Edge template VI1a

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.

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 (stub)

Details to follow

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.

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: