Edge template VI1a

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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.

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:

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At this point, Red can use Tom's move to connect:

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Remaining intrusions

The only possible remaining intrusions for Blue are the following:

fedcab

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:

2x1y

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.

24310568179

If Blue plays at y, Red has the following simple win, using the trapezoid template:

26475183

Intrusion at b (stub)

If Blue intrudes at b, Red can respond at 2:

2xy1wz

Apart from intrusions into the bridge, which Red defends, Blue has only four possible moves x,y,z,w, because if Blue moves anywhere else, Red connects with either the ziggurat or edge template III1b.

If Blue intrudes at x, Red can set up a parallel ladder and connect using Tom's move:

24385617

If Blue intrudes at y or z (both shown simultaneously in the following diagram), Red can set up Tom's move on the opposite side:

2843153

Finally, if Blue intrudes at w, Red can connect by the following variant of Tom's move:

246513

Intrusion at c (stub)

1

Intrusion at d (stub)

1

Red should go here:

21

Details to follow. See more details here.

Intrusion at e

1

Red should move here (or the equivalent mirror-image move at "+"):

21

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 "+":

132

If Blue yields, or Red starts out with a 2nd row ladder, the escape fork works anyway:

1736542

Intrusion at f

1

First establish a parallel ladder on the right.

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Then use Tom's move:

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