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.
(In reply to re: Final Answer ?? (spoiler)
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 ...