Difference between revisions of "Edge template V1b"
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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" | ||
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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]], | |
− | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
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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" | ||
/> | /> | ||
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− | |||
If Blue plays the right of those two, | If Blue plays the right of those two, | ||
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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 |
− | + | * 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]]. | |
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.
Contents
[hide]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:
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: