100 monkeys have together 1600 bananas. Show that at least four monkeys have the same number of bananas.
Since the average number of bananas is 16 each monkey, the widest range for not having 2 monkeys with the same number of bananas varies from 1 to 32. Three times 33 equals 99, so there are 33 groups of three monkeys with the same number of bananas varying from 1 to 33. The 100th monkey has 16 bananas and so thera re at least four monkeys with 16 bananas.