100 monkeys have together 1600 bananas. Show that at least four monkeys have the same number of bananas.
(In reply to Answer
by Giorgio Rivieccio)
Though I'd agree with the general logic, there are some gaps, since it concludes "there are at least four monkeys with 16 bananas", while I can think of many arrangements WITHOUT any monkey having 16 bananas.
Granted, in those arrangements there would be at least 4 monkeys with the same number of bananas, but NOT 16, and that's what this reasoning says they should have.