So, you have a two equal sized buckets. One contains water and the other contains the same amount of wine. You transfer a cup of wine to the water bucket and mix it in. Next you transfer a cup of the mixture back to the wine bucket. Is there more wine in the water, or water in the wine?

As ever, please do NOT post your answers, but do feel free to say if you have solved it and how long it took. I will post the solution on Monday. Have a good weekend!

128 comments

    1. Now you went and did it Richard! I already solved it the other way using the displacement from the overflow! So had to do it again this way in a few seconds….. do I get extra credit for doing it both ways!?

  1. more water with wine in first bucket and more wine with water in the second bucket..->a generalized answer as you didnt mention which bucket took 2 min

  2. Took me about two minutes. I came to the answer by considering two extreme cases (not going to give any more details).

    I then confirmed the answer with a little bit or algebra.

    1. The extreme cases should not be trusted… what if the answer was a quadratic in the ratio of the cup to bucket size (symmetric about cup/bucket=1/2? Then the extreme cases would be misleading.

  3. Answered straight away as I think I’d heard it before, but took a minute or two trying different model conditions to feel completely confident.

  4. To throw the reader off, this puzzle is often accompanied by much irrelevant detail: we might be told the precise size of the buckets and cup in ml, or that the transfer operation is carried out three times, or some such, none of which have any bearing on the answer.

  5. Now this is a good puzzle.

    I didn’t find it that obvious for some reason, but like the siener, if find extreme cases tend to make these things clearer.

  6. This was in no way obvious to me, and I had two false starts before I finally managed to work it out algebraically. Using actual values for bucket volumes helped reassure me that I had the right answer.

    Fifteen minutes. Maybe 20.

    Excellent puzzle!

  7. This puzzle is lovely. The temptation is to pick a paper and do math, pictures or history of the exchange when the simple universal truth, kind of, “what color had the white horse of Napoleon?” struck us. Funny thing, even been obvious, the mind still rejects the right solution and need to pick paper to retrace it πŸ™‚

  8. I already knew the answer, but it took me years, literally, to understand it. I learned about the puzzle in school, and could do the math to get the correct answer, but it didn’t make any sense, until only a few years ago when it finally came to me, and it’s so obvious and simple πŸ™‚

  9. About 5 minutes. My intuitive guess was wrong. Scribbling and algebra yielded the right answer, confirmed afterwards by googling.

  10. Took no time at all, plus about five minutes of head-scratching second-guessing to make sure the very simple and obvious answer is the right one. It’s much simpler if, as someone suggested, you start each bucket with only two cups of fluid each.

  11. I did it by taste testing……it has to be 5 o’clock pm somewhere….oh no wait it’s Friday…you can start taste testing early…hehe…..confirmed my answer in a few seconds…..

  12. Ah yes, I know this one. I ran pubs for years and used this as an example to punters who used to drop shots in their pints. As you can imagine explaining the solution and how it works to drunk people was very laborious.
    Needless to say I didn’t do it often.

  13. I used to use this as an interview question. It’s amazing how many folks will argue about the answer. That is, until it is posed as a question using something more ‘concrete’ such as marbles…..

  14. Should we be taking into account the fact that wine is about 7% alcohol by volume and the rest is grape pee and water?

    Oh. And antioxidants. Can’t forget those.

  15. I thought that it was obvious until I did the math, and a few ‘corner examples’, such as when the buckets only start with a single cupfull of each liquid.
    I then found the real answer to be quite counter-intuitive!
    Thanks Richard for a reasonably hard one. (Oooh err.)

  16. We are not including the water in the wine, since wine IS part water (13% btw).

    Yes wine and water are homogeneous. But let’s use non homogeneous materials to demonstrate the example:

    Imagine padded wooden chairs vs pieces of wood. Each unit of either weighs the same. While calculating, you will have a chair in your pile of wood. Does this mean that we are left with wood plus padding? No. We have wooden chairs plus wood still.

    The question says to use wine. Wine without water is not wine.

    Then again since wine and water are homogeneous, the fact that wine was dumped into water means that mixture is neither wine nor water. This is because water involves hydrogen and water ONLY. Then that mixture dumped into the wine creates a substance that is no longer wine. This is because wine is 13% alcohol, and dumping the mixture dilutes it and is therefore wine no more. But, I don’t think we are meant to look that far into it.

    Like some one said above, marbles work best. Took me 5 minutes on paper btw.

  17. The solution took about as long as it took me to read it. There is an overflow problem but that does not seem to effect the outcome. I hope that is cheap wine you are wasting ….

  18. Got it. (Answer changes if there is more than one cup of water or wine in each bucket – also assuming large bucket w/out overflow.) Nice trick wording. About a minute.

  19. Heard this one in a psychology lecture early this year, so it didn’t take me long at all to figure out. One of my favourite puzzles though, nice and counterintuitive.

  20. Just to be persnickety, the first sentence has a typo.
    “So, you have a two equal sized buckets.”
    And, with everyone hinting at the answer, it really kinda sucks…
    Here’s one for y’all: Who do you think is actually buried in Grant’s tomb?

  21. The size of the buckets does not matter (as long as you avoid overflow).
    How much liquid is originally in the buckets does not matter.
    How much you transfer does not matter (as long as the amount stays the same).

    So pick an amount that makes the problem trivial, and voila, you have the answer!

  22. The best way to visualise this is to use amounts that are easy to juggle in your head.
    In my case I decided on two buckets of Lego blocks.
    Each bucket contains 100 blocks each, in one the blocks are white and the other they are red.
    I didn’t have enough white and red blocks to make it 100 of each colour in each bucket (which is a bit disturbing as this is a mental exercise). So the white bucket have some yellow and green blocks to make up the numbers and the red bucket have some brown, blue and orange blocks mixed in.
    I then take a cup that can contain 10 blocks and fills it from the red bucket and empties it into the white bucket. Unfortunately Lego blocks do not behave as liquid, so nothing flows over, so I decide to shake the bucket until 10 blocks falls out.
    6 white blocks falls out along with 3 yellow and 1 green blocks. I would like to remind people not to leave the Lego blocks on the floor. If you have to go to the bathroom during the night, nothing hurts more than stepping on a Lego block. I remembered this as I went out of bed during the night, I knew where they were but stubbed my toe on a table when I was trying to avoid them.
    I mix the blocks in the white bucket thoroughly and then fill my cup with 10 blocks from it. The cup now contains 5 white, 2 yellow, 2 green and 1 blue blocks.
    After emptying the cup into the red bucket it’s a simple matter of counting up the ratios of coloured blocks in each bucket.

    How easy is that?

    1. Did you actually try to make sense of that?

      Lots of other people gave much more away, but thanks for calling me smart.

    2. Smart enough to have a relatively good command of the language, but not smart enough to know when your attempt to be clever is doomed. Smart enough to recognize a bucket, not smart enough to know into which end you pour the wine.

    3. You call that “speeding”?

      If you read through all that and pick out the superfluous information, then you would actively be seeking out the solution and not just stumble upon a blurted out answer.

      It would be faster to Google it.

    4. TS doing all this in your head?….wow…. did you try tasting your Lego to find the right answer? Does the blue and yellow ones together taste like the green ones? Or did they taste cheap wine?…..lol….. :}
      komincents….I play in the rain, run whilst holding scissors, don’t always play well with others and yes I would jump off a cliff if all my friends did too! Everyone else does speed….. and it’s FUN…lol…… :}

  23. I have not heard this one before so it took me a couple of minutes to think it through, but I have come up with an answer which I think is right-Will find out on Monday. Thanks

  24. Your question asks if there is more wine in the water, or water in the wine, but you do not specify to which bucket you refer. I assume you mean the wine bucket, but it is not absolutely clear.

    Situation: Jim has two 10 gallon buckets. One bucket has 3 gallons of orange juice and the other bucket has 5 gallons of urine. Jane, being the prankster that she is takes a measuring cup and scoops out exactly one cup of juice from the juice bucket and then pours it into the bucket with the urine. The beeotch stirs that bucket with the juice/urine mixture, then she takes the same cup and scoops up exactly one cup of the mixture from that bucket and dumps it into the juice bucket. and stirs it up. She sets up her Nanny Cam to catch her rotten husband’s reaction when he tastes what she did to his precious bucket of juice. Maybe next time he will think twice about sharing his effing juice.

    Question: Does the liquid in the original juice bucket now contain more juice that urine, or more urine than juice?

  25. I think I actually figured it out! I’ve never heard this before, so I’m excited that I may have solved it entirely on my own. It took me probably 5 minutes of mentally moving cups. Exercise for the brain!

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    All players are workers and soldiers from day one and in time they can become political party members, congressman, party presidents, even country president, members of special military service, newspapers owner, successful businessman and owners of international business chains… The higher ambitions you have the more time you’ll need to spend in game…

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    http://www.erepublik.com/en/referrer/Zoli1108

  27. Question to the question before answering the question: If already the two buckets were full of water, there is a chance of overflow. so let us know if the bucket is full. Don’t say, that mixing one in the other will not cause overflow [:P]

    1. durga ……Within the first few minutes of the puzzle being posted it was corrected as it read two buckets filled to the brim and the first few of us asked just that…..really my first answer at the top shows where I answered it both ways……any who Richard fixed it and no they are not filled to the top but are equal… “If the two buckets were full of water…” no one has water and the other has wine in the beginning. :}

  28. I assume that no liquid is spilled and that both buckets end up with the same amount of liquid in as they started with. For me that leads to just one logical answer.

  29. It took me like one seconed 2 get it that was mad easy hey i got a question what is the worst thing that can happen to u

  30. Concusion 1 relying on first thought, more than 1cupful per bucket, took a couple of seconds.

    Then Conclusion 2 relying on more thoughtful data, ie what if there was only ever 1 cup in each bucket, took a minute.

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