MathDB

184

Part of 1973 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 184 All Soviet Union MO 1973 king moves in a 8x8 chessboard

Source:

7/4/2019
The king have revised the chess-board 8×88\times 8 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 2828 steps parallel the sides of the board only.
b) Prove that he could not make less than 2828 such a steps.
c) What is the maximal and minimal length of the broken line if the side of a field is 11?
combinatoricsChessboard