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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.

Bottles.gif

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

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