HexWiki - User contributions [en]

Edge template VI1a

2009-01-15T15:10:45Z

Taral:

This template is the first one stone 6th row [[edge template|template]] for which a proof has been handwritten.

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6
</hex>

== Elimination of irrelevant Blue moves ==

Red has a couple of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.

=== [[edge template IV1a]] ===

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Pi3 Pj3
Ph4 Ri4
Pf5 Pg5 Ph5 Pi5 Pj5
Pe6 Pf6 Pg6 Ph6 Pi6 Pj6
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7
</hex>

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Pi3 Pj3
Ri4 Pj4
Pg5 Ph5 Pi5 Pj5 Pk5
Pf6 Pg6 Ph6 Pi6 Pj6 Pk6
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7
</hex>

=== [[edge template IV1b]] ===

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Pi3 Pj3
Ph4 Ri4 Pj4
Pf5 Pg5 Ph5 Pi5 Pj5 Pk5
Pe6 Pf6 Pg6 Pi6 Pj6 Pk6
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7
</hex>
=== Using the [[parallel ladder]] trick ===

6 moves can furthermore be discared thanks to the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half!

We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Pg5
Pf6
Pe7
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7
</hex>

At this point, we can use the [[Parallel ladder]] trick as follows:

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Pg5
Pf6
Pe7
Ri4 Bi5 Rh5 Bg7 Rh6 Bh7
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3
</hex>

=== [[Overlapping connections|Remaining possibilities]] for Blue ===
Blue's first move must be one of the following:
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Pi3 Pj3
Pi4
Ph5 Pi5
Pg6 Pi6
Pf7 Pg7 Ph7 Pi7
</hex>

== Specific defence ==
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!

===One remaining intrusion on the first row===
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bf7
</hex>

===The other remaining intrusion on the first row===
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bg7
</hex>

===The remaining intrusion on the second row===
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bg6
</hex>

===The remaining intrusion on the third row===
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bh5
</hex>

===The remaining intrusion on the fourth row===
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4
</hex>

Red should move here:

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
</hex>

==== Elimination of irrelevant Blue moves ====
This gives Red several immediate threats:
From III1a:
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Rg5
Pg4 Ph4
Ph5
Pf6 Pg6 Ph6
Pe7 Pf7 Pg7 Ph7
</hex>

From III1a again:
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Rg5
Pg4 Ph4
Pf5
Pe6 Pf6 Pg6
Pd7 Pe7 Pf7 Pg7
</hex>

From III1b :
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Rg5
Pg4 Ph4
Pf5 Ph5
Pe6 Pf6 Pg6 Ph6
Pd7 Pe7 Pg7 Ph7
</hex>

From IV1a:
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Rg4
Pf4
Pd5 Pe5 Pf5 Pg5 Ph5
Pc6 Pd6 Pe6 Pf6 Pg6 Ph6
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7
</hex>

From IV1b:
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Rg4
Pf4 Ph4
Pd5 Pe5 Pf5 Pg5 Ph5 Pi5
Pc6 Pd6 Pe6 Pg6 Ph6 Pi6
Pb7 Pc7 Pd7 Pe7 Pf7 Pg7 Ph7 Pi7
</hex>

The intersection of all of these leaves:
<hex>
R7 C14 Q1
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Pg4
Pg5
Pg6
Pe7 Pg7
</hex>

==== Specific defence ====
So we must deal with each of these responses. (Which will not be too hard!)

===== Bg4 =====
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3

N:on Bg4 Rh4 Bg6 Rh5
</hex>
And now either
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3

Bg4 Rh4 Bg6 Rh5
N:on Bh6 Rj5
Pk3 Pi5
</hex>

or

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3

Bg4 Rh4 Bg6 Rh5
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5
Pk3 Pi5
</hex>
===== Bg5 =====
<hex>
R7 C14 Q1
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3

N:on Bg5 Rf4
</hex>
Threatening:
<hex>
R7 C14 Q1
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Bg5 Rf4
Pe4
Pc5 R4d5 Pe5
Pb6 Pc6 Pd6
Pa7 Pb7 Pc7 Pd7
</hex>
<hex>
R7 C14 Q1
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Bg5 Rf4
Pe5 Pf5
R4e6
Pd7 Pe7
</hex>

<hex>
R7 C14 Q1
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Bg5 Rf4
Pd5 R4e5 Pf5
Pc6 Pd6 Pe6 Pf6
Pb7 Pc7 Pe7 Pf7
</hex>
So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:

<hex>
R7 C14 Q1
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi4 Rh3
Bg5 Rf4
N:on Be5 Rf5 Be7 Rf6 Bf7 Rg6 Bg7 Rj5
Pk3 Pi5
</hex>
===== Bg6 =====
===== Be7 =====
===== Bg7 =====
'''To be continued...'''

===The remaining intrusion on the fifth row===
<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi3
</hex>

First establish a [[double ladder]] on the right.

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi3
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5
</hex>

Then use [[Tom's move]]:

<hex>
R7 C14 Q0
1:BBBBBBBBBRBBBBB
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
Sa4 Sb4 Sc4 Sd4 Sn4
Sa5 Sb5
Sa6

Bi3
Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5 Rf5 Bf6
N:on Rf5 Bf6 Rf4 Bg5 Rh3
</hex>

[[category:edge templates]]
[[category:theory]]

User talk:Oriol

2006-07-18T17:24:04Z

Taral:

i wold like to make a page with hex problems

:Sounds good. May I suggest posting them on the [[Puzzles]] page? — [[User:Turing|turing]] 11:41, 25 Jun 2006 (CEST)

But I'm new in hexwiki and I'm not shure how it works. Can I create a new page? I wold like to make a "basic" hex problems for new players.

:Yes, creating a new page is perfectly ok too if you want. Just create a link somewhere, [[This page does not exist|like this]], so that you can go to the page and add content to it. Good luck! And [[Wikipedia:Wikipedia:Be bold in updating pages|be bold]]. — [[User:Turing|turing]] 15:05, 3 Jul 2006 (CEST)

I just making some test to know how wiki works

Problem X
Vertical to play and win
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Ve7 Hd9 Hd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9</hex>

Wrong
Playing in the lader don't seems good
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Ve7 Hd9 Hd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Vg8 Vf8 Ve8 Hf9 He9 Hd8</hex>

Correct
<hex>R9 C9 Q1 Vg3 Vf4 Vf5 Vg5 Vh6 Vh7 Ve7 Hd9 Hd7 Hc6 Hd6 Hf7 Hg7 Hi7 Hg9 Vf8</hex>

its a test

== Puzzle X2 ==
(from templates seccion)

Blue seems connected. How can Red block it?
<hex>R7 C7 Vd5 Ve6 Hd4 He4</hex>

==Solution Puzzle X2 ==

Blue is connected to the right due to A3 template.
Blue is not connected to the left. Can connect if play in b5. Then Red must to play in one of the following *

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Sa5 Sa6 Sb5 Sc4 Sc5</hex>

a6, b5 and c5 can be responded by c3 connecting with A3 template

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Va6 Vb5 Vc5 Hc3</hex>

a5 can be responded by c4 connecting with B3 template

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Va5 Hc4</hex>

correct solution: c4
althougt it's not sure who win

<hex>R7 C7 Vd5 Ve6 Hd4 He4 Vc4</hex>

'''Note: it's only a test, not the final hex problems page. I'm testing the edit in wiki. Can somebody help me? How I can delete or modify my talk page? I only know add comments but no modify the existing ones. Thanks'''

:To edit the page, simply click the ''edit'' button at the top of this page. Until now you have presumably clicked the +, which is next to the ''edit'' and allows you to add extra comments, but not modify the earlier ones. Note that in the diagram above, blue has an easy win if he plays b3. [[User:Taral|Taral]] 19:24, 18 Jul 2006 (CEST)

Edge templates with two adjacent pieces

2006-02-16T16:32:10Z

Taral:

== [[Third row]] [[edge template III2]] ==
[[Image:Template-2-3.png]]


== [[Fourth row]] [[edge template IV2]] ==
[[Image:Template-2-4.png]]


== [[Fifth row]] [[edge template V2]] ==
[[Image:Template-2-5.png]]


== [[Sixth row]] [[edge template VI2]] ==
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex>

''See also [[Defending against intrusions in template VI2]].''

Edge templates with one stone

2006-02-16T16:30:36Z

Taral:

Here you can see all known [[Edge template|edge templates]] with one stone to be connected to the bottom row. Not all of them are useful to know. The [[Fifth row|fifth-row]] [[template]] occurs very seldom in real play.

There is some overlap with the article [[Edge templates everybody should know]].

== First row edge template ==
<hex>R1 C1 Va1</hex>

== Second row edge template ==
<hex>R2 C2 Vb1 Sa1</hex>

== Third row edge templates ==
[[Image:Ziggurat.png]]
[[Image:Template-1-3b.png]]



== Fourth row edge templates ==
[[Image:Template-1-4a.png]]
[[Image:Template-1-4b.png]]



== Fifth row edge template ==
<hex>R5 C10 Vg1 Sa1 Sa2 Sa3 Sa4 Sb1 Sb2 Sb3 Sc1 Sc2 Sd1 Sd2 Se1 Si1 Sj1 Sj2</hex>

There are almost certainly no edge templates with one stone on the [[Sixth row|sixth row]]. This hasn´t been proved, though.

Liberty

2006-02-16T16:11:46Z

Taral:

A '''liberty''' of an [[isolated piece]] or a [[group]] is the number of unoccupied [[Hex (board element)|cells]] [[adjacent]] to it. A piece with few liberties is generally weaker than one with many liberties.

''Do not play an isolated piece with three or fewer liberties.'' Such a move is always a bad move — it is always possible to find a better one.

Bottleneck

2006-02-16T15:53:18Z

Taral:

The '''bottleneck''' is a common [[Defense pattern|defense pattern]]. The board fragment below shows a position where the vertical player (red) wants to connect to the bottom, but is being hindered by blue in a bottleneck formation.

[[Image:bottleneck.png]]



The bottleneck formation invariably leads to a [[Ladder|ladder]] situation.

Help:Contents

2006-02-16T15:44:49Z

Taral:

[[HexWiki]] is a [http://en.wikipedia.org/wiki/Wiki wiki] for the game of [[Hex]], i.e., it is a website written collaboratively by people from around the world.

The [http://en.wikipedia.org/wiki/Help:Contents help page for Wikipedia] contains guidance and information about participating which is mostly applicable to HexWiki as well (since both the Wikipedia and HexWiki are based on the MediaWiki software).

Minimaxing

2006-02-16T15:42:38Z

Taral:

The idea behind the term '''minimax''' is that you are playing a move that maintains a '''mini'''mal connectivity in one direction while building up (i.e. '''max'''imizing) your strength in the other direction.

{{stub}}

Hex

2006-02-16T15:42:07Z

Taral:

'''Hex''' is a game played by two [[player]]s on a [http://en.wikipedia.org/wiki/Rhombus rhombic] [[board]] consisting of [[Hex (board element)|hexagons]]. Each player owns two of the [[Edge|sides]] of the board, and a player [[win]]s if he creates an unbroken [[chain]] between his two sides. Hex is classified as a [[Connection game]].

Hex is a game of deep [[complexity]] and its corresponding decision-type problem is shown to be [[PSPACE-complete]].

For a description of how to play the game, see the article [[Rules]].

== More playing ==

If you already have read the [[Rules]] article and you want more thorough information on how to play Hex, proceed to the article about [[Strategy]].

== History of Hex ==

The [[History of Hex]] article contains an account of the events surrounding the game so far.

Template:Delete

2006-02-16T15:40:10Z

Taral:

''This page has no content and can be deleted.''

Template:Delete

2006-02-16T15:39:18Z

Taral:

This page has no content and can be deleted.

A3 escape trick

2006-02-16T15:36:44Z

Taral: rv

{{wrongtitle|title=a3 escape trick}}

The term '''a3 escape trick''' denotes the fact that though a red piece on a3 is not part of an [[edge template]] to the [[Top edge|top]], it can still be useful as a [[ladder escape]], when handled correctly.

Consider the following position:

<hex>R8 C8 Q1 Va3 Vg3 Vf5 Hg2 Hh2 He4 He5 Ve6</hex>

The a3 escape trick consists of laddering to e3 (making a three-hex [[gap]] between the ladder and a3) and then [[connecting]] a3 through a [[bridge]]:

<hex>R8 C8 Q1 Va3 Vg3 Vf5 Hg2 Hh2 He4 He5 Ve6 Vf3 Hf2 Ve3 He2 Vb4</hex>

[[Blue (player)|Blue]]'s only working response is d3, to which [[Red (player)|Red]] responds with another bridge:

<hex>R8 C8 Q1 Va3 Vg3 Vf5 Hg2 Hh2 He4 He5 Ve6 Vf3 Hf2 Ve3 He2 Vb4 Hd3 Vc5</hex>

No matter what Blue plays Red can either connect with the ladder or directly to the [[Bottom edge|bottom]].

Blue can also play c3 instead of d3 but the outcome is the same.

This escape does not always work, depending on the [[Board size|size of the board]] and the pieces already on it.

Wall

2006-02-16T15:36:00Z

Taral: Reverted to original version

A '''wall''' is a [[group]] of [[piece]]s forming a straight line inside the [[board]]. Walls are strategically strong because they can serve as edges within the board, allowing [[edge templates]] to be played with the walls as support.

A popular way to create a wall is to [[ladder]] in the "wrong direction". The example below shows the lower part of a board:

<hex>R5 C10 Ve2 Hf2 Hd4 Vc4</hex>

While [[Red (player)|Red]] could easily connect two the [[bottom edge]] by means of her leftmost red piece, instead she ladders to the right, giving the following position:

<hex>R5 C10 Ve2 Hf2 Hd4 Vc4 Ve3 He4 Vf3 Hf4 Vg3 Hg4 Vh3 Hh4 Vi3 Hi4</hex>

''Now'' Red connects the pieces to the left. The newly created wall can come in handy as play goes on near the top of the board (not shown here).

Note that this illustrates suboptimal play by [[Blue (player)|Blue]]. Since Red already has a connection to the bottom, Blue should not play the ladder allowing Red to set up a wall.

A wall can contain one-[[hex (board element)|hex]] [[hole]]s without affecting its function, as long as the whole wall is a single [[group]]. The holes may be [[empty hex|empty]] or [[occupied hex|occupied]] by the opponent.

<hex>R5 C8 Vb3 Vc3 Vd4 Ve3 Ve4 Vf4 Hf3 Vg3 Vg3</hex>

HexWiki talk:Community Portal

2005-08-16T06:41:17Z

Taral: reverted advertising

I really like DJ's comments, but I think a better place for them would be on his [[User:Dj13|user page]]. A community portal, at least on the wikis I've seen, is something else:

* [http://en.wikipedia.org/wiki/Wikipedia:Community_Portal Wikipedia's community portal]
* [http://meta.wikimedia.org/wiki/Goings-on Meta-Wikipedia's "Goings-on page"]

Not wishing to offend or to seem elitist, merely suggesting that personal expressions of happiness be placed on user pages, where they belong. [[User:Turing|turing]] 09:46, 17 Feb 2005 (CET)

User talk:Kogorman

2005-08-15T19:53:55Z

Taral:

Aug 14: Reverting a community page: was overlaid by some hotel-related advertising.

Aug 14: What are these <hex> and </hex> annotations? Are they supposed to be
compiled into images? It does not appear to be working.

:They are supposed to be compiled into images, but this doesn't work at the moment. It worked earlier, when the wiki was hosted elsewhere, but after it was moved, all we have left are the <hex> tags. I believe that it is supposed to be fixed as soon as somebody has time to do it. I've written a Java program which converts the <hex> tags into pngs, and have manually inserted diagrams in a few pages, such as at [[Puzzles]] and [[Edge template]]. [[User:Taral|Taral]] 21:53, 15 Aug 2005 (CEST)

Bottleneck

2005-06-07T15:02:59Z

Taral: Diagram

File:Bottleneck.png

2005-06-07T15:01:51Z

Taral: Bottleneck

Bottleneck

A1 opening

2005-05-27T17:47:47Z

Taral: Diagram added

{{wrongtitle|title=a1 opening}}



The '''a1 opening''' (in the [[acute corner]]) is one of only two openings known to be defeatedable. The other is [[B1 opening|b1]].

(This does not mean that these are the worst possible opening moves. Compare with the diagrams on [http://www.cs.ualberta.ca/~queenbee/openings.html the openings page at the queenbee site])

[[image:acuteopening.png]]

Due to the [[Symmetries (board)|symmetry]] of the Hex board, the same is true of the [[opposite hex]]es, but they are not usually referred to explicitly because their [[Coordinates (board)|designation]] depends on the size of the board. References for proofs can be found on the [http://hex.kosmanor.com/hex/theory.html Hex Theory] page.

File:Acuteopening.png

2005-05-27T17:45:16Z

Taral: The A1 opening

The A1 opening

Wheel

2005-03-28T13:27:01Z

Taral:

The '''wheel''' consists of three [[Friendly piece|same-coloured pieces]] around a central point.

[[Image:Wheel.png]]



The red pieces are strongly [[Connection|connected]] to each other. [[Blue (player)|Blue]] cannot break the connection between them, and his available forcing moves are not very good. It also has a big circumference, so that it is easy to connect to it from other parts of the board. The drawback is that it requires three pieces and is rather compact, so that it is often not efficient enough.

Blue has three possible [[forcing move]]s, labelled A. If Blue plays in one of them, [[Red (player)|Red]] can restore the connection by playing in any of the other cells labelled A. (He can also play at B, but it's usually not so good.) By doing this, Red strengthens his connection, and the influence his pieces has on the rest of the board. It is therefore usually better for Blue not to [[Intrusion|invade]].

Blue should never attempt to invade by playing at B. Red can then [[Restoring|restore]] the connection between his pieces by playing at any A. Red's position improves, while Blue's piece is useless.

Note that the position below, where Blue has already intruded into one of the starred cells, is a very weak one. In this case, Blue should play at the midpoint, which is now the point where two [[bridge]]s overlap.

<hex>R5 C5 Vc2 Vd3 Vb4 Hc4</hex>

File:Wheel.png

2005-03-28T13:25:56Z

Taral:

Edge templates everybody should know

2005-03-28T12:26:27Z

Taral:

In all the diagrams Red is the vertical player and wants to connect his stone or stones to the bottom. Empty cells in the diagrams cannot be occupied by the opponent for the template to be valid; cells with a star may be empty or be occupied by either player.

== Third row edge templates with one stone ==
[[Image:Ziggurat.png]]
[[Image:Template-1-3b.png]]



== Fourth row edge templates with one stone ==
[[Image:Template-1-4a.png]]
[[Image:Template-1-4b.png]]



== Third row edge templates with two stones ==
[[Image:Template-2-3.png]]


== Fourth row edge templates with two stones ==
[[Image:Template-2-4.png]]


== Fifth row edge templates with two stones ==
[[Image:Template-2-5.png]]

File:Template-2-5.png

2005-03-28T12:25:11Z

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File:Template-2-4.png

2005-03-28T12:24:48Z

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File:Template-2-3.png

2005-03-28T12:24:14Z

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File:Template-1-5.png

2005-03-28T12:23:59Z

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File:Template-1-4b.png

2005-03-28T12:23:15Z

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File:Template-1-4a.png

2005-03-28T12:22:47Z

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File:Template-1-3b.png

2005-03-28T12:21:23Z

Taral:

Edge template

2005-03-28T11:13:04Z

Taral:

An '''edge template''' is a [[pattern]] which guarantees a [[connection]] the [[edge]].

Here is an example of a [[Third row|third-row]] edge template ([[template IIIa]], also known as the ''Ziggurat''):

[[Image:Ziggurat.png]]



The red stone has a certain connection to the bottom, using only the shaded hexagons, even if blue moves first.



Countless edge templates can be constructed, all of them of varying degrees of usefulness and frequency of occurance.

* [[Edge templates everybody should know]]
* [[Edge templates with one stone]]
* [[Edge templates with two adjacent stones]]
* [[Edge templates with a bridge]]

File:Ziggurat.png

2005-03-28T11:10:38Z

Taral: Template IIIa

Template IIIa

Bridge

2005-03-28T10:35:02Z

Taral:

A '''bridge''', or a two-bridge, is a type of [[connection]] between two [[piece]]s. It is the equivalent of a diagonal step on a chess board.

[[Image:Bridge.png]]



The idea is that when the opponent "[[Intrusion|intrudes]]" on the bridge by moving in one of the [[empty hex]]es between the pieces, you simply move in the other. Bridges are often very [[Strong connection|strong]], and a quick way to advance across the board. They can sometimes be exploited.

File:Bridge.png

2005-03-28T10:34:13Z

Taral:

Puzzles

2005-03-28T10:06:17Z

Taral: Added diagrams

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.

== Puzzle 1 ==
By [[Piet Hein]]

Blue to play and win.

[[Image:Piethein1.png]]



== Puzzle 2 ==
By [[Piet Hein]]

Blue to play and win.

[[Image:Piethein2.png]]



== Puzzle 3 ==
By [[Piet Hein]]

Blue to play and win.

[[Image:Piethein3.png]]



== Puzzle 4 ==
By [[Piet Hein]]

Blue to play and win.

[[Image:Piethein4.png]]



== Puzzle 5 ==
By [[Piet Hein]]

Blue to play and win.

[[Image:Piethein5.png]]



== Puzzle 6 ==
By [[Piet Hein]]

On the board of size 3 there are precisely two opening moves such that, with optimal play from both players, the board will be completely filled before the game is over. Which are the two opening moves?

== Puzzle 7 ==
By Unknown

Red (Vertical) to play and win

This is a very difficult puzzle whose complete solution is extremely complex.

[[Image:Puzzle7.png]]



== See also ==

* [[Solutions to puzzles]]
* [[Ladder puzzles]]

File:Puzzle7.png

2005-03-28T10:03:08Z

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File:Piethein5.png

2005-03-28T10:02:51Z

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File:Piethein4.png

2005-03-28T10:02:35Z

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File:Piethein3.png

2005-03-28T10:02:18Z

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File:Piethein2.png

2005-03-28T10:01:58Z

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File:Piethein1.png

2005-03-28T09:57:26Z

Taral: Puzzle by Piet Hein

Puzzle by Piet Hein