perplexus.info :: Logic : On a Grid

On a Grid (Posted on 2007-08-08)

Place eight 'A's and eight 'B's in a 4x4 grid such that each 'A' is orthogonally bordered by 1 or 3 'A's and each 'B' is orthogonally bordered by 0, 2, or 4 'B's.

Can a 6x6 grid be filled with 18 'A's and 18 'B's in this manner?

Note: 'orthogonally' means horizontally or vertically

No Solution Yet Submitted by Brian Smith

Rating: 4.2500 (4 votes)

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re: On a 12 x 12

| Comment 4 of 7 |

(In reply to On a 12 x 12 by Charlie)

The list got cut off based on the limitations of the size of a post. I've eliminated reflections and rotations so the non-trivial solutions for 12x12 are now down to 18. (Some are self-reflections or rotations, and so were not represented 8 times in the gross list.)

A A A A A A A A B A B B 
B A A A A A A B A A B B 
A A B B B B A A B A A A 
B A B A A B A B A A A B 
A B B B B B B A B B A A 
A B B A A B B A B B A B 
B A A B B A A B A A B A 
A B B B B B B A B B A A 
A B A B B A B A B B B A 
B B A A A A B B A B B B 
B A A A A A A B A A B B 
B B B B B B B B A B A A

A A A A A A A B A A B A 
B A A A A A B A B B A A 
A A B B B A A A B B B A 
B A B A B A A A A B B B 
A B B A B A B B B A B B 
A B A B B B B A B A A A 
B B A B B A A A B A A B 
B A B A A B A A B A A A 
B A A B B A A A B A B B 
B A B B B B B A B B B B 
B B B B B A B B A A B A 
A A B B A A A B B B B A

A A A A A A B A B B A B 
B A A A A B A A B B A A 
A A B B A A B A A A A B 
B A B B A B A A A A A A 
A B A A B A B B B B B B 
A A B B A A B A A A A B 
A B B B B A B B A A B B 
B B B B B B A B A A B A 
B B B B B B A B A A B A 
A B B B B A B B A A B B 
A A B B A A B A A A A B 
A B A A B A B B B B B B

A A A A A B A B A B A A 
B A A A B A A A A A B B 
A A B A A B B A B B B B 
B A A A B B B B B A B A 
A A A A B B B A A A B A 
B B B A A B A B A A B B 
B A B A B B A A A A A B 
B A B B B A A A B B B B 
B B A A A B B A B A A A 
A B B A B B B B B B A B 
A A B B B B B A B B B A 
A B A A B B A A A B B A

A A A A A B B A B A B B 
B A A A B B B A A A B B 
A A B A B B A A A A A A 
B A A B A A B B B B A B 
A A B A B B B A A B B A 
B A A A B A A B B A B A 
A A A A B B B B B A B B 
B B B A A A A B A B A B 
B A B A A A B B A A A B 
B A B A B A B A A A A B 
B B B B A B B B B B A B 
A A B B A B B A A B B B

A A A A A B B B A A B A 
B A A A B B A B B B A A 
A A B A B A A A A B B A 
B A A B B B B A B A B B 
A A B B B A B B A A A B 
B A B B A A A B B B B B 
A B A A B B B A A A A A 
A A B B B A B B A A A B 
A B B A A A A B A B A A 
B B A B A B B B B A A B 
B A A A B B A B B B A A 
B B B B B A A A B B A B

A A A A B B A B B B A B 
B A A B B B A B A B A A 
A A A B B A B B A B A B 
B B A A A A B A B B B A 
B B A A A A B A B B B A 
A A A B B A B B A B A B 
B A A B B B A B A B A A 
A A A A B B A B B B A B 
B B B B A A B A A A B A 
B A A B B B A B A B A A 
B B B A A B A A B A B A 
A A B B B B A B A A A B

A A A A B B B A A A B A 
B A A B B A B B A B A A 
A A A B A A A B B A B A 
B B A B B B B A B A A B 
B B B A A A B A B A B A 
A B B B A B B B B B A A 
A A B B B B B A B B B A 
A B A B A B A A A B B B 
B A A B A B B B B A B B 
A B A B B A A A B A A A 
A A B A B B A B B A A B 
A B A A A B B B A A A A

A A A B A A B B B B A A 
B A B A B B B A A B B B 
A B A A B A A B B A A B 
A A B A B B B B B B B B 
A B A B A A A B B A A A 
B A A A B A B A A B A B 
A B B B A B A B B A B A 
A B A B A A A B B A A A 
B B A B A A A A A A A A 
B A B B A B B A A B B A 
B A B A B B B A A B B B 
B B B A B B A A A A B B

A A A B B A B B A B A B 
B A B B B A B B A A A A 
A B B B A B A A A A B B 
A B B A A A B A B A B B 
B A A B B B A B A B A A 
A B B B A B A A A A B B 
A B A A A B A A B B B B 
B B B A A B A A B A B A 
B B B A A B A A B A B A 
A B A A A B A A B B B B 
A B B B A B A A A A B B 
B A A B B B A B A B A A

A A A B B B A A B B A A 
B A B B A B B B B B B B 
A B B A A A A A B B A B 
A B A B B A A B A A A B 
B B A B B A A A B A A B 
B A B A A A B B A A A B 
B A A B A A B B B B A B 
B A B A A A A B A B B B 
B B A B B B B B A A A A 
A B A B A A A A A A A B 
A B B B B A A A B B A A 
B A A B B A B A B B A B

A A B A A A A A B B B B 
B B A B A A A B B A A B 
B B A A A B A B A B B B 
A A A A A A B B A B A A 
B A B B B B B A B B B B 
A B B A A A A A B B A B 
A B A B A A A A A A A B 
B B A A A B B B A A A B 
B A A A A B A B A B A B 
B B B B A B A B B A B B 
A A A B B B B A B A B A 
B A B A A B B A B B B A

A A B A B A A A A B B A 
B B A A A B A A B B B A 
B B B B B A A A B B A B 
A B A A B B B A A A A A 
A B B B A A B A A A B B 
B A A B B B B A B A B B 
A B B A A A A B A B A A 
A B B B A A B A A A B B 
B A B B A A A B B B B B 
A A A A A B B B A A B A 
B B A A A B A A B B B A 
B B A B A B B B B A A B

A A B B A A B A A A A B 
B B B B B B A B A A B A 
B A B B A B A A A A A A 
B A A A A B A A B B A A 
B A A A A B A A B B A A 
B A B B A B A A A A A A 
B B B B B B A B A A B A 
A A B B A A B A A A A B 
B B A A B B A B B B B A 
B B B B B B A B A A B A 
A B A A B A B B B B B B 
A B B B B A B B A A B B

B A A A A A B B A B A B 
A B A A A B B B A A A A 
A A A B A B B A A A B B 
A A A A B A A B B A B B 
A B B B A B B B B B A A 
B B A B A B A B B B B B 
B A A B B B A A B B A B 
B B A A A A A B A A A B 
A B A A A A A A B A A B 
A B A B B B B B A A A B 
B B B B A A A B B B A B 
B B A A B A B A A B B B

B A A B B A A A B A B B 
A B B B B B A B A A B B 
A B A B B B B A B A A A 
B B A A B B B A A A A B 
B A A B A B A A A B A A 
B B A A A B B B A A A B 
A B A A A A A B A A A A 
A B A B B A B B A B B B 
B B B B B B B A B B A B 
B B A B B A A A B A A B 
A A A A A B A A B B A B 
B A B A B A A A A B B B

B A B A A B B B A B B B 
A A A B B B A B A B A B 
B B B B A A A B B B A B 
B A A A B A A A A A B B 
B B A B A A B A A B B A 
A B B A B A A A A B A A 
A A B A A A A B A B B A 
A B B A A B A A B A B B 
B B A A A A A B A A A B 
B A B B B A A A B B B B 
B A B A B A B B B A A A 
B B B A B B B A A B A B

B B A A A B A B A B B B 
B B B A B A A A A B A B 
A B B B A B B A A B A B 
A A B B A B B A A B B B 
A B A A B A A A A A A A 
B A B B A B A B B A A B 
A A B B A A B B B A A A 
B A A A A B B B A A B B 
A A A A A B B A B A B B 
B B B B A A A A A B A A 
B A A B A A A B B A B B 
B B B B A B A B B A B B

Posted by Charlie on 2007-08-08 15:34:59

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