Finding maximum number of fleas on a 10x10 chessboard.
Source:
February 8, 2011
geometrygeometric transformationreflectioncombinatorics unsolvedcombinatorics
Problem Statement
Several fleas sit on the squares of a chessboard (at most one fea per square). Every minute, all fleas simultaneously jump to adjacent squares. Each fea begins jumping in one of four directions (up, down, left, right), and keeps jumping in this direction while it is possible; otherwise, it reverses direction on the opposite. It happened that during one hour, no two fleas ever occupied the same square. Find the maximal possible number of fleas on the board.