. They have mostly been changed to accomodate the transfer to the Wiki format.<br />
<br />
* [[Basic (strategy guide)|Basic]]<br />
* [[Intermediate (strategy guide)|Intermediate]]<br />
* [[Advanced (strategy guide)|Advanced]]<br />
<br />
== Specific topics ==<br />
* [[Opening|Openings]]<br />
* [[Connection|Connections]]<br />
* [[Bottleneck|Bottlenecks]]<br />
* [[Ladders]]<br />
* [[Ladder handling]]<br />
* [[Switchback]]<br />
* [[Templates]]<br />
* [[Equivalent patterns]]<br />
* [[Common mistakes]]<br />
* [[Tips and tricks]]<br />
* [[Territory]]<br />
* [[Local play]], [[Global play]]<br />
* [[Wall|Walls]]<br />
* [[Rope|Ropes]]<br />
* [[Glossary]]<br />
* [[Puzzles]], sometimes also called [[Problems]]<br />
* [[Proverbs]]<br />
* [[Tactics]]<br />
<br />
[[category:strategy]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-16T23:56:32Z
<p>HappyHippo: /* Intrusion at F4 */</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexes.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6 R0b5</hex><br />
<br />
And now Red has connected.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5 B9g6 R0g5</hex><br />
<br />
And Red is connected. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
== Intrusion at C6 or G6 ==<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
=== Block at G2 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-16T23:55:03Z
<p>HappyHippo: /* Block at F4 */</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexes.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5 B9g6 R0g5</hex><br />
<br />
And Red is connected. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
== Intrusion at C6 or G6 ==<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
=== Block at G2 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-15T16:04:56Z
<p>HappyHippo: /* Intrusion at E6 */</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexes.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
== Intrusion at C6 or G6 ==<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
=== Block at G2 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-15T16:01:21Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
== Intrusion at C6 or G6 ==<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
=== Block at G2 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-15T16:00:32Z
<p>HappyHippo: /* Block at G2 */</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
=== Intrusion at C6 or G6 ===<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
== Block at G2 ==<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-15T15:58:18Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
=== Intrusion at C6 or G6 ===<br />
<br />
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex><br />
<br />
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom. <br />
<br />
== Block at G2 ==<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red cannot be stopped. If Blue had played E6 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex><br />
<br />
And if Blue had played F5 for move five:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex><br />
<br />
Red threatens to connect in two non-overlapping ways.<br />
<br />
<br />
<br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-12T17:45:14Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-12T17:43:07Z
<p>HappyHippo: /* The edge template template VI2 */</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-12T17:14:14Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].<br />
<br />
=== Block at H2, G3, or G4 ===<br />
<br />
Red's responses are similar in all three cases:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-12T17:10:37Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at D6 or F6 ==<br />
<br />
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex><br />
<br />
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.<br />
<br />
=== Block at F4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex><br />
<br />
Or, if for move three Blue played G3:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex><br />
<br />
And Red cannot be stopped. Note that this method does not require the three right-most hexs. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.<br />
<br />
=== Block at G2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex><br />
<br />
Note that Red's F3 piece is connected via the two marked hexs. If Blue had played G3 for move three:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex><br />
<br />
And Red connects.<br />
<br />
=== Block at H2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
=== Block at G3 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
=== Block at G4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/User_talk:HappyHippo
User talk:HappyHippo
2009-06-12T16:37:14Z
<p>HappyHippo: </p>
<hr />
<div>Good job on template VI2 ! [[User:Halladba|Halladba]] 02:57, 12 June 2009 (CEST)<br />
<br />
Thanks, still have to finish off the other responses</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-11T19:17:26Z
<p>HappyHippo: /* Block at E3 */</p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
And now Red can connect via B5.<br />
Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work.<br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-11T19:15:20Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
<br />
== Intrusion at F4 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex><br />
<br />
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:<br />
<br />
=== Block at F2 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex><br />
<br />
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.<br />
<br />
=== Block at E3 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex><br />
<br />
The Red piece at H3 is connected to the top and threatening to connect. Blue has one defense:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex><br />
<br />
Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work<br />
<br />
And now Red can connect via B5. <br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-11T18:36:55Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has four options that don't immediately reduce to another edge template:<br />
=== Block at E4 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
<br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
<br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
=== Block at C6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
=== Block at E6 ===<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex><br />
<br />
Play continues...<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-11T18:05:29Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at G2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex><br />
<br />
Blue has a few options:<br />
=== Block at E4 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex><br />
Red's G3 piece is connected to the top via F3 or H2.<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex><br />
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.<br />
<br />
=== Block at D5 ===<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex><br />
<br />
And Red has connected. If blue choose to play at E6 instead of E5:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-11T17:40:49Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
== Intrusion at E6 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex><br />
<br />
Red threatens to connect via D4. Blue must respond in one of the marked hexs.<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex><br />
<br />
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex><br />
<br />
and<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex><br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_VI2a
Edge template VI2a
2009-06-11T17:23:17Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template template VI2 ==<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex><br />
<br />
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.<br />
<br />
There are two obvious options:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex><br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex><br />
<br />
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex><br />
<br />
== Intrusion at E5 and F5 ==<br />
<br />
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]<br />
<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex><br />
<br />
Likewise if blue blocks at F5:<br />
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex><br />
<br />
[[Category:Edge templates]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV1b
Edge template IV1b
2009-06-08T16:08:07Z
<p>HappyHippo: Template IVb moved to Defending against intrusions in template IVb</p>
<hr />
<div>==The edge template IVb==<br />
<br />
<hex> R4 C8<br />
Sa1 Sb1 Sc1 Sd1 Vf1 Sh1<br />
Sa2 Sb2 <br />
Sa3 Se3<br />
</hex><br />
<br />
Red has two threats using [[defending against intrusions in template 1-IIIa|template III-1-a]]:<br />
<br />
<hex> R4 C8<br />
Sa1 Sb1 Sc1 Sd1 Pe1 Vf1 Sh1<br />
Sa2 Sb2 Pc2 Vd2 Pe2 <br />
Sa3 Pb3 Pc3 Pd3 Se3<br />
Pa4 Pb4 Pc4 Pd4<br />
</hex>and<br />
<br />
<hex> R4 C8<br />
Sa1 Sb1 Sc1 Sd1 Vf1 Pg1 Sh1<br />
Sa2 Sb2 Pf2 Vg2 Ph2<br />
Sa3 Se3 Pf3 Pg3 Ph3<br />
Pe4 Pf4 Pg4 Ph4<br />
</hex><br />
These moves lead to easy direct connection. Because there is no common [[hex (board element)|hex]] used in both threats, Blue cannot prevent Red to link to the bottom.<br />
<br />
== See also ==<br />
<br />
[[Multiple threats]]<br />
<br />
[[category:edge templates]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Template_IVb
Template IVb
2009-06-08T16:08:07Z
<p>HappyHippo: Template IVb moved to Defending against intrusions in template IVb</p>
<hr />
<div>#REDIRECT [[Defending against intrusions in template IVb]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV1b
Edge template IV1b
2009-06-08T16:07:14Z
<p>HappyHippo: </p>
<hr />
<div>==The edge template IVb==<br />
<br />
<hex> R4 C8<br />
Sa1 Sb1 Sc1 Sd1 Vf1 Sh1<br />
Sa2 Sb2 <br />
Sa3 Se3<br />
</hex><br />
<br />
Red has two threats using [[defending against intrusions in template 1-IIIa|template III-1-a]]:<br />
<br />
<hex> R4 C8<br />
Sa1 Sb1 Sc1 Sd1 Pe1 Vf1 Sh1<br />
Sa2 Sb2 Pc2 Vd2 Pe2 <br />
Sa3 Pb3 Pc3 Pd3 Se3<br />
Pa4 Pb4 Pc4 Pd4<br />
</hex>and<br />
<br />
<hex> R4 C8<br />
Sa1 Sb1 Sc1 Sd1 Vf1 Pg1 Sh1<br />
Sa2 Sb2 Pf2 Vg2 Ph2<br />
Sa3 Se3 Pf3 Pg3 Ph3<br />
Pe4 Pf4 Pg4 Ph4<br />
</hex><br />
These moves lead to easy direct connection. Because there is no common [[hex (board element)|hex]] used in both threats, Blue cannot prevent Red to link to the bottom.<br />
<br />
== See also ==<br />
<br />
[[Multiple threats]]<br />
<br />
[[category:edge templates]]</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV2b
Edge template IV2b
2008-12-12T20:20:52Z
<p>HappyHippo: /* The Edge template IV2b */ Typo</p>
<hr />
<div>== The Edge template IV2b ==<br />
<hex> R4 C5 <br />
Sa1 Sb1 Vc1 Se1<br />
Sa2 Vb2<br />
Sa3 </hex><br />
<br />
Red has two threats:<br />
<br />
<hex> R4 C5 Sa1 Sb1 Vc1 Vb3 Pa4 Pb4 Se1 Sa2 Vb2 Sa3 </hex><br />
and<br />
<hex> R4 C5 Sa1 Sb1 Vc1 Vd2 Pd1 Pc2 Pe2 Pc3 Pd3 Pe3 Pb4 Pc4 Pd4 Pe4 Se1 Sa2 Vb2 Sa3 </hex><br />
<br />
These threats overlap on one hex at b4:<br />
<br />
<hex> R4 C5 Sa1 Sb1 Vc1 H1b4 V2b3 H3a4 V4d3 Se1 Sa2 Vb2 Sa3 </hex><br />
<br />
The d3 piece is connected to the bottom, and connects to the template pieces through either c3, or a bridge with d2.</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV2b
Edge template IV2b
2008-12-12T20:17:35Z
<p>HappyHippo: </p>
<hr />
<div>== The Edge template IV2b ==<br />
<hex> R4 C5 <br />
Sa1 Sb1 Vc1 Se1<br />
Sa2 Vb2<br />
Sa3 </hex><br />
<br />
Read has two threats:<br />
<br />
<hex> R4 C5 Sa1 Sb1 Vc1 Vb3 Pa4 Pb4 Se1 Sa2 Vb2 Sa3 </hex><br />
and<br />
<hex> R4 C5 Sa1 Sb1 Vc1 Vd2 Pd1 Pc2 Pe2 Pc3 Pd3 Pe3 Pb4 Pc4 Pd4 Pe4 Se1 Sa2 Vb2 Sa3 </hex><br />
<br />
These threats overlap on one hex at b4:<br />
<br />
<hex> R4 C5 Sa1 Sb1 Vc1 H1b4 V2b3 H3a4 V4d3 Se1 Sa2 Vb2 Sa3 </hex><br />
<br />
The d3 piece is connected to the bottom, and connects to the template pieces through either c3, or a bridge with d2.</div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV2b
Edge template IV2b
2008-12-12T20:04:59Z
<p>HappyHippo: </p>
<hr />
<div>== The Edge template IV2b ==<br />
<hex> R4 C5 <br />
Sa1 Sb1 Vc1 Se1<br />
Sa2 Vb2<br />
Sa3 </hex><br />
<br />
Read has two threats:<br />
<br />
<hex> R4 C5 Sa1 Sb1 Vc1 Vb3 Pa4 Pb4 Se1 Sa2 Vb2 Sa3 </hex><br />
and<br />
<hex> R4 C5 Sa1 Sb1 Vc1 Vd2 Pd1 Pc2 Pe2 Pc3 Pd3 Pe3 Pb4 Pc4 Pd4 Pe4 Se1 Sa2 Vb2 Sa3 </hex></div>
HappyHippo
https://www.hexwiki.net/index.php/Edge_template_IV2a
Edge template IV2a
2008-12-12T17:06:26Z
<p>HappyHippo: </p>
<hr />
<div>== The edge template IV-2-a ==<br />
<br />
<hex>R4 C4 Vc1 Vd1 Sa1 Sa2 Sa3 Sb1 </hex><br />
<br />
Red has two relevant threats:<br />
<hex>R4 C4 Vc1 Vd1 Vb3 Pb2 Pc2 Pa4 Pb4 Sa1 Sa2 Sa3 Sb1 </hex><br />
and<br />
<hex>R4 C4 Vc1 Vd1 Vc3 Pc2 Pd2 Pb4 Pc4 Sa1 Sa2 Sa3 Sb1 </hex><br />
<br />
This leaves blue with two options: <br />
<br />
<hex>R4 C4 Vc1 Vd1 Pc2 Pb4 Sa1 Sa2 Sa3 Sb1 </hex><br />
<br />
=== Solution to the intrusion at c2 ===<br />
<br />
<hex>R4 C4 Vc1 Vd1 H1c2 V2d2 H3c4 V4b3 Sa1 Sa2 Sa3 Sb1 </hex><br />
The b3 piece is connected to the bottom and connects to the top via either b2 or c3.<br />
<br />
=== Solution to the intrusion at b4 ===<br />
<br />
<hex>R4 C4 Vc1 Vd1 H1b4 V2d3 H3d2 V4b3 Sa1 Sa2 Sa3 Sb1 </hex><br />
The b3 piece connects via either a4 or c3.</div>
HappyHippo
https://www.hexwiki.net/index.php/Solutions_to_Piet_Hein%27s_puzzles
Solutions to Piet Hein's puzzles
2008-12-12T15:27:02Z
<p>HappyHippo: /* Puzzle 7 */ Explained more</p>
<hr />
<div>== Puzzles ==<br />
=== Puzzle 1 ===<br />
<hex><br />
R11 C11 Q1<br />
Vd1 Vd2 Vd3 Vd4 Vd5 Vd6 Vd7 Vd9 Vd10 Vd11 Vh6 Vh7 Hc2 Hd8 Hh9 Hi4<br />
H1f7 +g5 +g8<br />
</hex><br />
<br />
No matter what Red does, Blue can connect via either g5 or g8. Both blue stones at the right are connected to the right (see the [[Strategy#General strategy guide|Strategy guide]] for details). The stone at d8 is connected to the left because of the ladder breaker at c2.<br />
<br />
=== Puzzle 2 ===<br />
<hex>R3 C3 Ha1 Va2 Vb3 N:on Hb2</hex><br />
<br />
=== Puzzle 3 ===<br />
<hex>R6 C6 Vc3 Vf3 Vd5 Hb1 Hb5 N:on He2</hex><br />
<br />
=== Puzzle 4 ===<br />
<hex>R4 C4 Vd1 Va4 Hc2 N:on Hb3</hex><br />
Using twice [[Edge templates with two adjacent pieces|edge template III 2b]]<br />
=== Puzzle 5 ===<br />
<hex>R4 C4 Va4 Ha1 N:on Hb3</hex><br />
<br />
Blue 1 is connected to the right via [[Template IIIa]] and threatens to connect directly to the left. The only possibility to prevent this connection is to play out the ladder:<br />
<br />
<hex>R4 C4 Va4 Ha1 N:on Hb3 Va3 Hb2 Va2 Hb1</hex><br />
<br />
Since the cells for the ladder and those for the edge template do not overlap, Red cannot do anything against the connection.<br />
<br />
=== Puzzle 6 ===<br />
Not posted yet...<br />
=== Puzzle 7 ===<br />
<hex>R5 C5<br />
Ra2<br />
Ba3 Rb3 Bc3<br />
Rb4<br />
Ba5 B1c2</hex><br />
The two blue pieces are connected to the right using [[Edge templates with two adjacent pieces|edge template III2a]]. Red must block the connection to the left at B2<br />
<br />
<hex>R5 C5<br />
Ra2<br />
Ba3 Rb3 Bc3<br />
Rb4<br />
Ba5 Bc2 R2b2 B3b5 R4c4 B5c5 R6e4 B7d4 R8e3 B9d3</hex><br />
<br />
And now blue can connect with either E2 or E1.<br />
Had red played 4. E3 blue could respond with D4 with a similar outcome.<br />
Had red played 2. D3 to block the future ladder, blue could respond with 3. C4, keeping the connection to the right and connecting to the left in two different ways (via B2 and B5).<br />
<br />
== See also ==<br />
* Back to [[Piet Hein's puzzles]].<br />
* Main page: [[Puzzles]].<br />
<br />
[[category:puzzle]]<br />
{{stub}}</div>
HappyHippo
https://www.hexwiki.net/index.php/Solutions_to_Piet_Hein%27s_puzzles
Solutions to Piet Hein's puzzles
2008-12-12T15:21:46Z
<p>HappyHippo: /* Puzzle 7 */ Added solution, hope it's right!</p>
<hr />
<div>== Puzzles ==<br />
=== Puzzle 1 ===<br />
<hex><br />
R11 C11 Q1<br />
Vd1 Vd2 Vd3 Vd4 Vd5 Vd6 Vd7 Vd9 Vd10 Vd11 Vh6 Vh7 Hc2 Hd8 Hh9 Hi4<br />
H1f7 +g5 +g8<br />
</hex><br />
<br />
No matter what Red does, Blue can connect via either g5 or g8. Both blue stones at the right are connected to the right (see the [[Strategy#General strategy guide|Strategy guide]] for details). The stone at d8 is connected to the left because of the ladder breaker at c2.<br />
<br />
=== Puzzle 2 ===<br />
<hex>R3 C3 Ha1 Va2 Vb3 N:on Hb2</hex><br />
<br />
=== Puzzle 3 ===<br />
<hex>R6 C6 Vc3 Vf3 Vd5 Hb1 Hb5 N:on He2</hex><br />
<br />
=== Puzzle 4 ===<br />
<hex>R4 C4 Vd1 Va4 Hc2 N:on Hb3</hex><br />
Using twice [[Edge templates with two adjacent pieces|edge template III 2b]]<br />
=== Puzzle 5 ===<br />
<hex>R4 C4 Va4 Ha1 N:on Hb3</hex><br />
<br />
Blue 1 is connected to the right via [[Template IIIa]] and threatens to connect directly to the left. The only possibility to prevent this connection is to play out the ladder:<br />
<br />
<hex>R4 C4 Va4 Ha1 N:on Hb3 Va3 Hb2 Va2 Hb1</hex><br />
<br />
Since the cells for the ladder and those for the edge template do not overlap, Red cannot do anything against the connection.<br />
<br />
=== Puzzle 6 ===<br />
Not posted yet...<br />
=== Puzzle 7 ===<br />
<hex>R5 C5<br />
Ra2<br />
Ba3 Rb3 Bc3<br />
Rb4<br />
Ba5 B1c2</hex><br />
The two blue pieces are connected to the right. Red must block the connection to the left at B2<br />
<br />
<hex>R5 C5<br />
Ra2<br />
Ba3 Rb3 Bc3<br />
Rb4<br />
Ba5 Bc2 R2b2 B3b5 R4c4 B5c5 R6e4 B7d4 R8e3 B9d3</hex><br />
<br />
And now blue can connect with either E2 or E1.<br />
Had Red played 4. E3 blue could respond with D4 with a similar outcome.<br />
<br />
== See also ==<br />
* Back to [[Piet Hein's puzzles]].<br />
* Main page: [[Puzzles]].<br />
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[[category:puzzle]]<br />
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