Difference between revisions of "Fifth row edge templates"

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(→‎Two stones on the fifth row: Removed false statement.)
(Fixed links.)
 
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== Fifth row edge templates with one stone ==
 
== Fifth row edge templates with one stone ==
  
−
=== [[Template_Va|V-1-a]] ===
+
=== [[Edge_template_V1a|V-1-a]] ===
  
 
<hexboard size="5x10"
 
<hexboard size="5x10"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 R g1 E *:i1 E *:j1 E *:a2 E *:b2 E *:c2 E *:d2 E *:j2 E *:a3 E *:b3 E *:a4"
+
  edges="bottom"
−
  />
+
  visible="area(f1,c3,a5,j5,j3,h1)"
 +
  contents="R g1"
 +
  />
  
−
Although the next two templates look like 6th row templates with two stones, note that the 6th row stone plays no role in connecting the template to the edge. It has simply been added to show one possibility for how the 5th row red stone may be connected up. We regard these as one-stone 5th row templates.
+
=== [[Edge_template_V1d|V-1-d]] ===
 +
 
 +
<hexboard size="5x13"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(a5,m5,m3,k1,g1,c3)"
 +
  contents="R g1"
 +
  />
 +
 
 +
Although the next two templates take up 6 rows, they are considered 5th row templates because the stone to be connected is on the 5th row.
  
 
=== [[Edge_template_V1b|V-1-b]] ===
 
=== [[Edge_template_V1b|V-1-b]] ===
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 E *:i1 E *:j1 E *:k1 E *:l1 E *:m1 E *:n1 E *:a2 E *:b2 E *:c2 E *:d2 R e2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E *:n3 E *:a4 E *:b4 E *:a5"
+
  edges="bottom"
−
  />
+
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2"
 +
  />
  
 
=== [[Edge_template_V1c|V-1-c]] ===
 
=== [[Edge_template_V1c|V-1-c]] ===
  
 
<hexboard size="6x16"
 
<hexboard size="6x16"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 E *:e1 R f1 E *:g1 E *:k1 E *:l1 E *:m1 E *:n1 E *:o1 E *:p1 E *:a2 E *:b2 E *:c2 E *:d2 E *:e2 R f2 E *:o2 E *:p2 E *:a3 E *:b3 E *:c3 E *:d3 E *:p3 E *:a4 E *:b4 E *:a5"
+
  edges="bottom"
−
  />
+
  visible="area(f2,c4,a6,p6,p4,n2,j1,h1)"
 +
  contents="R f2"
 +
  />
  
 
== Fifth row edge templates with two stones ==
 
== Fifth row edge templates with two stones ==
Line 29: Line 44:
  
 
<hexboard size="5x6"
 
<hexboard size="5x6"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R d2"
+
  edges="bottom"
−
  />
+
  visible="area(e1,a5,f5,f1)"
 +
  contents="R d2 e1"
 +
  />
  
 
=== V-2-b ===
 
=== V-2-b ===
Line 38: Line 55:
  
 
<hexboard size="5x7"
 
<hexboard size="5x7"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R f1 E *:g1 E *:g2"
+
  edges="bottom"
−
  />
+
  visible="area(e1,a5,g5,g3,f1)"
 +
  contents="R e1 f1"
 +
  />
 
    
 
    
−
 
 
=== V-2-c ===
 
=== V-2-c ===
  
Line 48: Line 66:
  
 
<hexboard size="5x5"
 
<hexboard size="5x5"
−
  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,a5,e5,e1)"
 +
  contents="R b4 e1"
 +
  />
  
 
=== V-2-d ===
 
=== V-2-d ===
  
 
<hexboard size="5x7"
 
<hexboard size="5x7"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R d2 E *:e5 E *:g1 *:g2"
+
  edges="bottom"
−
  />
+
  visible="area(e1,a5,g5,g3,f1)"
 +
  contents="R d2 e1 S e5"
 +
  />
 +
The shaded cell is not part of the template. It can be occupied by Blue.
  
 
=== V-2-e ===
 
=== V-2-e ===
Line 64: Line 87:
  
 
<hexboard size="5x6"
 
<hexboard size="5x6"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R f1 E *:a2 E *:b2 E *:a3 E *:a4 R d3 E *:b3 *:c2 *:d1 *:e1 *:d2"
+
  edges="bottom"
−
  />
+
  visible="area(c3,a5,f5,f1)"
 +
  contents="R d3 arrow(12):f1"
 +
  />
 +
 
 +
Red can choose to connect either stone to the edge, but Red cannot guarantee to connect both.
  
 
=== V-2-f ===
 
=== V-2-f ===
Line 73: Line 100:
  
 
<hexboard size="5x7"
 
<hexboard size="5x7"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 R e1 E *:a2 E *:b2 E *:a3 E *:a4 R c3 E *:b3 *:c2 *:d1 *:g1 *:g2"
+
  edges="bottom"
−
  />
+
  visible="area(e1,a5,g5,g3,f1)"
 +
  contents="R c3 arrow(12):e1"
 +
  />
 +
 
 +
Red can choose to connect either stone to the edge, but Red cannot guarantee to connect both.
  
 
=== V-2-g ===
 
=== V-2-g ===
  
−
This template is called L-5a and L-5b in [http://www.mseymour.ca/hex_book/hexstrat9.html Seymour's book], depending on whether Red wants to connect stone 1 or 2 to the edge. The template guarantees that Red can connect, at Red's choice, either stone 1 or stone 2 to the edge. However, unlike [[Edge_template_IV2l|template IV-2l]], Red is not guaranteed to be able to connect them both.
+
This template is called L-5a in [http://www.mseymour.ca/hex_book/hexstrat9.html Seymour's book]. Red can connect either one of the stones to the edge, but unlike [[Edge_template_IV2l|template IV-2l]], Red is not guaranteed to be able to connect them both.
  
 
<hexboard size="5x8"
 
<hexboard size="5x8"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R 1:e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R 2:g1"
+
  edges="bottom"
−
  />   
+
  visible="area(e1,a5,h5,h1)"
 +
  contents="R arrow(12):e1 g1"
 +
  />
 +
 
 +
=== V-2-h ===
 +
 
 +
This template is called L-5b in [http://www.mseymour.ca/hex_book/hexstrat9.html Seymour's book].
 +
 
 +
<hexboard size="5x8"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(e1,a5,g5,h3,h1)"
 +
  contents="R e1 arrow(12):g1"
 +
  />
 +
 
 +
=== V-2-i ===
 +
<hexboard size="5x8"
 +
 
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(a5,h5,h3,f1,e1)"
 +
  contents="R arrow(12):e1 g2"
 +
  />
 +
 
 +
Red can choose to connect either stone to the edge, but Red cannot guarantee to connect both.
 +
 
 +
=== V-2-j ===
 +
 
 +
<hexboard size="5x11"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(a5,k5,k3,i1,g1,c3)"
 +
  contents="R h1 i1 S h2"
 +
  />
 +
The shaded cell is not part of the template. It can be occupied by Blue.
 +
 
 +
=== V-2-k ===
 +
 
 +
<hexboard size="5x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="-a1--a4 b1"
 +
  contents="R b2 b4 c1"
 +
  />
 +
 
 +
=== V-2-l ===
 +
 
 +
<hexboard size="5x7"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(d1,b3,a5,g5,g3,e1)"
 +
  contents="R d1 c2"
 +
  />
 +
 
 +
=== V-2-m ===
 +
 
 +
<hexboard size="5x10"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(d1,c2,a5,j5,j3,h1)"
 +
  contents="R d1 c2"
 +
  />
 +
 
 +
=== V-2-n ===
 +
 
 +
<hexboard size="5x9"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(c1,a4,a5,i5,i3,g1)"
 +
  contents="R arrow(12):c1,a4 B c2"
 +
  />
 +
 
 +
=== V-2-o ===
 +
 
 +
<hexboard size="6x12"
 +
   coords="none"
 +
  edges="bottom"
 +
  visible="area(c2,a6,l6,l4,j2,f1,d1)"
 +
  contents="R arrow(12):c2,b4 B c3"
 +
  />
  
 
== Two stones on the fifth row ==
 
== Two stones on the fifth row ==
Line 90: Line 200:
 
If Red has two stones on the fifth row with two or more empty hexes between them and the space shown below, Red can connect either one of the stones (at Red's choice) to the edge.  
 
If Red has two stones on the fifth row with two or more empty hexes between them and the space shown below, Red can connect either one of the stones (at Red's choice) to the edge.  
 
<hexboard size="5x9"
 
<hexboard size="5x9"
−
  coords="hide"
+
  coords="hide"
−
  contents="E *:a1 E *:b1 E *:c1 E *:d1 R 1:e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R 2:i1"
+
  edges="bottom"
−
  />  
+
  visible="area(e1,a5,i5,i1)"
 +
  contents="R A:e1 B:i1"
 +
  />
  
−
Red's strategy is as follows. Say Red wants to connect stone 1 to the edge. Then no matter where Blue plays, Red can get at least a 3rd row ladder from stone 1. Red can then use stone 2 as a [[switchback]] to a 5th row ladder going in the opposite direction, which connects to stone 1. For example:
+
Red's strategy is as follows. Say Red wants to connect stone A to the edge. Then no matter where Blue plays, Red can get at least a 3rd row ladder from A. Red can then use stone B as a [[switchback]] to a 5th row ladder going in the opposite direction, which connects to A. For example:
 
<hexboard size="5x9"
 
<hexboard size="5x9"
 
   coords="hide"
 
   coords="hide"
−
   contents="E *:a1 E *:b1 E *:c1 E *:d1 R 1:e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R 2:i1
+
  edges="bottom"
−
             B 3:e2 R 4:d2 B 5:c4 R 6:d3 B 7:d4 R 8:e3 B 9:e4 R 10:f3 B 11:f4 R 12:h3 B 13:g3
+
  visible="area(e1,a5,i5,i1)"
−
             R 14:h1 B 15:g2 R 16:g1 B 17:f2 R 18:f1"
+
   contents="R A:e1 B:i1
 +
             B 1:e2 R 2:d2 B 3:c4 R 4:d3 B 5:d4 R 6:e3 B 7:e4 R 8:f3 B 9:f4 R 10:h3 B 11:g3
 +
             R 12:h1 B 13:g2 R 14:g1 B 15:f2 R 16:f1"
 
   />   
 
   />   
  
−
Note that Red must choose to connect either stone 1 or stone 2 (Red cannot generally guarantee to connect them both). For example, if Blue plays here:
+
Note that Red must choose to connect either stone A or stone B (Red cannot generally guarantee to connect them both). For example, if Blue plays here:
 
<hexboard size="5x8"
 
<hexboard size="5x8"
 
   coords="hide"
 
   coords="hide"
−
   contents="E *:a1 E *:b1 E *:c1 E *:d1 R 1:e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R 2:h1
+
  edges="bottom"
 +
  visible="area(e1,a5,i5,i1)"
 +
   contents="R A:e1 B:h1
 
             B f2"
 
             B f2"
 
   />
 
   />
Line 111: Line 227:
 
<hexboard size="5x9"
 
<hexboard size="5x9"
 
   coords="hide"
 
   coords="hide"
−
   contents="E *:a1 E *:b1 E *:c1 E *:d1 R 1:e1 E *:a2 E *:b2 E *:c2 E *:a3 E *:b3 E *:a4 R 2:i1
+
  edges="bottom"
 +
  visible="area(e1,a5,i5,i1)"
 +
   contents="R A:e1 B:i1
 
             B f3"
 
             B f3"
 
   />   
 
   />   
−
then Red can choose to connect 1 or 2, but not both.
+
then Red can choose to connect A or B, but not both.
 
    
 
    
 
[[Category: Edge templates]]
 
[[Category: Edge templates]]

Latest revision as of 02:06, 1 November 2023

Fifth row edge templates with one stone

V-1-a

V-1-d

Although the next two templates take up 6 rows, they are considered 5th row templates because the stone to be connected is on the 5th row.

V-1-b

V-1-c

Fifth row edge templates with two stones

V-2-a

V-2-b

This template is called C-5 in Seymour's book.

V-2-c

This template is called J-5 in Seymour's book.

V-2-d

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

V-2-e

This template is called D-5a in Seymour's book.

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

V-2-f

This template is called D-5b in Seymour's book.

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

V-2-g

This template is called L-5a in Seymour's book. Red can connect either one of the stones to the edge, but unlike template IV-2l, Red is not guaranteed to be able to connect them both.

V-2-h

This template is called L-5b in Seymour's book.

V-2-i

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

V-2-j

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

V-2-k

V-2-l

V-2-m

V-2-n

V-2-o

Two stones on the fifth row

If Red has two stones on the fifth row with two or more empty hexes between them and the space shown below, Red can connect either one of the stones (at Red's choice) to the edge.

AB

Red's strategy is as follows. Say Red wants to connect stone A to the edge. Then no matter where Blue plays, Red can get at least a 3rd row ladder from A. Red can then use stone B as a switchback to a 5th row ladder going in the opposite direction, which connects to A. For example:

A161412B21151346811103579

Note that Red must choose to connect either stone A or stone B (Red cannot generally guarantee to connect them both). For example, if Blue plays here:

AB

or here:

AB

then Red can choose to connect A or B, but not both.

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