Difference between revisions of "Edge template V1b"

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m (Intrusion at v or y or z: small typo)
m (Intrusion at x: minor copy-edits)
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If Blue plays one of the five upper-right of those cells
 
If Blue plays one of the five upper-right of those cells
 
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
Line 375: Line 374:
 
   contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S blue:(f3 f2 g2 g4 f4)"
 
   contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S blue:(f3 f2 g2 g4 f4)"
 
   />
 
   />
 
+
then Red still connects via [[Tom's move]],
, ​ then Red still connects via [[Tom's move]],
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 387: Line 385:
 
since at least two of the three cells marked "*" are still available to Red 1 to connect to Red's left group.
 
since at least two of the three cells marked "*" are still available to Red 1 to connect to Red's left group.
  
This leaves only two
+
This leaves only two remaining tries for Blue:
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 395: Line 393:
 
   contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S e4 f5"
 
   contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S e4 f5"
 
   />
 
   />
 
remaining tries for Blue.
 
  
 
If Blue plays the right of those two,
 
If Blue plays the right of those two,
Line 420: Line 416:
 
Now, it does not matter which of the two shaded cells Blue 2 is at, since
 
Now, it does not matter which of the two shaded cells Blue 2 is at, since
  
* if Blue plays the other too then the order in which they were played doesn't matter
+
* if Blue plays the other too then the order in which they were played doesn't matter, and
* and
+
* if instead Red plays the other, then whichever one Blue played will be [[Dead cell|dead]].
* if instead Red plays the other, then whichever one Blue played will be [[Dead cell|dead]]
+
  
, ​ so this is equivalent to Red having a [[Theorems_about_templates#Corner_clipping|clipped]] version of [[Edge template IV1d]].
+
So this is equivalent to Red having a [[Theorems_about_templates#Corner_clipping|clipped]] version of [[Edge template IV1d]].
  
 
In particular, Red is connected down.
 
In particular, Red is connected down.

Revision as of 12:40, 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:

 [Expand

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.

Continuation:

 [Expand