Difference between revisions of "Edge template VI1a"

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(The remaining intrusion on the fourth row: -- starting the solution)
(The remaining intrusion on the fourth row: eliminated two blue answers (one explicitly, the other with template III1b))
Line 205: Line 205:
 
</hex>
 
</hex>
  
 +
==== Elimination of irrelevant Blue moves ====
 
This gives Red several immediate threats:
 
This gives Red several immediate threats:
 
From III1a:
 
From III1a:
Line 240: Line 241:
 
Pe6 Pf6 Pg6
 
Pe6 Pf6 Pg6
 
Pd7 Pe7 Pf7 Pg7  
 
Pd7 Pe7 Pf7 Pg7  
 +
</hex>
 +
 +
From III1b :
 +
<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
 +
Rg5
 +
Pg4 Ph4
 +
Pf5 Ph5
 +
Pe6 Pf6 Pg6 Ph6
 +
Pd7 Pe7 Pg7 Ph7
 
</hex>
 
</hex>
  
Line 280: Line 299:
 
The intersection of all of these leaves:  
 
The intersection of all of these leaves:  
 
<hex>
 
<hex>
R7 C14 Q0
+
R7 C14 Q1
 
1:BBBBBBBBBRBBBBB
 
1:BBBBBBBBBRBBBBB
 
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2  
 
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2  
Line 289: Line 308:
  
 
Bi4 Rh3
 
Bi4 Rh3
Pg4
+
Pg4
Pg5
+
  Pg5
Pg6  
+
  Pg6  
Pe7 Pf7 Pg7  
+
Pe7 Pg7  
 
</hex>
 
</hex>
+
 
 +
==== Specific defense ====
 
So we must deal with each of these responses.  (Which will not be too hard!)
 
So we must deal with each of these responses.  (Which will not be too hard!)
  
To be continued....
+
===== Bg4 =====
 +
<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 Bg4 Rh4 Bg6 Rh5
 +
</hex>
 +
And now either
 +
<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
 +
 
 +
Bg4 Rh4 Bg6 Rh5
 +
N:on Bh6 Rj5
 +
Pk3 Pi5
 +
</hex>
 +
 
 +
or
 +
 
 +
<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
 +
 
 +
Bg4 Rh4 Bg6 Rh5
 +
N:on Bh7 Rh6 Bg7 Rj6 Bi6 Rj5
 +
Pk3 Pi5
 +
</hex>
 +
===== Bg5 =====
 +
===== Bg6 =====
 +
===== Be7 =====
 +
===== Bg7 =====
 +
'''To be continued...'''
  
 
===The remaining intrusion on the fifth row===
 
===The remaining intrusion on the fifth row===

Revision as of 13:09, 14 January 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 discared 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 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:

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
Bg6
Be7
Bg7

To be continued...

The remaining intrusion on the fifth row