Difference between revisions of "Edge template V1b"

Revision as of 02:12, 25 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:

Intrusion at a

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

or like this:

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:

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:

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.

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

Continuation:

[Expand]

Continuation after 2nd row ladder

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

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

Continuation:

[Expand]

@@ Line 222: / Line 222: @@
 <div class="toccolours mw-collapsible  mw-collapsed">
-Now Red has two threats:
+Red has several threats. Via [[double threat]]s:
 <hexboard size="6x14"
@@ Line 228: / Line 228: @@
     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"
+    contents="R e2 R g3 R d4 B c5 B d5 E *:e5 R f5 B e6 e3 R d3 S area(f2,d6,f6,g4,g2)-e6"
     />
-and
+Via [[double threat]] and [[edge template III2b]]:
 <hexboard size="6x14"
@@ Line 237: / Line 237: @@
     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 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 S f2 g2 f3 R g3 R d4 S e4 f4 E *:g4 S h4 B c5 B d5 S e5 R f5 S g5 S h5 B e6 S f6 g6 h6 B e3 R d3 S g3 g4 f5"
     />
-Blue must play in the overlap:
+Via [[bridge]]s and [[Tom's move]]:
-<hexboard size="6x14"
-   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"
-   />
-''7. f2''
 <hexboard size="6x14"
@@ Line 255: / Line 246: @@
     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: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 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:f2 S area(f2,f6,l6,l4,j2)"
     />
-''7. g2''
+Via a [[wheel]] and [[Tom's move]]:
 <hexboard size="6x14"
@@ Line 264: / Line 255: @@
     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"
+    contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:e4 S area(f3,e4,e5,f6,l6,l4,j2,h2)"
     />
+Via a [[double threat]] and [[Tom's move]]:
-''7. f3''
 <hexboard size="6x14"
@@ Line 274: / Line 264: @@
     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 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 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:f4 S area(f2,f6,l6,l4,j2)+e4-g4"
     />
-is now connected to the left and to the bottom by [[Tom's move]].
-''7. e4''
+Via a different [[double threat]] and [[Tom's move]]:
 <hexboard size="6x14"
@@ Line 284: / Line 273: @@
     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"
+    contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:e5 S area(f2,f6,l6,l4,j2)+e4+e5+d6-f6"
     />
-is again connected to the left and to the bottom by [[Tom's move]].
-''7. f4''
-<hexboard size="6x14"
+Blue [[mustplay region|must play]] in the overlap:
-   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 must 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"
@@ Line 303: / Line 283: @@
     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 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 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 S f3 f4"
     />
-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"
-   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 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"
-   />
-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.
-''7. g4''
-<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:g4 R 6:i4 E *:a5 B c5 B d5 R 4:e5 R f5 B 5:d6 B e6 B 3:f6"
-   />
-Once again 6 is now connected to the bottom and to the left in a similar way as in [[Tom's move]].
-''7. e5''
-<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 R 4:i4 E *:a5 B c5 B d5 B 1:e5 R f5 B e6 B 3:f6"
-   />
-And [[Tom's move]] at the end again.
-''7. 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 *: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"
-   />
-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"
-   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"
-   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 must play in 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 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>

Difference between revisions of "Edge template V1b"

Revision as of 02:12, 25 July 2022

Contents

Defense against intrusions

Reduction

Intrusion at a

Intrusion at b

Intrusion at c

Continuation after 3rd row ladder

Intrusion at p, q, r

Intrusion at s

Intrusion at t

Intrusion at u

Intrusion at v

Intrusion at w

Intrusion at x

Intrusion at y

Intrusion at z

Continuation after 2nd row ladder

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