Difference between revisions of "Edge template VI2a"
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<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex> | <hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5</hex> | ||
| − | And Red cannot be stopped. Note that this method does not require the three right-most | + | And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6. |
=== Block at G2 === | === Block at G2 === | ||
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<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex> | <hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex> | ||
| − | Note that Red's F3 piece is connected via the two marked | + | Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three: |
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex> | <hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex> | ||
| − | And Red connects. | + | And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]]. |
| − | === Block at H2 === | + | === Block at H2, G3, or G4 === |
| + | |||
| + | Red's responses are similar in all three cases: | ||
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex> | <hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex> | ||
| − | |||
| − | |||
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex> | <hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex> | ||
| − | |||
| − | |||
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex> | <hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex> | ||
Revision as of 17:14, 12 June 2009
Contents
The edge template template VI2
Let us first see what possibilities Red has if he moves first.
There are two obvious options:
In both diagrams the possible intrusion points are marked by (+). So we only have to consider the intersection of the intrusion points. They are:
Intrusion at E5 and F5
If Blue blocks at E5 then Red plays F3, reducing to Template IVb
Likewise if blue blocks at F5:
Intrusion at E6
Red threatens to connect via D4. Blue must respond in one of the marked hexs.
The H4 piece is connected to the bottom with template III-1-a, and is connected to the top in two non-overlapping ways:
and
Intrusion at F4
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:
Block at F2
Red is now connected to the bottom via template III-1-a. Note that neither of Red's threats overlapped.
Block at E3
The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:
And now Red can connect via B5. Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work.
Intrusion at G2
Blue has four options that don't immediately reduce to another edge template:
Block at E4
Red's G3 piece is connected to the top via F3 or H2.
Here Red has created a Ladder escape fork. If blue blocks the ladder Red plays at D3.
Block at D5
And Red has connected. If blue choose to play at E6 instead of E5:
Block at C6
Block at E6
Play continues...
Intrusion at D6 or F6
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.
Block at F4
Or, if for move three Blue played G3:
And Red cannot be stopped. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.
Block at G2
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:
And Red connects via template III-1-a.
Block at H2, G3, or G4
Red's responses are similar in all three cases:
