Six sealed barrels, one holds beer — spot it without opening any
A merchant has six sealed barrels holding 15, 16, 18, 19, 20 and 31 gallons. Five contain wine, one contains beer, but none are labelled. He sells one buyer some wine, and a second buyer exactly twice as much wine, handing over whole barrels just as they are and keeping the beer barrel for himself. Which barrel holds the beer?
Reveal the answer
The 20-gallon barrel. The five wine barrels must split into two groups in a 1:2 ratio, so their combined total has to divide evenly by 3. All six barrels together hold 119 gallons; only removing the 20-gallon barrel leaves 99, which splits neatly into 33 (the 15- and 18-gallon barrels) and 66 (the 16-, 19- and 31-gallon barrels) — exactly double. Puzzle No. 76, "The Barrel of Beer," from Henry Dudeney's Amusements in Mathematics (1917).
— Henry Ernest Dudeney, Amusements in Mathematics — Puzzle No. 76, "The Barrel of Beer" (1917)
Go deeper: get the book →