A game on a 100x100 chessboard
Source: German Mathematical Competition BWM 2005, 2nd round, problem 1
September 1, 2005
floor functioncombinatorics proposedcombinatorics
Problem Statement
Two players and have one stone each on a chessboard. They move their stones one after the other, and a move means moving one's stone to a neighbouring field (horizontally or vertically, not diagonally). At the beginning of the game, the stone of lies in the lower left corner, and the one of in the lower right corner. Player starts.
Prove: Player is, independently from that what does, able to reach, after finitely many steps, the field 's stone is lying on at that moment.