Problem #PRU-64618

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Methods Pigeonhole principle Pigeonhole principle (other) Proof by contradiction
 13–15  3.0

Problem

We are given 111 different natural numbers that do not exceed 500. Could it be that for each of these numbers, its last digit coincides with the last digit of the sum of all of the remaining numbers?