MathDB

Dirock has a very neat rectangular backyard that can be represented as a

32\times 32

grid of unit squares. The rows and columns are each numbered

1,2,\ldots, 32

. Dirock is very fond of rocks, and places a rock in every grid square whose row and column number are both divisible by

3

. Dirock would like to build a rectangular fence with vertices at the centers of grid squares and sides parallel to the sides of the yard such that [*] The fence does not pass through any grid squares containing rocks; [*] The interior of the fence contains exactly 5 rocks. In how many ways can this be done?
Ray Li

Problem Statement