The Perplexed Cellarman

dudeney cellarman puzzle

One last puzzle from Henry Dudeney’s Canterbury Puzzles:

Abbott Francis sends for his cellarman and complains that a particular bottling of wine is not to his taste. He asks how many bottles he had produced. The cellarman tells him that there had been 12 large and 12 small bottles, and that 5 of each have been drunk. The abbot replies that three men are waiting at the gate, and orders the cellarman to give each of them some combination of full and empty bottles so that each man receives the same quantity of wine and combination of bottles.

How can the cellarman do this? He has seven large and seven small bottles full of wine, and five large and five small bottles that are empty. A large bottle holds twice as much wine as a small one, but a large bottle when empty is not worth two small ones — hence the abbot’s order that each man must take away the same number of bottles of each size.

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