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?

Bob's canteen: 11-pints   camel's 50-pint keg: 32 pints

1. 9/9  11/11  ??/50  --> ? = 32 
2. 0/9  11/11  ??/50  --> ? = 41 
3. 9/9   2/11  ??/50  --> ? = 41 
4. 0/9   2/11  50/50  all unknowns now known!

As it is, it is necessary for Bob and Alan to know the quantity of pints in the keg. Else, though they might be able end up with one pint in each canteen with the keg topped off with the reserve, they could not ascertain the quantity in each canteen would in fact have one pint each. Thus, the first four steps are necessary for Bob and Alan to fairly redistribute the water. And, in order for Alan and Bob to be certain when to stop pouring there must be a total of 52 pints between the canteens and keg. 

5. 2/9   0/11  50/50
6. 2/9  11/11  39/50
7. 9/9   4/11  39/50
8. 0/9   4/11  48/50
9. 4/9   0/11  48/50
10. 4/9  11/11  37/50
11. 9/9   6/11  37/50
12. 0/9   6/11  46/50
13. 6/9   0/11  46/50
14. 6/9  11/11  35/50
15. 9/9   8/11  35/50
16. 0/9   8/11  44/50
17. 8/9   0/11  44/50
18. 8/9  11/11  33/50
19. 9/9  10/11  33/50
20. 0/9  10/11  42/50
21. 9/9   1/11  42/50
22. 1/9   1/11  50/50

 

Edited on August 23, 2010, 8:23 am

Posted by Dej Mar on 2010-07-01 07:17:31