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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)

See The Solution Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips re: Stumped again 3rd HINT- spoiler | Comment 4 of 12 |
(In reply to Stumped again by Steve Herman)

First observe that a very special thing happens when you work with just two buckets, where one has an even quantity and one has an odd quantity.

Analyze the cycle.
Add a third bucket with even qty of water.
Solve  the general EEO case.
Show that any initial position can be converted to EEO.

GOOD LICK.


  Posted by Ady TZIDON on 2017-06-01 03:08:33
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