A hundred empty glasses and the dregs

Question

At a whisky tasting, the dregs left in 10 empty glasses can be poured together to make 1 full glass. At the end of the evening you find 100 empty glasses. How many full glasses can you make and drink? Remember that each glass you drink becomes a new empty glass.

Accepted Answer

Eleven glasses. Round one. Pool the 100 empties, ten at a time, into 10 full glasses. Drink them. You now have 10 empty glasses. Round two. Pool those 10 empties into 1 full glass. Drink it. You now have 1 empty glass, which cannot make anything more. Total: 10 + 1 = 11. The general rule. If e empties make one full glass, then starting from n empties you get roughly n / (e minus 1) drinks, because each drink "costs" e empties but gives one back, a net cost of e minus 1. For n = 100 and e = 10 that is 100/9, about 11.1, and the whole-number answer is 11 with one glass left over. The borrowing …

A hundred empty glasses and the dregs

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