perplexus.info :: Just Math : Drinking Dwarfs

Drinking Dwarfs (Posted on 2013-10-23)

Seven dwarfs are sitting at a round table.
Each has a cup, and some cups contain milk.
Each dwarf in turn pours all his milk into the other six cups, dividing it equally among them.

After the seventh dwarf has done this, they find that each cup again contains its initial quantity of milk.

How much milk does each cup contain, if there were 42 ounces of milk altogether?

Source: 1977 All Soviet Union Math Olympiad Problem

No Solution Yet Submitted by Ady TZIDON

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re: solution (Two for the price of one.) (spoiler)

| Comment 4 of 6 |

(In reply to solution (Two for the price of one.) (spoiler) by broll)

It was a long way to Tipperary.

If you try to solve it with 3 dwarfs, you get a 2-1-0 distribution

immediately and understand how it works with 4 dwarfs : 3-2-1-0

so for 7 dwarfs it is 6-5-4-3-2-1-0, summing up to 21.

In our case - double the portions to get 42.

At each stage the distribution remains the same, shifting circullary one place to the right.

I will not address the other ("all equal") problem - it could not be presented at a high school competition where one has 20 minutes and no calculating aids.

I agree that it is a nice, albeit not so complicated puzzle.

Posted by Ady TZIDON on 2013-10-24 01:43:42

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