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Puzzle for Today

Puzzle No. 355 – Tuesday 13 November

While your partner is away, you take delivery of a full barrel of wine on their behalf. You drink 5 glasses of wine the first night. Fearing your partner might get angry, you top the barrel up with water. The following night you are thirsty and you drink six glasses of the diluted wine. You observe that you are equally tipsy on both nights. How many glasses of wine does the barrel hold?

Today’s #PuzzleForToday has been set by the School of Mathematics and Statistics at the University of Sheffield.

The barrel contains 30 glasses of wine.

If we suppose that the barrel contains n glasses of wine then on the second night each glass contains (n-5)/n of the amount of alcohol that the glasses on the first night contained. You are equally tipsy on both nights, so we see that

The barrel contains 30 glasses of wine.

If we suppose that the barrel contains n glasses of wine then on the second night each glass contains (n-5)/n of the amount of alcohol that the glasses on the first night contained. You are equally tipsy on both nights, so we see that

5=6(n-5/n)

5n=6n-30

N=30

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