Math Is Fun Forum

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Jugs Puzzle

In Level 6 of the Decanting Puzzle – http://www.mathsisfun.com/games/jugs-puzzle.html – it is claimed that the best possible solution involves only 14 moves. However, no matter how I try, I can’t ever solve the puzzle in fewer than 20 moves.

How is a 14-move solution possible?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Jugs Puzzle

Hmm ... good question. I don't know. Can anyone solve it?

Or perhaps we should give up and look in the source code.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Jugs Puzzle

So this one is your game?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Jugs Puzzle

No, by Duncan Keith of subtangent.com, but it is "open source", which can be downloaded here: http://www.mathsisfun.com/download/source-code.html (but needs Flash)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Jugs Puzzle

If I repeatedly pour 11 into 12, I get 20 moves.
If I repeatedly pour 12 into 11, I get 22 moves.

web find:
For each pair of values s and t below, use repeated division to find gcd(s, t)
the greatest common divisor of s and t and then use the Euclidean Algorithm
to solve the equation gcd(s, t) = xs + yt, where x and y are integers. In other
words, solve the decanting problems for decanters of sizes s and t.

Last edited by John E. Franklin (2008-04-06 12:01:01)

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igloo myrtilles fourmis

firefly3141

Member

Registered: 2009-02-14

Posts: 1

Re: Jugs Puzzle

I e-mailed the guy who made the puzzle game, and he said the actual minimum is 20.  He wrote:

"The minimal solution is 20 moves:
0-11, 11-0, 11-11, 12-10, 0-10, 10-0, 10-11, 12-9, 0-9, 9-0, 9-11, 12-8,
0-8, 8-0, 8-11, 12-7, 0-7, 7-0, 7-11, 12-6."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Jugs Puzzle

Thanks, firefly3141.