Problem of the Week

This problem was suggested by Dr. Michael Lang of Bradley University's Department of Mathematics.

Each square on a 9 × 9 checkerboard contains a jumping beetle.  At an agreed upon moment, they all jump from the square they are on to a diagonally adjacent square, that is, to a square which shares a single vertex with the square.  After they jump, what is the fewest number of checkerboard squares that must contain at least two jumping beetles?

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ã2003 Alberto L. Delgado