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A Black and White Issue (Posted on 2013-06-18) Difficulty: 3 of 5
In a 984 x 984 square grid, each square is colored either white or black. Each black square not on the border has exactly five white squares among its eight neighbors. Each white square not on the border has exactly four black squares among its eight neighbors. How many black squares are there?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 1.0000 (2 votes)

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Some Thoughts And more solutions ? Comment 3 of 3 |
Here's a 3X6 that I think does the trick.

B B -
-  - B
-  B -
B - B
-  B -
B - -

I am starting to think that any tiling works, as long as the tiles are not rotated and the sides are a multiple of 3 and every 3x3 section of every tile has 4 black squares in it.

Edited on June 18, 2013, 8:08 pm
  Posted by Steve Herman on 2013-06-18 16:53:32

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