posted by James101 .
91 5-digit number are written on the board, how do u PROVE that there are 3 numbers on the board that the sum of the digits are equal?
The possible digit sums, for five-digit numbers, ranges from 1 (for 10000) to 45 (for 99999) That makes 45 possibilities. With 90 numbers selected, the least possible number of times any sum occurs is two, when each sum occurs twice. When you pick a 91st number, it has to be a third time for one of them.