Difference between revisions of "Edge template VI1a"

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(Some copy-editing.)
(Converted to new hexboard diagrams)
Line 10: Line 10:
 
Sa6
 
Sa6
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2"
 +
/>
  
 
This template is the first one stone 6th row [[edge template|template]] for which a proof of validity has been written out. The template has been verified by computer, and also verified to be minimal.
 
This template is the first one stone 6th row [[edge template|template]] for which a proof of validity has been written out. The template has been verified by computer, and also verified to be minimal.
Line 34: Line 40:
 
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7
 
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R i4 j2 E +:d7 +:e6 +:e7 +:f5 +:f6 +:f7 +:g5 +:g6 +:g7 +:h4 +:h5 +:h6 +:h7 +:i3 +:i5 +:i6 +:i7 +:j3 +:j5 +:j6 +:j7"
 +
/>
  
 
<hex>
 
<hex>
Line 50: Line 62:
 
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7
 
Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R i4 j2 E +:e7 +:f6 +:f7 +:g5 +:g6 +:g7 +:h5 +:h6 +:h7 +:i3 +:i5 +:i6 +:i7 +:j3 +:j4 +:j5 +:j6 +:j7 +:k5 +:k6 +:k7"
 +
/>
  
 
=== [[edge template IV1b]] ===
 
=== [[edge template IV1b]] ===
Line 68: Line 86:
 
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7
 
Pd7 Pe7 Pf7 Pg7 Ph7 Pi7 Pj7 Pk7
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R i4 j2 E +:d7 +:e6 +:e7 +:f5 +:f6 +:f7 +:g5 +:g6 +:g7 +:h4 +:h5 +:h7 +:i3 +:i5 +:i6 +:i7 +:j3 +:j4 +:j5 +:j6 +:j7 +:k5 +:k6 +:k7"
 +
/>
 +
 +
 
=== Using the [[parallel ladder]] trick ===
 
=== Using the [[parallel ladder]] trick ===
  
Line 88: Line 114:
 
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7
 
N:on Ri4 Bi5 Rh5 Bg7 Rh6 Bh7
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R 3:h5 5:h6 1:i4 j2 B 4:g7 6:h7 2:i5 E +:e7 +:f6 +:g5"
 +
/>
  
 
At this point, we can use [[Tom's move]] as follows:
 
At this point, we can use [[Tom's move]] as follows:
Line 106: Line 138:
 
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3
 
N:on Rk5 Bj6 Ri6 Bi7 Rl4 Bj5 Rk3
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R h5 h6 i4 3:i6 j2 7:k3 1:k5 5:l4 B g7 h7 i5 4:i7 6:j5 2:j6 E +:e7 +:f6 +:g5"
 +
/>
  
 
=== [[Overlapping connections|Remaining possibilities]] for Blue ===
 
=== [[Overlapping connections|Remaining possibilities]] for Blue ===
Line 130: Line 168:
 
Pi7
 
Pi7
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 E +:f7 +:g6 +:g7 +:h5 +:h7 +:i3 +:i4 +:i5 +:i6 +:i7 +:j3"
 +
/>
  
 
See
 
See
Line 151: Line 195:
 
Bf7  
 
Bf7  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 B f7"
 +
/>
  
 
Details to follow
 
Details to follow
Line 166: Line 216:
 
Bg7  
 
Bg7  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 B g7"
 +
/>
  
 
Red should go here:
 
Red should go here:
Line 180: Line 236:
 
Bg7  red M1h5
 
Bg7  red M1h5
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R 1:h5 j2 B g7"
 +
/>
  
 
See more details [[Template VI1/Other Intrusion on the 1st row| here]].
 
See more details [[Template VI1/Other Intrusion on the 1st row| here]].
Line 195: Line 257:
 
Bg6  
 
Bg6  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 B g6"
 +
/>
  
 
===The remaining intrusion on the third row (stub)===
 
===The remaining intrusion on the third row (stub)===
Line 208: Line 276:
 
Bh5  
 
Bh5  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 B h5"
 +
/>
  
 
Red should go here:
 
Red should go here:
Line 222: Line 296:
 
Bh5  red M1k3
 
Bh5  red M1k3
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 1:k3 B h5"
 +
/>
  
 
Details to follow.
 
Details to follow.
Line 237: Line 317:
 
Bi4  
 
Bi4  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 B i4"
 +
/>
  
 
Red should move here (or the equivalent mirror-image move at "+"):
 
Red should move here (or the equivalent mirror-image move at "+"):
Line 251: Line 337:
 
Bi4 Rh3 Pk3
 
Bi4 Rh3 Pk3
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R h3 j2 B i4 E +:k3"
 +
/>
  
 
For more details, see [[Template VI1/Intrusion on the 4th row|this page]].
 
For more details, see [[Template VI1/Intrusion on the 4th row|this page]].
Line 265: Line 357:
 
Bi3  
 
Bi3  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R j2 B i3"
 +
/>
  
 
First establish a [[double ladder]] on the right.
 
First establish a [[double ladder]] on the right.
Line 280: Line 378:
 
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5  
 
N:on Rj3 Bi5 Rk4 Bk5 Rj5 Bi7 Ri4 Bh5  
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R 7:i4 j2 1:j3 5:j5 3:k4 B 8:h5 i3 2:i5 6:i7 4:k5"
 +
/>
  
 
Then use [[Tom's move]]:
 
Then use [[Tom's move]]:
Line 296: Line 400:
 
N:on Rf5 Bf6 Rf4 Bg5 Rh3
 
N:on Rf5 Bf6 Rf4 Bg5 Rh3
 
</hex>
 
</hex>
 +
<hexboard size="7x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a7,n7,n5,k2,i2,c5)"
 +
  contents="R 3:f4 1:f5 5:h3 i4 j2 j3 j5 k4 B 2:f6 4:g5 h5 i3 i5 i7 k5"
 +
/>
  
  
 
[[category:edge templates]]
 
[[category:edge templates]]
 
[[category:theory]]
 
[[category:theory]]

Revision as of 02:12, 9 March 2021

Template VI1-a is a 6th row edge template with one stone.

This template is the first one stone 6th row template for which a proof of validity has been written out. The template has been verified by computer, and also verified to be minimal.

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
132546

At this point, we can use Tom's move as follows:

7561324
7561324

Remaining possibilities for Blue

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

See Template_VI1/Intrusion_on_the_3rd_row, Template_VI1/Intrusion_on_the_4th_row, Template_VI1/The_remaining_intrusion_on_the_fifth_row.

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

Red should go here:

1
1

See more details here.

The remaining intrusion on the second row (stub)

The remaining intrusion on the third row (stub)

Red should go here:

1
1

Details to follow.

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.

17382546
17382546

Then use Tom's move:

53142
53142
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