Problem #PRU-103780

Problems Methods Algebraic methods Partitions into pairs and groups; bijections Pigeonhole principle Pigeonhole principle (other) Proof by exhaustion
 11–13  3.0

Problem

In any group of 10 children, out of a total of 60 pupils, there will be three who are in the same class. Will it always be the case that amongst the 60 pupils there will be: 1) 15 classmates? 2) 16 classmates?