Difference between revisions of "Edge template V1b"

From HexWiki
Jump to: navigation, search
(Copy-edited top of article.)
(Added "see also", and some copy-editing.)
 
(15 intermediate revisions by 2 users not shown)
Line 14: Line 14:
 
== Defense against intrusions ==
 
== Defense against intrusions ==
  
Red has 3 main threats:
+
=== Reduction ===
 +
 
 +
Red has 3 main threats. Using the [[ziggurat]]:
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 20: Line 22:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   contents="R e2 R 1:d4 S d4 d3 e3 c4 S b5 c5 d5 a6 b6 c6 d6"
+
   contents="R e2 E *:d4 S d4 d3 e3 c4 S b5 c5 d5 a6 b6 c6 d6"
 
   />
 
   />
 
    
 
    
using the [[ziggurat]],
+
Using [[edge template III1b]]:
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 29: Line 31:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   contents="R e2 R 1:d4 S d3 e3 c4 d4 e4 b5 c5 d5 e5 a6 b6 d6 e6"
+
   contents="R e2 E *:d4 S d3 e3 c4 d4 e4 b5 c5 d5 e5 a6 b6 d6 e6"
 
   />
 
   />
 
    
 
    
using [[edge template III1b]] and
+
And using [[edge_template_IV1d]]:
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 38: Line 40:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   contents="R e2 R 1:f3 S area(e3,c6,k6,k4,i2,f2)"
+
   contents="R e2 E *:f3 S area(e3,c6,k6,k4,i2,f2)"
 
   />
 
   />
  
using [[edge_template_IV1d]].
+
For a blocking attempt, Blue [[mustplay region|must play]] in the overlap:
 
+
For a blocking attempt, Blue must play in the overlap:
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 52: Line 52:
 
   />
 
   />
  
=== Defense against a ===
+
=== Intrusion at a ===
 
+
Details yet to come...
+
 
+
=== Defense against b ===
+
Red can start like this:
+
 
+
<hexboard size="6x14"
+
  coords="hide"
+
  edges="bottom"
+
  visible="c3 area(f1,a6,n6,n4,l2,h1)"
+
  contents="R e2 2:d4 4:d3 6:g3 B c3 1:d5 3:e3 5:c5"
+
  />
+
 
+
Continuation:
+
 
+
<div class="toccolours mw-collapsible  mw-collapsed">
+
Red has this threat,
+
  
 +
If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   contents="R e2 2:d4 4:d3 6:g3 8:f4 B c3 1:d5 3:e3 5:c5 S f2 g2 f3 e4 area(d6,f4,g4,g6)"
+
   contents="R e2 B 1:e3 R 2:d3 B 3:c5 R 4:d4 B 5:d5"
 
   />
 
   />
 
+
or like this:
so Blue must play in the shaded area.
+
 
+
 
+
 
+
 
+
==== the top 3 of those cells ====
+
 
+
 
+
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   contents="R e2 2:d4 4:d3 6:g3 8:e4 B c3 1:d5 3:e3 5:c5 7:(f3 f2 g2) S d6 e5 e6"
+
   contents="R e2 B 1:e3 R 2:d3 B 3:d4 R 4:c4 B 5:b6 R 6:c5 B 7:c6 R 8:d5 B 9:d6"
 
   />
 
   />
  
Now Blue must play in one of the 3 shaded cells. ​ If Blue plays in the left 2 of those 3, then Red connects via [[Edge_template_IV2b|IV-2-b]]. ​ Otherwise, Red connects via [[Tom's move]].
+
Red's continuation will be discussed below.
 
+
<hexboard size="6x14"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  contents="R e2 2:d4 4:d3 6:g3 8:e4 10:e5 12:f5 14:i4 B c3 1:d5 3:e3 5:c5 7:(f3 f2 g2) 9:e6 11:d6 13:f6"
+
  />
+
 
+
 
+
 
+
==== ... 5. e4 ====
+
 
+
Yet to come ...
+
 
+
==== ... 5. f4 ====
+
 
+
Yet to come ...
+
 
+
==== ... 5. g4 ====
+
 
+
Yet to come ...
+
 
+
==== ... 5. e5 ====
+
 
+
Yet to come ...
+
 
+
==== ... 5. f5 ====
+
 
+
Yet to come ...
+
 
+
==== ... 5. g5 ====
+
 
+
Yet to come ...
+
  
==== ... 5. d6 ====
+
=== Intrusion at b ===
  
 +
If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:e4 R 2:f4 E *:a5 B c5 B d5 B 1:d6"
+
   contents="R e2 B 1:d5 R 2:d4 B 3:e3 R 4:d3 B 5:c5"
 
   />
 
   />
  
The group with 2 is connected to the top in two non-overlapping ways (see area marked with +) and to the bottom with [[Edge_template_IV2b|IV-2-b]].
+
Red's continuation will be discussed below.
  
==== ... 5. e6 ====
+
=== Intrusion at c ===
 
+
Red can respond here:
+
  
 +
If Blue intrudes at c, Red can start by forcing a 2nd row ladder like this:
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 R g3 E *:n3 E *:a4 E *:b4 R d4 E *:a5 B c5 B d5 R 2:f5 B 1:e6"
+
   contents="R e2 B 1:d6 R 2:d4 B 3:e3 R 4:d3 B 5:c5 R 6:d5 B 7:c6"
 
   />
 
   />
  
Continuation:
+
Red's continuation will be discussed below.
<div class="toccolours mw-collapsible  mw-collapsed">
+
  
Now Red has two threats:
+
=== Continuation after 3rd row ladder ===
 
+
<hexboard size="6x14"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:e4 E +:f4 E +:g4 E *:a5 B c5 B d5 R 1:e5 R f5 E +:d6 B e6 E +:f6"
+
  />
+
  
and
+
If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 168: Line 103:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:e4 E +:f4 R 1:g4 E +:h4 E *:a5 B c5 B d5 E +:e5 R f5 E +:g5 E +:h5 B e6 E +:f6 E +:g6 E +:h6"
+
   contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3"
 
   />
 
   />
  
Blue has to play on the overlap:
+
Now Red is connected by [[Tom's move for 3rd and 5th row parallel ladders]].
  
<hexboard size="6x14"
+
=== Continuation after 2nd row ladder ===
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:e4 E +:f4 E +:g4 E *:a5 B c5 B d5 E +:e5 R f5 B e6 E +:f6"
+
  />
+
  
 
+
If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.
''7. f2''
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 186: Line 116:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 B 1:f2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:e4 R 8:h4 E *:a5 B c5 B d5 R 4:e5 R f5 B 7:g5 R 6:h5 B 5:d6 B e6 B 3:f6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R 1:e5 B 2:e6 R 3:h4"
 
   />
 
   />
  
''7. g2''
+
Now Red connects in essentially the same way as [[Tom's move]].
  
<hexboard size="6x14"
+
Specifically, Red has these threats:
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 B 1:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R 2:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 6:h4 E *:a5 B c5 B d5 R f5 B 5:g5 R 4:h5 B e6 B 3:f6"
+
  />
+
 
+
 
+
''7. f3''
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 205: Line 127:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 B 1:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:e4 R 6:i4 E *:a5 B c5 B d5 R 4:e5 R f5 B 5:d6 B e6 B 2:f6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:f5 B 2:f6 R 3:g5 B 4:g6 R 5:i5 S area(f5,f6,i6,i4,h4)"
  />
+
6 is now connected to the left and to the bottom by [[Tom's move]].
+
 
+
''7. e4''
+
 
+
<hexboard size="6x14"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 R 2:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 B 1:e4 R 4:i4 E *:a5 B c5 B d5 R f5 B e6 B 3:f6"
+
  />
+
4 is again connected to the left and to the bottom by [[Tom's move]].
+
 
+
''7. f4''
+
 
+
<hexboard size="6x14"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:e4 B 1:f4 E *:a5 B c5 B d5 E +:e5 R f5 E +:d6 B e6 E +:f6"
+
 
   />
 
   />
 
    
 
    
Blue has to go on one of the 3 marked fields. However, d6 can't be any better than 35, so it's enough to look at e5 and g6. Let's have a look at g6 first:
 
 
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 R g3 E *:n3 E *:a4 E *:b4 R d4 R e4 B f4 R 4:i4 E *:a5 B c5 B d5 R 2:e5 R f5 B 3:d6 B e6 B 1:f6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:f5 B 2:f6 R 3:h5 S area(f5,f6,h6,h4,g4)"
 
   />
 
   />
 
    
 
    
4 is now connected to the bottom and to the left in a similar way as in [[Tom's move]]. (Just the piece on g3 is connected to the left in a slightly different way.)
 
 
The other possible move was e5:
 
 
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 R 2:h2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R g3 E *:n3 E *:a4 E *:b4 R d4 R e4 B f4 E *:a5 B c5 B d5 B 1:e5 R f5 B e6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:g3 S area(f2,f3,g4,f6,i6,i4,g2)"
 
   />
 
   />
 
    
 
    
Red 2 is connected to the left by two non-overlapping ways and to the bottom by a 5th row template that has yet to be added to this wiki.
+
The overlap in which Blue [[mustplay region|must play]] is:
 
+
''7. g4''
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 256: Line 150:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:e4 B 1:g4 R 6:i4 E *:a5 B c5 B d5 R 4:e5 R f5 B 5:d6 B e6 B 3:f6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 S area(f6,h6,h4)"
 
   />
 
   />
  
Once again 6 is now connected to the bottom and to the left in a similar way as in [[Tom's move]].
+
Four of these five possible moves can be analysed together. In the following diagram, assume Blue has played 1 in any one of the cells marked with +:
 
+
''7. e5''
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 267: Line 159:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 R 2:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 4:i4 E *:a5 B c5 B d5 B 1:e5 R f5 B e6 B 3:f6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 2:g5 B 3:f5 R 4:g3 B 5:f4 R 6:f2 E +:h5 E +:f6 E +:g6 E +:h6"
 
   />
 
   />
  
And [[Tom's move]] at the end again.
+
After Red 2, that group is safely connected to them bottom, now matter which of the pluses Blue chose before.
  
''7. f6''
+
That leaves only one Blue move to deal with:
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 278: Line 170:
 
   edges="bottom"
 
   edges="bottom"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
 
   visible="area(f1,a6,n6,n4,l2,h1)"
   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 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:i4 E *:a5 B c5 B d5 R f5 B e6 B 1:f6"
+
   contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 10:f3 R 8:g3 R 4:i3 B 9:f4 B 5:g4 R 2:f5 B 1:g5 B 3:f6 R 6:h2 B 7:g2"
 
   />
 
   />
 
 
Red 2 is connected to the bottom and to at least one of the red pieces in the middle by [[Tom's move]]. Red now has three threats to connect both these pieces to the top:
 
  
<hexboard size="6x14"
+
Note that Red 4 connects to the bottom with [[Edge_template_IV2b|IV-2-b]].
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 R 1:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:f4 E +:g4 R i4 E *:a5 B c5 B d5 R f5 B e6 B f6"
+
  />
+
 
+
<hexboard size="6x14"
+
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:e4 R 1:f4 R i4 E *:a5 B c5 B d5 R f5 B e6 B f6"
+
  />
+
 
+
and
+
  
<hexboard size="6x14"
+
== See also ==
  coords="hide"
+
  edges="bottom"
+
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 1:e4 E +:f4 E +:g4 R i4 E *:a5 B c5 B d5 E +:e5 R f5 B e6 B f6"
+
  />
+
 
+
Blue has to play on the overlap:
+
  
<hexboard size="6x14"
+
* [[Tom's move]]
  coords="hide"
+
* [[Tom's move for 3rd and 5th row parallel ladders]]
  edges="bottom"
+
* [[Fourth row edge templates]]
  visible="area(f1,a6,n6,n4,l2,h1)"
+
  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 +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:f4 R i4 E *:a5 B c5 B d5 R f5 B e6 B f6"
+
  />
+
  
First move:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 B 1:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:e4 B 3:f4 R i4 E *:a5 B c5 B d5 R 4:e5 R f5 R 6:g5 B 5:d6 B e6 B f6"
 
  />
 
 
Second move:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R 2:f3 R g3 R 4:h3 E *:n3 E *:a4 E *:b4 R d4 B 1:f4 B 3:g4 R i4 E *:a5 B c5 B d5 R f5 B e6 B f6"
 
  />
 
</div>
 
==== ... 5. f6 ====
 
 
Red can start like this:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R g3 E *:n3 E *:a4 E *:b4 R d4 E *:a5 B c5 B d5 R 2:e5 B 1:f6"
 
  />
 
 
 
Red now has these threats:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 +:d3 E +:e3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 1:e4 E *:a5 B c5 B d5 R e5 E +:d6 E +:e6 B f6"
 
  />
 
 
 
and
 
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R 1:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:f4 E +:g4 E +:h4 E *:a5 B c5 B d5 R e5 E +:f5 E +:g5 E +:h5 E +:d6 E +:e6 B f6 E +:g6 E +:h6"
 
  />
 
 
 
using [[Edge_template_IV2e|IV-2-e]].
 
 
Blue has to play on the overlap:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R g3 E *:n3 E *:a4 E *:b4 R d4 E *:a5 B c5 B d5 R e5 E +:d6 E +:e6 B f6"
 
  />
 
 
 
First move:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R 4:f2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R g3 E *:n3 E *:a4 E *:b4 R d4 B 3:e4 B 5:f4 R 6:g4 E *:a5 B c5 B d5 R e5 B 7:f5 B 8:h5 B 1:d6 R 2:e6 B f6"
 
  />
 
 
 
You get the the defense against the other move by just swapping 1 and 2 in the diagram above.
 
 
==== ... 5. g6 ====
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R g3 E *:n3 E *:a4 E *:b4 R d4 R 2:f4 R 6:h4 E *:a5 B c5 B d5 B 5:f5 B 7:g5 R 8:i5 B 3:e6 R 4:f6 B 1:g6"
 
  />
 
 
Note that 2 is safely connected to the top, so 3 is forced.
 
 
 
</div>
 
 
=== Defense against c ===
 
 
Red has this line:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R 2:d4 R 8:h4 E *:a5 B 3:c5 R 4:d5 R 6:e5 B 5:c6 B 1:d6 B 7:e6"
 
  />
 
 
Blue 3, 5 and 7 are forced.
 
 
Continuation:
 
<div class="toccolours mw-collapsible  mw-collapsed">
 
 
Red has these threats:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R d4 R h4 E +:i4 E *:a5 B c5 R d5 R e5 R 1:f5 R 3:g5 E +:h5 R 5:i5 B c6 B d6 B e6 B 2:f6 B 4:g6 E +:h6 E +:i6"
 
  />
 
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R d4 E +:g4 R h4 E *:a5 B c5 R d5 R e5 R 1:f5 E +:g5 R 3:h5 B c6 B d6 B e6 B 2:f6 E +:g6 E +:h6"
 
  />
 
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R 1:g3 E +:h3 E *:n3 E *:a4 E *:b4 R d4 E +:f4 E +:g4 R h4 E +:i4 E *:a5 B c5 R d5 R e5 E +:g5 E +:h5 E +:i5 B c6 B d6 B e6 E +:f6 E +:g6 E +:h6 E +:i6"
 
  />
 
 
 
The overlap in which Blue has to play is:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R d4 R h4 E *:a5 B c5 R d5 R e5 E +:g5 E +:h5 B c6 B d6 B e6 E +:f6 E +:g6 E +:h6"
 
  />
 
 
Four of these five possible moves can be analysed in one line. In the following diagram assume Blue has played 1 on any of the fields marked with +:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 R 6:f2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R 4:g3 E *:n3 E *:a4 E *:b4 R d4 B 5:f4 R h4 E *:a5 B c5 R d5 R e5 B 3:f5 R 2:g5 E +:h5 B c6 B d6 B e6 E +:f6 E +:g6 E +:h6"
 
  />
 
 
After Red 2 that group is safely connected to them bottom, now matter which of the pluses Blue chose before.
 
 
That leaves only one Blue move to deal with:
 
 
<hexboard size="6x14"
 
  coords="hide"
 
  edges="bottom"
 
  visible="area(f1,a6,n6,n4,l2,h1)"
 
  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 B 7:g2 R 6:h2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R 10:f3 R 8:g3 R 4:i3 E *:n3 E *:a4 E *:b4 R d4 B 9:f4 B 5:g4 R h4 E *:a5 B c5 R d5 R e5 R 2:f5 B 1:g5 B c6 B d6 B e6 B 3:f6"
 
  />
 
 
Note that Red 4 connects to the bottom with [[Edge_template_IV2b|IV-2-b]].
 
</div>
 
 
[[category:edge templates]]
 
[[category:edge templates]]

Latest revision as of 20:44, 26 July 2022

Edge template V1b is a 5th row edge template with 1 stone.

The validity and minimality of this template has been checked by computer. The template was mentioned on 2016-05-19 by the user shalev in this Little Golem thread, but likely predates that post.


Defense against intrusions

Reduction

Red has 3 main threats. Using the ziggurat:

Using edge template III1b:

And using edge_template_IV1d:

For a blocking attempt, Blue must play in the overlap:

abc

Intrusion at a

If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this

21435

or like this:

214368579

Red's continuation will be discussed below.

Intrusion at b

If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:

43251

Red's continuation will be discussed below.

Intrusion at c

If Blue intrudes at c, Red can start by forcing a 2nd row ladder like this:

4325671

Red's continuation will be discussed below.

Continuation after 3rd row ladder

If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.

1

Now Red is connected by Tom's move for 3rd and 5th row parallel ladders.

Continuation after 2nd row ladder

If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.

312

Now Red connects in essentially the same way as Tom's move.

Specifically, Red has these threats:

13524
132
1

The overlap in which Blue must play is:

Four of these five possible moves can be analysed together. In the following diagram, assume Blue has played 1 in any one of the cells marked with +:

64532

After Red 2, that group is safely connected to them bottom, now matter which of the pluses Blue chose before.

That leaves only one Blue move to deal with:

76108495213

Note that Red 4 connects to the bottom with IV-2-b.

See also