My pal is very fond of puzzles, but can't always remember all the details correctly.
This one for example:
‘Two explorers are on a long journey across the desert. Water is running short. Alan has a 9-pint canteen and Bob a larger one…’
‘How big?
‘I can't remember how big exactly but it wasn't more than twice as big as Alan’s; anyway, both of them are full. Their camel is carrying a 50 pint keg, which contains a quantity of water…’
‘How much?’
‘Errrm, unfortunately I can’t remember that either. In any case, it turns out that, by trial and error, Alan and Bob are able to redistribute the water between their canteens and the keg, by pouring only, and without wasting a single precious drop, so that each of their canteens contains exactly one pint at the end. The original puzzle was about how to do the redistribution in the shortest number of steps, and there sure were a lot of them, but it worked out in the end.’
I don’t think I need to know how much water was in the keg to start with, but can anyone help me with the size of Bob’s container, so that I can solve the original puzzle?

(In reply to solution? by monica)

Hi Monica!

Congratulations on leaping the first hurdle, but unfortunately it is not quite so simple as that.

My pal said "The original puzzle was about how to do the redistribution in the shortest number of steps..."

and you have reconstructed a problem (and in fact, the problem) that has the minimum number of steps. There are many such possible reconstructions.

But my pal also said:

"...and there sure were a lot of them, but it worked out in the end."

As you have rightly shown, any reconstruction of the problem will have a minimum number of steps, for that particular reconstruction, but there is only one reconstruction of the problem whose minimum number of steps for that reconstruction will also be the longest 'minimum' for any valid reconstruction.

And I am afraid that is the problem that I need to be solved.

Good Luck!

 

Posted by broll on 2010-05-21 11:37:23