# It’s the Friday puzzle!

125

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!

## 125 comments on “It’s the Friday puzzle!”

1. titaniumtux says:

Pretty sure I’ve got it…took me all of five seconds. I just had to visualize the action

2. Chris says:

Do we have to take into account the fact that, already filled to the brim, these buckets are going to overflow?

• Richard says:

Good point. Fixed.

• lilabyrd says:

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!?

3. Dave Crow says:

Do the buckets start off with more than a cup full each?

• Gus Snarp says:

Good question. It does matter.

• Gus Snarp says:

Oh no! Unless…. I really hope it matters, otherwise it’s kind of a lame trick.

4. Natasha says:

I have an answer and it only took about a minute.

5. RaMdOmDuDe says:

6. Brian G says:

The solution is homeopathy! Wait a second…

• Gus Snarp says:

That’s what I was thinking!

7. RaMdOmDuDe says:

Although it did take me twice to read it before i really understood the question

8. Took me a few minutes of calculations before the penny finally dropped! :p

9. rj's mama says:

i think i got it

10. john bergoon says:

solved it I think. took a minute or do of contemplation, mainly to make sure it was/want was nt a trick question.

11. Cosmin Romania says:

This one took me 2 minutes.

12. DrBob says:

Already familiar with this puzzle.

13. Aish says:

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

14. siener says:

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.

• Simon says:

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.

15. Nick Sharratt says:

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.

16. ~Rachel~ says:

10 seconds or so to come to my initial conclusion, then another 2 minutes or so to be certain.

17. Anonymous says:

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.

• Ania says:

Actually, working in values makes it much easier to prove

• Richmix says:

Part of Anonymous’s comment gives away the answer…

18. Tony says:

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.

19. Kevin says:

I shtried thish ash a practigal exprigment but theresh no wine left in my buggit.

• Katy M says:

My instincts exactly!

• TS says:

Me too and I cant hold me wine, at least I had a bucket handy…

20. Ania says:

Knew the answer intuitively, but checked it with calculation to verify, so took a couple of mins.

21. Mchl says:

Isn’t it obvious?

22. 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!

23. Joao Pedro Afonso says:

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

24. Mark Probst says:

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

25. Rob says:

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

26. Shig says:

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.

27. Ythaca says:

I got it pretty quickly and my head aches almost constantly! Must have been an easy one.

28. Fran6co says:

Errr… isn’t wine ALREADY full of water ?
Wine without water would be deshydrated wine… powder.

• Simon says:

that was my first thought….

29. lilabyrd says:

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…..

30. D says:

Solved it algebraically to check that my answer was sound, so it took a couple of minutes.

31. Steve says:

32. Federico says:

I have my answer, it took me like 2 minutes! see you all!

33. Gib says:

2 minutes with a pen and paper and assuming a bucket of 100 units, and a cup of 10 units.

34. Gregor says:

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.

• Johan says:

What did they do with their shots in pints that made this relevant?

35. Darcia says:

Maybe I am missing something but isn’t the answer obvious?

• Darcia says:

Oh wait, I see what I was missing. Duh. I get it now.

36. Thomas John Brown says:

I think I got it! We’ll see on Monday!

http://tjbrown1980.wordpress.com/

37. Mark says:

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…..

38. savitrii says:

Got it! Took me about 5 min to scratch it out on paper

39. Icepick says:

Needed some scratch paper and about 2 or 3 minutes

40. Fatfish says:

Are we including the water that’s in the wine in the first place?

41. T9sus4 says:

Oldie but goldie. All those years ago, I solved it quickly with a little sketch.

42. Will says:

Good old algebra!

43. RCFairy says:

I realised the answer instantaneously

44. I got it – about 2 seconds. Hadn’t heard the puzzle before, but I’m quite confident . . .

45. sunshineliz says:

Why would you want to ruin a perfectly good bucket of wine??

46. Comedy Mike says:

I finally got one, sweet!

47. Rick H. says:

Hmm. It took a couple seconds. It seems obvious to me.

48. Jeremy says:

Always less wine for me, because I wouldn’t be able to resist tasting it whilst doing the transfer!

49. KJP says:

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.

50. rolak says:

Instant solution with special cupsize

51. Rex says:

I did it on paper. *guilty*

52. jrjonesguitarist says:

3 seconds…

53. Jon says:

Intuited it while reading the questionâ€¦ I think.

54. Eddie C says:

interesting

55. Jane says:

If the solution is as simple as I think it is, I got it.

56. Jonny says:

Never mind that. What are you doing wasting good wine?

57. Michael K Gray says:

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.)

58. Anthony P. says:

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.

59. hisfool says:

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 ….

60. Deeza says:

I think I’ve got it, but after reading a few comments, I’m thinking I may be incorrect. We shall see on Monday!

61. Alek says:

i think i figured it out – took about a minute.

62. Johanne says:

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.

63. Rachael says:

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.

64. komincents says:

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?

65. rc_moore says:

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!

66. TS says:

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?

• komincents says:

Did you not read the part about not revealing your answer? So many smart people with no sense whatsoever…

• TS says:

Did you actually try to make sense of that?

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

• komincents says:

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.

• komincents says:

And, really, the old “everyone else was speeding too” is SUCH a lame defense!

• TS says:

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.

• lilabyrd says:

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…… :}

67. Jo Hatton says:

This was much easier to solve once I had drunk some wine and abandoned the maths. A proper ‘Aha’ moment. Love it.

68. Marion says:

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

69. Benjamin says:

Really, though, it’s obvious once you think about it. A few seconds.

70. b says:

New this one. Its a nice one

71. komincents says:

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?

• komincents says:

Hey, Bucket, there are actually two typos. The period and one other…

72. komincents says:

And, just to be persnickety, my question has a typo…can you find it?

• Bucket says:

“the juice bucket. and stirs it up.”

That period shouldn’t be there…

73. Katie says:

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!

74. Bucket says:

as usual, I got an answer, but I don’ think it’s the one you’re looking for. sigh. I hate Friday puzzles.

75. Savo says:

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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…

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

76. Lakia says:

I got it I got it!

77. Anonymous says:

It took about ten seconds to get a answer then 1 seconds to second guess myself. But I got it.

78. Micho says:

Can’t say more,you guys all said

I say it’s more like water in wine. In other words, more wine than water.

Oh the shame I feel. Oops.

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82. nebetya says:

Yes, figured it out. Only took me about a minute for this one.

83. OHHH! Good question! Took some thought

84. sylwilson says:

wow…embarrassed to say how long it took me…but excited for Monday!

85. durga says:

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]

• lilabyrd says:

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. :}

86. sravan953 says:

Took me around 2 minutes… I think I got the correct answer…

http://www.fotolusion.com

87. J. Joseph says:

I first opened an Excel sheet, but closed it soon. Trying to figure it out in my head. Envying the smarter ones.

88. I first opened an Excel sheet too.

89. john says:

Guys new website in making will take the whole world join it…….
Don’t belive just wait

90. Chris says:

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.

91. pt4themind says:

I believe I have it.

92. N. E. Gma says:

This is Puzzle 408, in Henry E. Dudeney’s “536 Puzzles & Curious Problems.”

93. cutey161616 says:

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

94. josephalford says:

10 minutes using algebra. The answer is surprising to me, unlike some of those above who found it easy to visualise. I can’t tell you *why* the answer is the answer.

95. Dero says:

Loved the puzzle!

Intuitively solved within a second. Proof took a minute.

96. Sue M says:

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.

97. KMKerns says:

Visualization works for me too and, in about 10 seconds. Look forward to more. .K.

98. Samara says:

Took me about a min

99. praful says:

i got in 4 second