All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
On a Grid (Posted on 2007-08-08) Difficulty: 3 of 5
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: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: On a 12 x 12 | Comment 4 of 6 |
(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
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information