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You have three jugs with volumes of 12, 8, and 5 liters. The 12L jug is full of water, while the other two jugs are empty. You have no other source of water.

Using these jugs, how can you obtain exactly 6 liters of water in the 12L jug?

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  • $\begingroup$ I've tried a lot of things but can't seem to know what to do $\endgroup$
    – Cassey
    Sep 1, 2017 at 9:35
  • $\begingroup$ Hello and welcome to Puzzling. I've edited your question slightly for clarity. Please feel free to edit it further or to roll back my changes. $\endgroup$
    – Lawrence
    Sep 1, 2017 at 11:08
  • $\begingroup$ Possible duplicate of A Set of Water Jug Challenges $\endgroup$
    – Oray
    Sep 1, 2017 at 11:14
  • $\begingroup$ This is confusingly written. You mix units (inches or liters? Pick one!) and it seems likely that your intention is that the 12 jug is full and there is no other source of water, but it doesn't say that - if that's what you intend, please edit the puzzle so that is clear. $\endgroup$
    – Rubio
    Sep 1, 2017 at 11:28
  • 6
    $\begingroup$ Possible duplicate of A general solution to the decanting problem? (aka jug-pouring, water-pouring) $\endgroup$ Sep 1, 2017 at 12:04

3 Answers 3

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Answer

  1. 12j-12, 8j-0, 5j-0

  2. 12j-4, 8j-8, 5j-0

  3. 12j-4, 8j-3, 5j-5

  4. 12j-9, 8j-3, 5j-0

  5. 12j-9, 8j-0, 5j-3

  6. 12j-1, 8j-8, 5j-3

  7. 12j-1, 8j-6, 5j-5

  8. 12j-6, 8j-6, 5j-0 (done!)

Ends up with 6 inches of water in the 12-inch jug with no water wasted!

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    $\begingroup$ After step 6, you could fill 5 from 8, then pour 5 into 12 to not waste anything. $\endgroup$
    – Apep
    Sep 1, 2017 at 11:52
  • $\begingroup$ Right, that's even better. I'll update my answer, thank you! $\endgroup$ Sep 1, 2017 at 11:53
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    $\begingroup$ This is the only way to perform the task in seven transfers, and it is not possible with less. $\endgroup$ Sep 6, 2017 at 19:53
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Fill the 8L jug from the 12L jug, then fill the 5L jug from the 8L jug. This leaves 3L in the 8L jug. Discard that 3L. Empty the 5L jug into the 12L jug. Repeat.

This discards 6L and leaves 6L in the 12L jug.

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    $\begingroup$ If poring-with spilling counts as one step, then you can simplify this solution to 6 steps. $\endgroup$ Dec 22, 2023 at 8:42
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here is another way of doing this:

12j-12, 8j-0, 5j-0
12j-0, 8j-8, 5j-4
12j-8, 8j-4, 5j-0
12j-3, 8j-4, 5j-5
12j-3, 8j-8, 5j-1
12j-11, 8j-1, 5j-0
12j-6, 8j-1, 5j-5(Done!)

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  • $\begingroup$ I don't know how to hide the text, but these steps are correct to get the 6L in 12L jug $\endgroup$ Sep 6, 2017 at 19:22
  • $\begingroup$ It's another way yes, but do note that this takes nine transfers rather than the (minimal) seven (even though it was not asked of us to be optimal in transfers). $\endgroup$ Sep 6, 2017 at 19:52

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