Difference between revisions of "Edge template VI1a"

Revision as of 21:35, 1 March 2009 (view source) Kogorman (Talk | contribs) (→‎Third-row followup: i4: Filling in some details.) ← Older edit		Revision as of 21:38, 1 March 2009 (view source) Kogorman (Talk | contribs) m (→‎Third-row followup i4 and incursion at i6) Newer edit →
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	===== Third-row followup i4 and incursion at i6 =====		===== Third-row followup i4 and incursion at i6 =====
−	This the hardest of the variations; the others should be obvious.	+
	<hex>		<hex>
	R7 C14 Q0		R7 C14 Q0

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Revision as of 21:38, 1 March 2009

This template is the first one stone 6th row template for which a proof has been handwritten.

Elimination of irrelevant Blue moves

Red has a couple 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 the parallel ladder trick

6 moves can furthermore be discarded thanks to the Parallel ladder trick. Of course, symmetry will cut our work in half!

We can dispose of 3 moves on the left (and, using mirror symmetry, the corresponding 3 moves on the right), as follows:

At this point, we can use the Parallel ladder trick as follows:

Remaining possibilities for Blue

Blue's first move must be one of the following:

Specific defense

For the moves that intersect all the carriers, Red has to find specific answers. Let's deal with the remaining intrusions!

One remaining intrusion on the first row (stub)

Details to follow

The other remaining intrusion on the first row (stub)

Details to follow

The remaining intrusion on the second row (stub)

The remaining intrusion on the third row (stub)

Red should go here:

The Red 1 hex is connected to the bottom, and threatens to connect to the top through either one of the "+" hexes. Thus these are the only important incursions. An incursion to the right of the number 1 hex is important only in connection with the two indicated here, and will be seen in the treatement below transposed into the sequel.

Third-row followup: i4

Red threatens to play at "+" points above, with these two templates:

Edge template IV1a

We need only consider the intersection of these two templates

Third-row followup i4 and incursion at k4

Third-row followup i4 and incursion at j5

Third-row followup i4 and incursion at i6

Third-row followup i4 and incursion at j6

Third-row followup i4 and incursion at h7

Third-row followup i4 and incursion at i7

Third-row followup: j3 (stub)

The remaining intrusion on the fourth row

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

Elimination of irrelevant Blue moves

This gives Red several immediate threats: From III1a:

From III1a again:

From III1b :

From IV1a:

From IV1b:

The intersection of all of these leaves:

Specific defense

So we must deal with each of these responses. (Which will not be too hard!)

Bg4

And now either

or

Bg5

Threatening:

So the only hope for Blue lies in the intersection of the threats, Be5, but it is unsufficient:

Bg6

3 could be played at + with the same effect; in any case now either

or

Be7

Either this

or a minor variation

Bg7

The remaining intrusion on the fifth row

First establish a double ladder on the right.

Then use Tom's move: