Difference between revisions of "Edge template VI1a"

Revision as of 04:39, 15 February 2009 (view source) Kogorman (Talk | contribs) (→‎Bg6: Filled in the details.) ← Older edit		Revision as of 04:48, 15 February 2009 (view source) Kogorman (Talk | contribs) (→‎Bg7: filled in the details) Newer edit →
Line 498:		Line 498:
	===== Be7 =====		===== Be7 =====
	===== Bg7 =====		===== Bg7 =====
−	'''To be continued...'''	+
		+	<hex>
		+	R7 C14 Q0
		+	1:BBBBBBBBBRBBBBB
		+	Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
		+	Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
		+	Sa4 Sb4 Sc4 Sd4 Sn4
		+	Sa5 Sb5
		+	Sa6
		+
		+	Bi4 Rh3
		+
		+	N:on Bg7 Rg5 Bf6 Rh6 Bh7 Rj6 Bi6 Rj5
		+	Pi5 Pk3
		+
		+	</hex>
	===The remaining intrusion on the fifth row===		===The remaining intrusion on the fifth row===

---

Revision as of 04:48, 15 February 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 defence

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

The other remaining intrusion on the first row

The remaining intrusion on the second row

The remaining intrusion on the third row

The remaining intrusion on the fourth row

Red should move here:

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 defence

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

Bg7

The remaining intrusion on the fifth row

First establish a double ladder on the right.

Then use Tom's move: