Puzzles
Buy exactly 100 birds with exactly 100 coins: roosters cost 5, hens 3, chicks 3-for-1
A 5th-century Chinese puzzle: a rooster costs 5 coins, a hen costs 3 coins, and three baby chicks together cost 1 coin. You must spend exactly 100 coins to buy exactly 100 birds total, buying at least one of each kind. How many of each did you buy?
Reveal the answer
There are three valid whole-number solutions: 4 roosters, 18 hens, 78 chicks; 8 roosters, 11 hens, 81 chicks; or 12 roosters, 4 hens, 84 chicks. The puzzle appears in Zhang Qiujian's 5th-century 'Mathematical Classic' without a general method for finding all solutions, making it one of the earliest known problems in indeterminate (Diophantine) equations.