ASU 184 All Soviet Union MO 1973 king moves in a 8x8 chessboard
Source:
July 4, 2019
combinatoricsChessboard
Problem Statement
The king have revised the chess-board having visited all the fields once only and returned to the starting point. When his trajectory was drawn (the centres of the squares were connected with the straight lines), a closed broken line without self-intersections appeared. a) Give an example that the king could make steps parallel the sides of the board only. b) Prove that he could not make less than such a steps. c) What is the maximal and minimal length of the broken line if the side of a field is ?