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Empty the bucket (Posted on 2017-05-29) Difficulty: 3 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughts@ Steve & Brian - the official postsAdy TZIDON2017-06-04 14:50:45
Solutionthe original solution -----p2---spoilerAdy TZIDON2017-06-04 14:44:21
Solutionre(4): Still stumped original solution p1 - spoilerAdy TZIDON2017-06-04 14:37:20
re(3): Still stumpedSteve Herman2017-06-03 14:27:59
re(2): Still stumpedSteve Herman2017-06-03 14:09:51
Some Thoughtsre: Still stumpedBrian Smith2017-06-03 11:14:55
Still stumpedSteve Herman2017-06-03 09:05:41
re(2): Stumped again 3rd HINT- spoilerSteve Herman2017-06-01 09:21:20
Hints/Tipsre: Stumped again 3rd HINT- spoilerAdy TZIDON2017-06-01 03:08:33
Hints/Tipsre: Stumped again 2ND HINT- spoilerAdy TZIDON2017-05-31 04:57:22
Hints/Tipsre: Stumped againi....small tipAdy TZIDON2017-05-30 15:54:08
Stumped againSteve Herman2017-05-30 09:37:35
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