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Part of 2016 Federal Competition For Advanced Students, P2

Problems(1)

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

5/25/2019
Consider arrangements of the numbers 11 through 6464 on the squares of an 8×88\times 8 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
combinatoricsChessboard