arrangements no 1 to 64 on the squares of an 8x8 chessboard
Source: 47th Austrian Mathematical Olympiad National Competition (Final Round, part 2 ) May 25, 2016 p3
May 25, 2019
combinatoricsChessboard
Problem Statement
Consider arrangements of the numbers through on the squares of an chess board, where each square contains exactly one number and each number appears exactly once.
A number in such an arrangement is called super-plus-good, if it is the largest number in its row and at the same time the smallest number in its column. Prove or disprove each of the following statements:
(a) Each such arrangement contains at least one super-plus-good number.
(b) Each such arrangement contains at most one super-plus-good number.Proposed by Gerhard J. Woeginger