Difference between revisions of "Edge template VI2a"

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(The edge template template VI2)
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== The edge template template VI2 ==
 
== The edge template template VI2 ==
  
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex>
+
<hex>R6 C10 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex>
  
 
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.
 
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.

Revision as of 17:43, 12 June 2009

The edge template template VI2

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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

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Likewise if blue blocks at F5:

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Intrusion at E6

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Red threatens to connect via D4. Blue must respond in one of the marked hexs.

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The H4 piece is connected to the bottom with template III-1-a, and is connected to the top in two non-overlapping ways:

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and

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Intrusion at F4

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The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:

Block at F2

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Red is now connected to the bottom via template III-1-a. Note that neither of Red's threats overlapped.

Block at E3

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The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:

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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

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Blue has four options that don't immediately reduce to another edge template:

Block at E4

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Red's G3 piece is connected to the top via F3 or H2.

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Here Red has created a Ladder escape fork. If blue blocks the ladder Red plays at D3.

Block at D5

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And Red has connected. If blue choose to play at E6 instead of E5:

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Block at C6

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Block at E6

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Play continues...

4321

Intrusion at D6 or F6

The D6 case is shown here, but Red's responses work symmetrically for the F6 case.

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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

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Or, if for move three Blue played G3:

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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

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Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:

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And Red connects via template III-1-a.

Block at H2, G3, or G4

Red's responses are similar in all three cases:

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