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TOT 149 1987 Spring Main S6 game with 1 knight on an 8x8 chessboard

Source:

April 17, 2020
Chessboardcombinatorics

Problem Statement

Two players play a game on an 88 by 88 chessboard according to the following rules. The first player places a knight on the board. Then each player in turn moves the knight , but cannot place it on a square where it has been before. The player who has no move loses. Who wins in an errorless game , the first player or the second one? (The knight moves are the normal ones. )
(V . Zudilin , year 12 student , Beltsy (Moldova))