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 Final Answer? (spoiler) by Steve Herman)

There is another pattern that is sometimes better than either of these.
There is yet another pattern that, in one case is tied for the best.  It is never the sole best pattern.

Posted by Jer on 2012-02-09 10:47:34