Difference between revisions of "Edge template VI1a"
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===The remaining intrusion on the fifth row=== | ===The remaining intrusion on the fifth row=== | ||
<hex> | <hex> | ||
Revision as of 21:51, 1 March 2009
This template is the first one stone 6th row template for which a proof has been handwritten.
Contents
- 1 Elimination of irrelevant Blue moves
- 2 Specific defense
- 2.1 One remaining intrusion on the first row (stub)
- 2.2 The other remaining intrusion on the first row (stub)
- 2.3 The remaining intrusion on the second row (stub)
- 2.4 The remaining intrusion on the third row (stub)
- 2.5 The remaining intrusion on the fourth row
- 2.6 The remaining intrusion on the fifth row
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 "+"):
For more details, see this page.
The remaining intrusion on the fifth row
First establish a double ladder on the right.
Then use Tom's move:
