Rook moves on 10x10 board
Source: 43rd International Tournament of Towns, Senior A-Level P2, Fall 2021 & Kvant Magazine No. 11-12 2021 M2675
February 18, 2023
boardChess rookTournament of TownscombinatoricsKvant
Problem Statement
There was a rook at some square of a chessboard. At each turn it moved to a square adjacent by side. It visited each square exactly once. Prove that for each main diagonal (the diagonal between the corners of the board) the following statement is true: in the rook’s path there were two consecutive steps at which the rook first stepped away from the diagonal and then returned back to the diagonal.Alexandr Gribalko