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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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Solution Other solutions (spoiler) | Comment 2 of 3 |
There are other 3 X 3 grids which can be used as the basis for a solution.

For instance:
WBB       or  BWW  or BBB     
WBB            WBB       BWW
WWW           WBW     WWW

lead to different arrangements.  Probably any 3x3 with 4 black squares will do.

But I agree that 4/9 of all of the squares are black.

  Posted by Steve Herman on 2013-06-18 16:46:33
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