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## June 24, 2005

### A Drinking Problem

*Another puzzle from The Chicken From Minsk (and another tip o' the hat to Erik).*

Besides chess playing and problem solving, drinking is and always has been the most common form of recreation in Russia. Vassily has acquired a 12-liter bucket of vodka and wishes to share it with Pyotr. However, all Pyotr has is an empty 8-liter bottle and an empty 5-lite bottle. How can the vodka be divided evenly?

The authors add this note: *Bottles were in short supply, particularly during the last stages of the Communist regime. Often, to fill a prescription it would be necessary to arrive at the pharmacy with an empty bottle.*

See the figure below.

The amounts of vodka in each container are:

a. (12,0, 0) - initial condition

b. (4, 8, 0) - fill the 8-liter bottle from the 12-liter bucket

c. (4, 3, 5) - fill the 5-liter bottle from the 8-liter bottle

d. (9, 3, 0) - empty the 5-liter bottle into the bucket

e. (9, 0, 3) - pour the 3 liters from the 8-liter bottle into the 5-liter bottle

f. (1, 8, 3) - fill the 8-liter bottle from the bucket, leaving 1 liter behind

g. (1, 6, 5) - fille the 5-liter bottle by decanting 2 liters from the 8-liter bottle, leaving 6 liters behind.

You now have 6 liters in the 8-liter bottle. Empty the 5-liter bottle into the bucket and you have 6 liters for Vasily and 6 for Pyotr.

Posted by joke du jour at June 24, 2005 06:59 PM

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