32 black pawns and 32 white pawns on the chessboard
Source: Russian 2007
September 4, 2007
inequalitiescombinatorics proposedcombinatorics
Problem Statement
On the chessboard, black pawns and white pawns are arranged. In every move, a pawn can capture another pawn of the opposite color, moving diagonally to an adjacent square where the captured one stands. White pawns move only in upper-left or upper-right directions, while black ones can move in down-left or in down-right directions only; the captured pawn is removed from the board. A pawn cannot move without capturing an opposite pawn. Find the least possible number of pawns which can stay on the chessboard.