Difference between revisions of "Edge template VI1a"

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m (→‎The remaining intrusion on the third row (stub))
(→‎Third-row followup: i4: Filling in some details.)
Line 212: Line 212:
  
 
Bh5  MR Mi5 Mi4 Mk3  
 
Bh5  MR Mi5 Mi4 Mk3  
−
  Pj5 Pl4
+
  Pj5 Pk4 Pl4
 +
</hex>
 +
 
 +
Red threatens to play at "+" points above, with these two templates:
 +
 
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
Rj5
 +
Pk4 Pj4
 +
Ph6 Pi6 Pj6 Pg7 Ph7 Pi7
 +
</hex>
 +
 
 +
 
 +
 
 +
Edge template IV1a
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
Rl4
 +
                         
 +
                  Pl3
 +
              Pk4            Pm4
 +
          Pj5    Pk5    Pl5    Pm5    Pn5
 +
      Pi6    Pj6    Pk6    Pl6    Pm6    Pn6
 +
  Ph7    Pi7    Pj7    Pk7      Pl7    Pm7    Pn7
 +
</hex>
 +
 
 +
We need only consider the intersection of these two templates
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
Pj5
 +
Pk4
 +
Pi6 Pj6
 +
Ph7 Pi7
 +
</hex>
 +
 
 +
===== Third-row followup i4 and incursion at k4 =====
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
MB Mk4 Mj4
 +
Pj5 Ph6 Pi6 Pj6
 +
Pg7 Ph7 Pi7 Pj7
 +
</hex>
 +
 
 +
===== Third-row followup i4 and incursion at j5 =====
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
MB Mj5 Mj4 Mh7 Mi6 Mi7 Mk6
 +
Pj6 Pl4
 +
</hex>
 +
 
 +
===== Third-row followup i4 and incursion at i6 =====
 +
This the hardest of the variations; the others should be obvious.
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
MB Mi6 Mj5
 +
Ph6 Pj6
 +
</hex>
 +
 
 +
===== Third-row followup i4 and incursion at j6 =====
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
MB Mj6 Mk4
 +
Ph7 Pl5
 +
</hex>
 +
 
 +
===== Third-row followup i4 and incursion at h7 =====
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
MB Mh7 Mj6 Mj5 Ml4 Mk5 Ml5
 +
Pm5
 +
Pk6 Pl6 Pm6
 +
Pj7 Pk7 Pl7 Pm7
 +
</hex>
 +
 
 +
===== Third-row followup i4 and incursion at i7 =====
 +
<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
 +
 
 +
Bh5  Ri5 Bi4 Rk3
 +
MB Mi7 Mj5
 +
Ph6 Pk6
 
</hex>
 
</hex>
  
−
Red threatens to play at "+" points
 
−
Details to follow.
 
 
==== Third-row followup: j3 (stub) ====
 
==== Third-row followup: j3 (stub) ====
 
<hex>
 
<hex>

Revision as of 21:35, 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:

132546

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

7561324

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:

1

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

321

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
21
Third-row followup i4 and incursion at j5
214635
Third-row followup i4 and incursion at i6

This the hardest of the variations; the others should be obvious.

21
Third-row followup i4 and incursion at j6
21
Third-row followup i4 and incursion at h7
435621
Third-row followup i4 and incursion at i7
21

Third-row followup: j3 (stub)

21

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:

abcdefghijklmn1234567

Specific defense

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

Bg4
1243

And now either

21

or

625431
Bg5
abcdefghijklmn123456721

Threatening:

abcdefghijklmn12345674
abcdefghijklmn12345674
abcdefghijklmn12345674

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

abcdefghijklmn123456712846357
Bg6
2431

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

21

or

625431
Be7

Either this

246351

or a minor variation

24103698175
Bg7
28347615

The remaining intrusion on the fifth row

First establish a double ladder on the right.

17382546

Then use Tom's move:

53142
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