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)

You found all that I have except for the one case that doesn't really matter (it is tied for the best tiling at only 1 point).  As you point out, we may have missed one, but I don't know how to exhaustively try every possibility.

You do have an algebra error:
(8x+3)/4 > (6x+1)/2
x < 1/4 (you have 1/2)

Posted by Jer on 2012-02-09 21:27:41