Difference between revisions of "Fourth row edge templates"

From HexWiki
Jump to: navigation, search
(new page containing only IV-1-a)
 
(Added a 4th row edge template corresponding to Tom's move)
 
(31 intermediate revisions by 3 users not shown)
Line 1: Line 1:
−
== Third row edge templates with one stone ==
+
== Fourth row edge templates with one stone ==
  
−
=== [[Defending_against_intrusions_in_template_1-IVa|IV-1-a]] ===
+
=== [[Edge template IV1a|IV-1-a]] ===
  
 
<hexboard size="4x7"
 
<hexboard size="4x7"
 
   coords="hide"
 
   coords="hide"
−
   contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 E *:g1 E *:a2 E *:b2 E *:a3"
+
  edges="bottom"
 +
  visible="area(e1,c2,a4,g4,g2,f1)"
 +
   contents="R e1"
 
   />
 
   />
 +
 +
=== [[Edge template IV1b|IV-1-b]] ===
 +
 +
<hexboard size="4x8"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(e1,c2,a4,h4,h2,g1)"
 +
  contents="R f1 S e3"
 +
  />
 +
The shaded cell is not part of the template; it can be occupied by Blue.
 +
 +
=== [[Edge_template_IV1c|IV-1-c]] ===
 +
 +
<hexboard size="5x11"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(g1,c3,a5,k5,k3,i1)"
 +
  contents="R f2 S c5"
 +
  />
 +
 +
=== [[Edge_template_IV1d|IV-1-d]] ===
 +
 +
<hexboard size="5x11"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(g1,c5,k5,k3,i1)"
 +
  contents="R f2"
 +
  />
 +
 +
== Fourth row edge templates with two stones ==
 +
 +
=== [[Edge_template_IV2a|IV-2-a]] ===
 +
 +
<hexboard size="4x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a4,d4,d1)"
 +
  contents="R c1 d1"
 +
  />
 +
 +
=== [[Edge_template_IV2b|IV-2-b]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a4,e4,e2,d1)"
 +
  contents="R c1 b2"
 +
  />
 +
 +
 +
=== [[Edge_template_IV2c|IV-2-c]] ===
 +
 +
<hexboard size="4x7"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(e1,c2,a4,g4,g2,f1)"
 +
  contents="R e1 f1 S e2"
 +
  />
 +
 +
=== [[Edge_template_IV2d|IV-2-d]] ===
 +
 +
<hexboard size="4x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,d4)"
 +
  contents="R d1 b3"
 +
  />
 +
 +
=== [[Edge_template_IV2e|IV-2-e]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,e4,e2)"
 +
  contents="R d1 b3 S c4"
 +
  />
 +
 +
=== [[Edge_template_IV2f|IV-2-f]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,e4,e1)"
 +
  contents="R a4 e1"
 +
  />
 +
 +
=== [[Edge_template_IV2g|IV-2-g]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,b3,b4,e4,e1)"
 +
  contents="R b4 e1"
 +
  />
 +
 +
=== [[Edge_template_IV2h|IV-2-h]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,e4,e1)"
 +
  contents="R e1 c4"
 +
  />
 +
 +
=== [[Edge_template_IV2i|IV-2-i]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,d4,e2,e1)"
 +
  contents="R c2 e1"
 +
  />
 +
 +
Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).
 +
 +
=== [[Edge_template_IV2j|IV-2-j]] ===
 +
 +
<hexboard size="4x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="-(a1 a2 a3 b1)"
 +
  contents="R b2 arrow(12):d1"
 +
  />
 +
 +
=== [[Edge_template_IV2k|IV-2-k]] ===
 +
 +
<hexboard size="4x6"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c2,a4,f4,f1)"
 +
  contents="R d2 arrow(12):f1"
 +
  />
 +
 +
Red can choose to connect either stone to the bottom, but Red cannot guarantee to connect them both.
 +
 +
=== [[Edge_template_IV2l|IV-2-l]] ===
 +
 +
<hexboard size="4x6"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,f4,f1)"
 +
  contents="R d1 f1"
 +
  />
 +
 +
Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).
 +
 +
=== [[Edge_template_IV2m|IV-2-m]] ===
 +
 +
<hexboard size="4x7"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,f4,g2,g1)"
 +
  contents="R g1 arrow(12):d1"
 +
  />
 +
 +
Red can connect the stone marked "↑" to the bottom. There are infinitely many related templates, with the two red stones arbitrarily far apart. See [[edge template IV2m]] for more details.
 +
 +
=== [[Edge_template_IV2n|IV-2-n]] ===
 +
 +
<hexboard size="4x8"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,h4,h1)"
 +
  contents="R d1 h1"
 +
  />
 +
 +
Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).
 +
 +
=== IV-2-o ===
 +
 +
<hexboard size="4x6"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(a4,f4,f2,e1,d1)"
 +
  contents="R d1 a4"
 +
  />
 +
 +
=== IV-2-p ===
 +
 +
<hexboard size="4x6"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(a4,f4,f2,e1,d1)"
 +
  contents="R d1 b3 S d4"
 +
  />
 +
 +
=== IV-2-q ===
 +
 +
<hexboard size="4x7"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a4,g4,g2,f1)"
 +
  contents="R c1 e1"
 +
  />
 +
 +
Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).
 +
 +
=== IV-2-r ===
 +
 +
<hexboard size="5x7"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a4,a5,g5,g3,e1)"
 +
  contents="R arrow(12):b2,a4 B b3"
 +
  />
 +
 +
== Fourth row edge templates with three stones ==
 +
 +
=== [[Edge_template_IV3a|IV-3-a]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a4,c4,e2,e1)"
 +
  contents="R c1 d1 e1"
 +
  />
 +
 +
If the middle red piece is removed, the template stays valid, as long as the two remaining stones are connected to each other in some other way.
 +
 +
=== [[Edge_template_IV3b|IV-3-b]] ===
 +
 +
<hexboard size="4x5"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="-(a1 a2 a3 b1)"
 +
  contents="R c1 d1 e1 S d2"
 +
  />
 +
 +
If the middle red piece is removed, the template stays valid, as long as the two remaining stones are connected to each others in some other way.
 +
 +
=== [[Edge_template_IV3c|IV-3-c]] ===
 +
 +
<hexboard size="4x6"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,b3,a4,f4)"
 +
  contents="R b3 d2 arrow(12):f1"
 +
  />
 +
 +
Red can choose to connect rightmost stone or the middle stone to the bottom, but Red cannot guarantee to connect both of these. The leftmost stone is already connected to the bottom by [[captured cell|capture]] and Red can always maintain its connection.
  
 
[[Category: Edge templates]]
 
[[Category: Edge templates]]

Latest revision as of 02:47, 17 October 2023

Fourth row edge templates with one stone

IV-1-a

IV-1-b

The shaded cell is not part of the template; it can be occupied by Blue.

IV-1-c

IV-1-d

Fourth row edge templates with two stones

IV-2-a

IV-2-b


IV-2-c

IV-2-d

IV-2-e

IV-2-f

IV-2-g

IV-2-h

IV-2-i

Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).

IV-2-j

IV-2-k

Red can choose to connect either stone to the bottom, but Red cannot guarantee to connect them both.

IV-2-l

Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).

IV-2-m

Red can connect the stone marked "↑" to the bottom. There are infinitely many related templates, with the two red stones arbitrarily far apart. See edge template IV2m for more details.

IV-2-n

Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).

IV-2-o

IV-2-p

IV-2-q

Red can connect both stones to the bottom (i.e., Red does not have to choose which stone to connect).

IV-2-r

Fourth row edge templates with three stones

IV-3-a

If the middle red piece is removed, the template stays valid, as long as the two remaining stones are connected to each other in some other way.

IV-3-b

If the middle red piece is removed, the template stays valid, as long as the two remaining stones are connected to each others in some other way.

IV-3-c

Red can choose to connect rightmost stone or the middle stone to the bottom, but Red cannot guarantee to connect both of these. The leftmost stone is already connected to the bottom by capture and Red can always maintain its connection.

Retrieved from "https://www.hexwiki.net/index.php?title=Fourth_row_edge_templates&oldid=8328"