Difference between revisions of "Edge template VI2a"

From HexWiki
Jump to: navigation, search
(Converted to new hexboard diagrams)
m (Updated some links.)
Line 73: Line 73:
 
/>
 
/>
  
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:
+
The H4 piece is connected to the bottom with [[ziggurat|template III-1a]], and is connected to the top in two non-overlapping ways:
  
 
<hexboard size="6x9"
 
<hexboard size="6x9"
Line 111: Line 111:
 
/>
 
/>
  
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.
+
Red is now connected to the bottom via [[ziggurat|template III-1a]]. Note that neither of Red's threats overlapped.
  
 
=== Block at E3 ===
 
=== Block at E3 ===
Line 260: Line 260:
 
/>
 
/>
  
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].
+
And Red connects via [[ziggurat|template III-1a]].
  
 
=== Block at H2, G3, or G4 ===
 
=== Block at H2, G3, or G4 ===
Line 298: Line 298:
 
/>
 
/>
  
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom.  
+
Red's F4 piece is connected to the bottom via [[ziggurat|template III-1a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom.  
  
 
=== Block at G2 ===
 
=== Block at G2 ===
Line 327: Line 327:
 
/>
 
/>
  
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].
+
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[ziggurat|template III-1a]].
  
 
[[Category:Edge templates]]
 
[[Category:Edge templates]]
 
{{stub}}
 
{{stub}}

Revision as of 21:42, 20 June 2021

The edge template template VI2

abcdefghi123456

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

abcdefghi12345621

Likewise if blue blocks at F5:

abcdefghi12345621

Intrusion at E6

abcdefghi12345621

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

abcdefghi1234562341

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

abcdefghi1234562341

and

abcdefghi1234562341

Intrusion at F4

abcdefghi12345621

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

Block at F2

abcdefghi1234561324

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

Block at E3

abcdefghi12345661257834109

And now Red can escape the ladder:

abcdefghi123456642531

And now Red has connected. Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.

Intrusion at G2

abcdefghi12345621

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

Block at E4

abcdefghi12345621

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

abcdefghi1234562143

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

Block at D5

abcdefghi123456625413

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

abcdefghi12345687625431

Block at C6

abcdefghi123456625431

Block at E6

abcdefghi123456234651

Play continues...

abcdefghi1234564321

Intrusion at D6 or F6

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

abcdefghi12345621

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

abcdefghi12345634561287

Or, if for move three Blue played G3:

abcdefghi12345621345610897

And Red is connected. This method can be used by Red in the symmetrical case of Blue intruding at F6.

Block at G2

abcdefghi12345612465387

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

abcdefghi123456123456

And Red connects via template III-1a.

Block at H2, G3, or G4

Red's responses are similar in all three cases:

abcdefghi123456124365
abcdefghi123456214365
abcdefghi123456243165

Intrusion at C6 or G6

The G6 case is shown here, but Red's responses work symmetrically for the C6 case.

abcdefghi12345621

Red's F4 piece is connected to the bottom via template III-1a. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom.

Block at G2

abcdefghi123456123456

And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:

abcdefghi12345612346857

And if Blue had played F5 for move five:

abcdefghi123456123465

Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with template III-1a.