MathDB
TOT 1999 Spring AJ6 64 moves of a rook in a 8x8 chessboard

Source:

May 11, 2020
combinatoricsChessboardRook

Problem Statement

A rook is allowed to move one cell either horizontally or vertically. After 6464 moves the rook visited all cells of the 8×88 \times 8 chessboard and returned back to the initial cell. Prove that the number of moves in the vertical direction and the number of moves in the horizontal direction cannot be equal.
(A Shapovalov, R Sadykov)