Zhang Qiujian: 2 puzzles worth knowing

2 puzzles from Zhang Qiujian, each explained in a minute and credited to the original work. Free on Savvy.

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…
— Zhang Qiujian, Zhang Qiujian Suanjing (Zhang Qiujian's Mathematical Manual)
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 to…
— Zhang Qiujian, Zhang Qiujian Suanjing (The Mathematical Classic of Zhang Qiujian)

Five ideas worth knowing, every week