There is a frog jumping on a 2k×2k chessboard, composed of unit squares. The frog's jumps are \sqrt{1 \plus{} k^2} long and they carry the frog from the center of a square to the center of another square. Some m squares of the board are marked with an ×, and all the squares into which the frog can jump from an ×'d square (whether they carry an × or not) are marked with an ∘. There are n ∘'d squares. Prove that n≥m. combinatorics unsolvedcombinatorics