Please solve
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Well -> 5L
5L -> 7L
Well -> 5L
5L -> 7L (3L remain in 5L)
Empty 7L
5L -> 7L (3L now in 7L)
Well -> 5L
5L -> 7L (1L remain in 5L)
Empty 7L
5L -> 7L (1L now in 7L)
Well -> 5L
5L -> 7L (6L now in 7L)
7L to scale
This is one of the older measuring puzzles, and even made an appearance in Die Hard with a Vengeance (not that they figured it out, they guessed...)
I didn't trust your spreadsheet, and ran it on a honeymonkey machine...
Infinity, the root origin of the word is Greek - that the French are attributed it is one thing, but does not change that either the Germans got it from Greek as well (or from the French) and then pulled it to English. As I said, English is a dialect of German - how the French got a mention at all is beyond me :)
Sofa comes from Arabic, and has equally nothing to do with the question at hand :))
And Kdo, careful, we are still an international site, and if the last 50 years are anything to go by... :P
Except that in German it's 'liter', not 'litre'. In French and UK English, it's 'litre'.
Btw, English is based both on old German and on Latin (via French). The English and French have a lot of history, and it's normal that a lot of words were taken over from the French :) [http://french.about.com/l
This type of puzzle can be solved with a linear Diophantine equation. Unfortunately, I did not get to play around with the SWF movie, but I see the gist. You have a 5-liter jug and a 7-liter jug. You need exactly 6 liters. This can be modeled as:
5x + 7y = 6
All solutions of (x, y) will give you the correct way to solve this. For example, x = -3 and y = 3. This tells you that you will fill the 7-liter jug from the well 3 times and empty the 5-liter jug into the well 3 times.
So, you fill the 7-liter jug (which I'll call Y) and use that water to fill the 5-liter jug (which I'll call X).
You dump X and pour the remainder of Y into X, so you have 2 liters.
You fill Y again and use that water to fill X.
You dump X and pour the remainder of Y into X, so you now have 4 liters.
You fill Y again (for the third time) and use that water to fill X. This leaves you with 6 liters in Y.
You dump X (for the third time) so you have exactly 6 liters, which is your goal.
Another solution is x = 4 and y -2. Now, you are going to fill the 5-liter jug from the well 4 times and empty the 5-liter jug into the well 2 times.
So, you fill X and pour the contents into Y.
You fill X again and use that water to fill Y.
You dump Y and pour the remainder of X into Y, so you now have 3 liters.
You fill X again and use that water to fill Y.
You dump Y (for the second time) and pour the remainder of X into Y, so you now have 1 liter.
You fill X again (for the fourth time) and pour it into Y, so you now have a total of 6 liters.
In fact, there are an infinite number of ways of doing this, but it really boils down to these two solutions. Sure, x = 24 and y = -12 will work, but you would end up with 6 liters several times.
You can create any number of these puzzles just by finding a, b, and c to fit this model:
ax + by = c
where x and y are integer solutions.
It's important to note that if a and b have a common factor, this must also be a factor of c. Otherwise, x and y cannot be integers, and the system will not work for the water jug puzzle. For example, it is impossible to get 7 liters from a 4-liter jug and a 10-liter jug. You would have 4x + 10y = 7. There is no solution for x and y which are integers, so you cannot solve this with the jugs. On the other hand, you can solve 8x + 6y = 10, as 8 and 6 have a common divisor of 2, which is a factor of 10. In actuality, this has the same solution as 4x + 3y = 5. So, you can expand the jug puzzle by multiplying all the numbers by the same factor. In the example above, you can do the same steps to get 30 liters of water out of a 25-liter jug and a 35-liter jug.
This link can help out too: http://www.wikihow.com/Sol
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by: Infinity08Posted on 2008-09-05 at 06:45:56ID: 22398827
fill the 5 liter bottle, and poor it in the 7 liter bottle
fill the 5 liter bottle, and poor it in the 7 liter bottle until it's full
the 5 liter bottle now contains 3 liters
empty the 7 liter bottle, and poor the 3 liters into it
fill the 5 liter bottle, and poor it in the 7 liter bottle until it's full
the 5 liter bottle now contains 1 liter
empty the 7 liter bottle, and poor the 1 liter into it
fill the 5 liter bottle, and poor it in the 7 liter bottle
the 7 liter bottle now contains exactly 6 liters