Difference between revisions of "Edge template V1b"
(→Continuation after 3rd row ladder: combined three 1-diagram cases into one 2-diagram case) |
(→Intrusion at x: slightly shortened analysis for one case) |
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 d4 d3 | + | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6" |
/> | /> | ||
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<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
− | Red | + | Red's main threat is as follows, |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | contents="R e2 d4 d3 1:g3 3:e5 5:f5 B c3 d5 e3 c5 2:e6 E *:e4 *:f2 S d6 e4 f3 f2 g2 g4 f4 f5 f6" |
/> | /> | ||
− | + | connecting back via one of the cells marked "*". | |
− | + | If Blue plays either of the two of those cells adjacent to the edge, then Red plays the | |
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<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | contents="R e2 d4 d3 1:g3 3:e5 5:f5 B c3 d5 e3 c5 2:e6 E *:(d6 f6 i4) S blue:(d6 f6)" |
/> | /> | ||
− | + | same move anyway, connecting down via the other of those two cells or [[Tom's move]]. | |
− | + | If Blue plays one of the five upper-right of those cells | |
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<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | 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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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | contents="R e2 d4 d3 1:g3 3:e5 5:e4 7:f5 9:i4 B c3 d5 e3 c5 2:e6 6:d6 8:f6 E *:(f3 f4 g4) S blue:(f3 f2 g2 g4 f4)" |
− | + | /> | |
+ | 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 | |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S e4 f5" |
/> | /> | ||
− | If Blue plays | + | remaining tries for Blue. |
+ | |||
+ | If Blue plays the right of those two, | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | contents="R e2 d4 d3 1:g3 3:e5 5:e4 B c3 d5 e3 c5 2:e6 4:f5 E *:d6 *:h4" |
/> | /> | ||
− | + | then Red connects via [[double threat]]. | |
− | + | Thus Blue instead plays the left of those two. Red responds as follows. | |
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<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
− | contents="R e2 | + | contents="R e2 d4 d3 1:g3 3:e5 5:f2 7:f3 B c3 d5 e3 c5 2:e6 4:e4 6:g2 S d6 e6" |
/> | /> | ||
− | + | 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 | |
− | + | * and | |
− | + | * if instead Red plays the other, then whichever one Blue played will be [[Dead cell|dead]] | |
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− | + | , so this is equivalent to Red having a [[Theorems_about_templates#Corner_clipping|clipped]] version of [[Edge template IV1d]]. | |
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− | + | In particular, Red is connected down. | |
</div> | </div> |
Revision as of 05:46, 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: