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 Boosted board (Posted on 2012-02-07)
Consider an infinite chessboard. Each square contains either a 1 or an X in some pattern. (X can be any real number but for a given board, all the X's are the same.)

Each square with an X on it has weight equal to zero.
Each square with a 1 on it has a weight of 1 + N*X where N is the total number of X's on the 8 surrounding squares.

For a given value of X, find a way of tiling the board with the highest average weight per square.

Inspired by various Tower Defense games.

 See The Solution Submitted by Jer Rating: 4.0000 (1 votes)

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 re(2): Final Answer ?? (spoiler) | Comment 10 of 11 |

Thanks, Jer.  Fun problem.

I agree that I had a math error, and that the range for the middle solution is X in (1/8, 1/4).

By the way, how does this related to Tower defenses?  I am not familiar ...

 Posted by Steve Herman on 2012-02-09 22:31:31

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