Pawns on a chessboard
Source: Indonesia Mathematics Olympiad 2006 Day 1 Problem 4
June 2, 2008
inductioncombinatorics proposedcombinatorics
Problem Statement
A black pawn and a white pawn are placed on the first square and the last square of a chessboard, respectively. Wiwit and Siti move alternatingly. Wiwit has the white pawn, and Siti has the black pawn. The white pawn moves first. In every move, the player moves her pawn one or two squares to the right or to the left, without passing the opponent's pawn. The player who cannot move anymore loses the game. Which player has the winning strategy? Explain the strategy.