Difference between revisions of "Edge template VI1a"
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For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions! | For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions! | ||
| − | === Intrusion at a | + | === Intrusion at a === |
| + | |||
| + | If Blue intrudes at a, Red has several winning responses. For example, White can play at 2: | ||
<hexboard size="7x14" | <hexboard size="7x14" | ||
coords="none" | coords="none" | ||
edges="bottom" | edges="bottom" | ||
visible="area(a7,n7,n5,k2,i2,c5)" | visible="area(a7,n7,n5,k2,i2,c5)" | ||
| − | contents="R j2 B 1:f7" | + | contents="R j2 B 1:f7 R 2:i4 E x:i5 y:h7" |
| + | /> | ||
| + | Apart from intrusion into the bridge, which Red defends, Blue's only possible moves are at x and y. If Blue plays at x, Red can set up a [[parallel ladder]] and connect using [[Tom's move]]. | ||
| + | <hexboard size="7x14" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(a7,n7,n5,k2,i2,c5)" | ||
| + | contents="R j2 B 1:f7 R 2:i4 B 3:i5 R 4:g5 B 5:e6 R 6:g6 B 7:g7 R 8:h6 B 9:h7 R 10:k5" | ||
| + | /> | ||
| + | If Blue plays at y, Red has the following simple win, using the [[trapezoid]] template: | ||
| + | <hexboard size="7x14" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(a7,n7,n5,k2,i2,c5)" | ||
| + | contents="R j2 B 1:f7 R 2:i4 B 3:h7 R 4:i5 B 5:j6 R 6:g5 B 7:e6 R 8:g7" | ||
/> | /> | ||
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=== Intrusion at b (stub) === | === Intrusion at b (stub) === | ||
Revision as of 18:49, 1 May 2021
Template VI1-a is a 6th row edge template with one stone.
This template is the first one stone 6th row template for which a proof of validity has been written out. The template has been verified by computer, and also verified to be minimal.
Contents
Elimination of irrelevant Blue moves
Red has a number of direct threats to connect, using smaller templates. Blue must play in the carrier of these threats in order to counter them. To prevent Red from connecting Blue must play in the intersection of Red's threats carriers.
Edge template IV1a
Edge template IV1b
Using Tom's move
6 intrusions can furthermore be discarded thanks to Tom's move, also known as the parallel ladder trick. Of course, symmetry will cut our work in half!
If Blue moves in any of the cells marked "1" on the left (and, using mirror symmetry, in the corresponding 3 cells on the right), Red can respond as follows:
At this point, Red can use Tom's move to connect:
Remaining intrusions
The only possible remaining intrusions for Blue are the following:
By symmetry, if is sufficient to consider the six possible intrusions at a – f.
Specific defense
For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!
Intrusion at a
If Blue intrudes at a, Red has several winning responses. For example, White can play at 2:
Apart from intrusion into the bridge, which Red defends, Blue's only possible moves are at x and y. If Blue plays at x, Red can set up a parallel ladder and connect using Tom's move.
If Blue plays at y, Red has the following simple win, using the trapezoid template:
Intrusion at b (stub)
Red should go here:
See more details here.
Intrusion at c (stub)
Intrusion at d (stub)
Red should go here:
Details to follow. See more details here.
Intrusion at e
Red should move here (or the equivalent mirror-image move at "+"):
Now the shaded area is a ladder creation template, giving Red at least a 3rd row ladder as indicated.
Red can escape both 2nd and 3rd row ladders using a ladder escape fork via "+". Specifically, Red escapes a third row ladder like this, and is connected by a ziggurat and double threat at "+":
If Blue yields, or Red starts out with a 2nd row ladder, the escape fork works anyway:
Intrusion at f
First establish a parallel ladder on the right.
Then use Tom's move:
