Puzzles
100 birds for 100 coins: mix roosters, hens and chicks at three very different prices
A rooster costs 5 coins, a hen costs 3 coins, and 3 chicks together cost 1 coin. You must buy exactly 100 birds for exactly 100 coins, buying at least one rooster, one hen, and one chick. How many of each do you buy?
Reveal the answer
There are three valid answers: 4 roosters, 18 hens, 78 chicks; or 8 roosters, 11 hens, 81 chicks; or 12 roosters, 4 hens, 84 chicks. Each satisfies roosters+hens+chicks=100 and 5×roosters + 3×hens + (chicks/3) = 100. This is the 'Hundred Fowls Problem,' the final and most famous problem in the 5th-century Chinese text Zhang Qiujian Suanjing — one of history's earliest known problems shown to have multiple valid integer solutions.