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 Shaky ground? by brianjn)

X is not necessarily an integer.  What you seem to be stating in each of your grids is the value of N -- the number of X's surrounding each 1.

Then your Grid Wt becomes a function of X.

Different configurations will be better for different values of X.

Posted by Jer on 2012-02-08 09:02:35