3

Part of 2001 Singapore Senior Math Olympiad

Problems(1)

1 to 50 insides a 50x50 square

Source: Singapore Senior Math Olympiad 2001 2nd Round p3 SMO

Each of the squares in a

50 \times 50

square board is filled with a number from

1

50

so that each of the numbers

1,2, ..., 50

appears exactly

50

times. Prove that there is a row or a column containing at least

8

distinct numbers.