Difference between revisions of "Fourth row edge templates"

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(added IV-3-b)
(Added a 4th row edge template corresponding to Tom's move)
 
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Line 1: Line 1:
 
== Fourth 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"
 
   />
 
   />
  
−
=== [[Defending_against_intrusions_in_template_IVb|IV-1-b]] ===
+
=== [[Edge template IV1b|IV-1-b]] ===
  
 
<hexboard size="4x8"
 
<hexboard size="4x8"
 
   coords="hide"
 
   coords="hide"
−
   contents="E *:a1 E *:b1 E *:c1 E *:d1 R f1 E *:h1 E *:a2 E *:b2 E *:a3 E *:e3"
+
  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]] ===
 
=== [[Edge_template_IV1c|IV-1-c]] ===
Line 19: Line 24:
 
<hexboard size="5x11"
 
<hexboard size="5x11"
 
   coords="hide"
 
   coords="hide"
−
   contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 E *:f1 E *:j1 E *:k1 E *:a2 E *:b2 E *:c2 E *:d2 R f2 E *:k2 E *:a3 E *:b3 E *:a4 E *:c5"
+
  edges="bottom"
 +
  visible="area(g1,c3,a5,k5,k3,i1)"
 +
   contents="R f2 S c5"
 
   />
 
   />
  
 
=== [[Edge_template_IV1d|IV-1-d]] ===
 
=== [[Edge_template_IV1d|IV-1-d]] ===
  
−
<hex> R5 C9
+
<hexboard size="5x11"
−
Sa1 Sb1 Sc1 Sd1 Sh1 Si1 Si2
+
  coords="hide"
−
Sa2 Sb2 Sc2 Vd2
+
  edges="bottom"
−
  Sa3 Sb3
+
  visible="area(g1,c5,k5,k3,i1)"
−
   Sa4
+
   contents="R f2"
−
    </hex>
+
  />
  
 
== Fourth row edge templates with two stones ==
 
== Fourth row edge templates with two stones ==
Line 35: Line 42:
 
=== [[Edge_template_IV2a|IV-2-a]] ===
 
=== [[Edge_template_IV2a|IV-2-a]] ===
  
−
<hex>R4 C4 Vc1 Vd1 Sa1 Sa2 Sa3 Sb1 </hex>
+
<hexboard size="4x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a4,d4,d1)"
 +
  contents="R c1 d1"
 +
  />
  
 
=== [[Edge_template_IV2b|IV-2-b]] ===
 
=== [[Edge_template_IV2b|IV-2-b]] ===
  
−
<hex> R4 C5
+
<hexboard size="4x5"
−
Sa1 Sb1 Vc1   Se1
+
   coords="hide"
−
Sa2 Vb2
+
  edges="bottom"
−
   Sa3 </hex>
+
  visible="area(c1,b2,a4,e4,e2,d1)"
 +
  contents="R c1 b2"
 +
   />
 +
 
  
 
=== [[Edge_template_IV2c|IV-2-c]] ===
 
=== [[Edge_template_IV2c|IV-2-c]] ===
  
 
<hexboard size="4x7"
 
<hexboard size="4x7"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 R f1 E *:g1 E *:a2 E *:b2 E *:e2 E *:a3"
+
  edges="bottom"
−
  />
+
  visible="area(e1,c2,a4,g4,g2,f1)"
 +
  contents="R e1 f1 S e2"
 +
  />
  
 
=== [[Edge_template_IV2d|IV-2-d]] ===
 
=== [[Edge_template_IV2d|IV-2-d]] ===
  
 
<hexboard size="4x4"
 
<hexboard size="4x4"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R d1 E *:a2 E *:b2 E *:a3 R b3"
+
  edges="bottom"
−
  />
+
  visible="area(d1,a4,d4)"
 +
  contents="R d1 b3"
 +
  />
  
 
=== [[Edge_template_IV2e|IV-2-e]] ===
 
=== [[Edge_template_IV2e|IV-2-e]] ===
  
 
<hexboard size="4x5"
 
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R d1 E *:e1 E *:a2 E *:b2 E *:a3 R b3 E *:c4"
+
  edges="bottom"
−
  />
+
  visible="area(d1,a4,e4,e2)"
 +
  contents="R d1 b3 S c4"
 +
  />
  
 
=== [[Edge_template_IV2f|IV-2-f]] ===
 
=== [[Edge_template_IV2f|IV-2-f]] ===
  
 
<hexboard size="4x5"
 
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 E *:a3 R a4"
+
  edges="bottom"
−
  />
+
  visible="area(d1,a4,e4,e1)"
 +
  contents="R a4 e1"
 +
  />
  
 
=== [[Edge_template_IV2g|IV-2-g]] ===
 
=== [[Edge_template_IV2g|IV-2-g]] ===
  
 
<hexboard size="4x5"
 
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 E *:a3 E *:a4 R b4"
+
  edges="bottom"
−
  />
+
  visible="area(d1,b3,b4,e4,e1)"
 +
  contents="R b4 e1"
 +
  />
  
 
=== [[Edge_template_IV2h|IV-2-h]] ===
 
=== [[Edge_template_IV2h|IV-2-h]] ===
  
 
<hexboard size="4x5"
 
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 E *:a3 R c4"
+
  edges="bottom"
−
  />
+
  visible="area(d1,a4,e4,e1)"
 +
  contents="R e1 c4"
 +
  />
  
 
=== [[Edge_template_IV2i|IV-2-i]] ===
 
=== [[Edge_template_IV2i|IV-2-i]] ===
  
 
<hexboard size="4x5"
 
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 R c2 E *:a3 E *:e3 E *:e4"
+
  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]] ===
 
=== [[Edge_template_IV2j|IV-2-j]] ===
  
−
<hexboard size="4x5"
+
<hexboard size="4x4"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 R c2 E *:a3 E *:a4"
+
  edges="bottom"
−
  />
+
  visible="-(a1 a2 a3 b1)"
 +
  contents="R b2 arrow(12):d1"
 +
  />
  
 
=== [[Edge_template_IV2k|IV-2-k]] ===
 
=== [[Edge_template_IV2k|IV-2-k]] ===
  
 
<hexboard size="4x6"
 
<hexboard size="4x6"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 R f1 E *:a2 E *:b2 R d2 E *:a3"
+
  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]] ===
 
=== [[Edge_template_IV2l|IV-2-l]] ===
  
 
<hexboard size="4x6"
 
<hexboard size="4x6"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3"
+
  edges="bottom"
−
  />
+
  visible="area(d1,a4,f4,f1)"
 +
  contents="R d1 f1"
 +
  />
  
−
Red can choose which of the two stones to connect to the bottom.
+
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 ==
 
== Fourth row edge templates with three stones ==
Line 121: Line 220:
  
 
<hexboard size="4x5"
 
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 R c1 R d1 R e1 E *:a2 E *:a3 E *:e3 E *:d4 E *:e4"
+
  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 others in some other way.
+
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]] ===
 
=== [[Edge_template_IV3b|IV-3-b]] ===
  
−
<hexboard size="4x6"
+
<hexboard size="4x5"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R e1 R f1 E *:a2 E *:b2 E *:d2 E *:a3"
+
  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.
 
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.

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