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 Empty the bucket (Posted on 2017-05-29)
You are in the desert and you have 3 buckets of water containing a,b,c liters respectively (a,b,c - positive integers).
You need an empty bucket for an unspecified purpose. Being in the desert you need the water and cannot just pour it away.
You have to pour the contents of one bucket into another one. But in any pouring, you must double the contents of the bucket which receives the water.
For example the sequence of bucket contents could be:

3 2 1
1 4 1
0 4 2

Now show that no matter what a,b,c are, you can always manage to empty a bucket under this constraint.

You may assume:
a>b>c

&
(capacity of each bucket)>(a+b)

 Submitted by Ady TZIDON Rating: 4.5000 (2 votes) Solution: (Hide) This problem is described in an article Five Algorithmic Puzzles by Peter Winkler that appeared in the Gathering for Gardner. The solution (slightly abridged): see my 2 comments: p1 and p2.

 Subject Author Date @ Steve & Brian - the official posts Ady TZIDON 2017-06-04 14:50:45 the original solution -----p2---spoiler Ady TZIDON 2017-06-04 14:44:21 re(4): Still stumped original solution p1 - spoiler Ady TZIDON 2017-06-04 14:37:20 re(3): Still stumped Steve Herman 2017-06-03 14:27:59 re(2): Still stumped Steve Herman 2017-06-03 14:09:51 re: Still stumped Brian Smith 2017-06-03 11:14:55 Still stumped Steve Herman 2017-06-03 09:05:41 re(2): Stumped again 3rd HINT- spoiler Steve Herman 2017-06-01 09:21:20 re: Stumped again 3rd HINT- spoiler Ady TZIDON 2017-06-01 03:08:33 re: Stumped again 2ND HINT- spoiler Ady TZIDON 2017-05-31 04:57:22 re: Stumped againi....small tip Ady TZIDON 2017-05-30 15:54:08 Stumped again Steve Herman 2017-05-30 09:37:35

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