Question 34
Consider arrangements of the numbers $1$ through $64$ on the squares of an $8 \times 8$ 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.
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.