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!
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January 29, 2010 at 6:43 am |
Pretty sure I’ve got it…took me all of five seconds. I just had to visualize the action
January 29, 2010 at 7:00 am |
Do we have to take into account the fact that, already filled to the brim, these buckets are going to overflow?
January 29, 2010 at 7:33 am
Good point. Fixed.
January 29, 2010 at 7:42 am
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!?
January 29, 2010 at 7:37 am |
Do the buckets start off with more than a cup full each?
January 29, 2010 at 8:08 pm
Good question. It does matter.
January 29, 2010 at 8:10 pm
Oh no! Unless…. I really hope it matters, otherwise it’s kind of a lame trick.
January 29, 2010 at 7:37 am |
I have an answer and it only took about a minute.
January 29, 2010 at 7:38 am |
Obvious answer
January 29, 2010 at 7:38 am |
The solution is homeopathy! Wait a second…
January 29, 2010 at 5:49 pm
That’s what I was thinking!
January 29, 2010 at 7:39 am |
Although it did take me twice to read it before i really understood the question
January 29, 2010 at 7:40 am |
Took me a few minutes of calculations before the penny finally dropped! :p
January 29, 2010 at 7:41 am |
i think i got it
my real story
my minute maid
January 29, 2010 at 7:42 am |
solved it I think. took a minute or do of contemplation, mainly to make sure it was/want was nt a trick question.
January 29, 2010 at 7:45 am |
This one took me 2 minutes.
January 29, 2010 at 7:48 am |
Already familiar with this puzzle.
January 29, 2010 at 7:52 am |
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
January 29, 2010 at 8:13 am |
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.
January 30, 2010 at 5:38 am
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.
January 29, 2010 at 8:17 am |
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.
January 29, 2010 at 8:28 am |
10 seconds or so to come to my initial conclusion, then another 2 minutes or so to be certain.
January 29, 2010 at 8:32 am |
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.
January 29, 2010 at 9:44 am
Actually, working in values makes it much easier to prove
January 29, 2010 at 5:24 pm
Part of Anonymous’s comment gives away the answer…
January 29, 2010 at 8:43 am |
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.
January 29, 2010 at 9:33 am |
I shtried thish ash a practigal exprigment but theresh no wine left in my buggit.
January 29, 2010 at 11:33 am
My instincts exactly!
January 30, 2010 at 7:28 am
Me too and I cant hold me wine, at least I had a bucket handy…
January 29, 2010 at 9:41 am |
Knew the answer intuitively, but checked it with calculation to verify, so took a couple of mins.
January 29, 2010 at 9:51 am |
Isn’t it obvious?
January 29, 2010 at 10:20 am |
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!
January 29, 2010 at 10:48 am |
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
January 29, 2010 at 12:16 pm |
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
January 29, 2010 at 12:17 pm |
About 5 minutes. My intuitive guess was wrong. Scribbling and algebra yielded the right answer, confirmed afterwards by googling.
January 29, 2010 at 12:23 pm |
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.
January 29, 2010 at 12:34 pm |
I got it pretty quickly and my head aches almost constantly! Must have been an easy one.
January 29, 2010 at 12:55 pm |
Errr… isn’t wine ALREADY full of water ?
Wine without water would be deshydrated wine… powder.
January 30, 2010 at 5:21 am
that was my first thought….
January 29, 2010 at 12:59 pm |
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…..
January 29, 2010 at 1:15 pm |
Solved it algebraically to check that my answer was sound, so it took a couple of minutes.
January 29, 2010 at 1:31 pm |
was this not super easy?
January 29, 2010 at 1:34 pm |
I have my answer, it took me like 2 minutes! see you all!
January 29, 2010 at 2:23 pm |
2 minutes with a pen and paper and assuming a bucket of 100 units, and a cup of 10 units.
January 29, 2010 at 2:38 pm |
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.
January 29, 2010 at 9:50 pm
What did they do with their shots in pints that made this relevant?
January 29, 2010 at 3:00 pm |
Maybe I am missing something but isn’t the answer obvious?
January 29, 2010 at 3:02 pm
Oh wait, I see what I was missing. Duh. I get it now.
January 29, 2010 at 3:26 pm |
I think I got it! We’ll see on Monday!
http://tjbrown1980.wordpress.com/
January 29, 2010 at 4:01 pm |
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…..
January 29, 2010 at 5:03 pm |
Got it! Took me about 5 min to scratch it out on paper
January 29, 2010 at 5:51 pm |
Needed some scratch paper and about 2 or 3 minutes
January 29, 2010 at 5:52 pm |
Are we including the water that’s in the wine in the first place?
January 29, 2010 at 6:07 pm |
Oldie but goldie. All those years ago, I solved it quickly with a little sketch.
January 29, 2010 at 6:12 pm |
Good old algebra!
January 29, 2010 at 6:22 pm |
I realised the answer instantaneously
January 29, 2010 at 6:44 pm |
I got it – about 2 seconds. Hadn’t heard the puzzle before, but I’m quite confident . . .
January 29, 2010 at 7:08 pm |
Why would you want to ruin a perfectly good bucket of wine??
January 29, 2010 at 7:28 pm |
I finally got one, sweet!
January 29, 2010 at 7:43 pm |
Hmm. It took a couple seconds. It seems obvious to me.
January 29, 2010 at 8:58 pm |
Always less wine for me, because I wouldn’t be able to resist tasting it whilst doing the transfer!
January 29, 2010 at 8:59 pm |
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.
January 29, 2010 at 9:09 pm |
Instant solution with special cupsize
January 29, 2010 at 9:11 pm |
I did it on paper. *guilty*
January 29, 2010 at 9:17 pm |
3 seconds…
January 29, 2010 at 9:21 pm |
Intuited it while reading the question… I think.
January 29, 2010 at 9:26 pm |
interesting
January 29, 2010 at 9:27 pm
yea
January 30, 2010 at 5:18 pm
mildly
January 29, 2010 at 10:17 pm |
If the solution is as simple as I think it is, I got it.
January 29, 2010 at 10:33 pm |
Never mind that. What are you doing wasting good wine?
January 29, 2010 at 11:10 pm |
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.)
January 29, 2010 at 11:42 pm |
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.
January 29, 2010 at 11:52 pm |
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 ….
January 30, 2010 at 12:10 am |
I think I’ve got it, but after reading a few comments, I’m thinking I may be incorrect. We shall see on Monday!
January 30, 2010 at 1:04 am |
i think i figured it out – took about a minute.
January 30, 2010 at 1:42 am |
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.
January 30, 2010 at 6:38 am |
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.
January 30, 2010 at 7:55 am |
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?
January 30, 2010 at 8:47 am |
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!
January 30, 2010 at 10:48 am |
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?
January 30, 2010 at 5:14 pm
Did you not read the part about not revealing your answer? So many smart people with no sense whatsoever…
January 30, 2010 at 5:38 pm
Did you actually try to make sense of that?
Lots of other people gave much more away, but thanks for calling me smart.
January 30, 2010 at 6:03 pm
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.
January 30, 2010 at 6:12 pm
And, really, the old “everyone else was speeding too” is SUCH a lame defense!
January 31, 2010 at 5:27 am
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.
January 31, 2010 at 6:05 am
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…… :}
January 30, 2010 at 12:04 pm |
This was much easier to solve once I had drunk some wine and abandoned the maths. A proper ‘Aha’ moment. Love it.
January 30, 2010 at 1:38 pm |
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
January 30, 2010 at 2:41 pm |
Really, though, it’s obvious once you think about it. A few seconds.
January 30, 2010 at 3:15 pm |
New this one. Its a nice one
January 30, 2010 at 5:50 pm |
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?
January 30, 2010 at 9:40 pm
January 30, 2010 at 9:42 pm
Hey, Bucket, there are actually two typos. The period and one other…
January 30, 2010 at 5:53 pm |
And, just to be persnickety, my question has a typo…can you find it?
January 30, 2010 at 7:14 pm
“the juice bucket. and stirs it up.”
That period shouldn’t be there…
January 30, 2010 at 6:57 pm |
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!
January 30, 2010 at 7:11 pm |
as usual, I got an answer, but I don’ think it’s the one you’re looking for. sigh. I hate Friday puzzles.
January 30, 2010 at 9:43 pm
I like Bucket
January 30, 2010 at 7:46 pm |
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January 30, 2010 at 9:21 pm |
I got it I got it!
January 30, 2010 at 10:22 pm |
It took about ten seconds to get a answer then 1 seconds to second guess myself. But I got it.
January 31, 2010 at 12:18 am |
Can’t say more,you guys all said
January 31, 2010 at 12:24 am |
I say it’s more like water in wine. In other words, more wine than water.
January 31, 2010 at 12:31 am |
Oh the shame I feel. Oops.
January 31, 2010 at 2:10 am |
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January 31, 2010 at 3:25 am |
Yes, figured it out.
Only took me about a minute for this one.
January 31, 2010 at 4:04 am |
OHHH! Good question! Took some thought
January 31, 2010 at 6:01 am |
wow…embarrassed to say how long it took me…but excited for Monday!
January 31, 2010 at 9:59 am |
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]
January 31, 2010 at 10:42 am
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. :}
January 31, 2010 at 10:19 am |
Took me around 2 minutes… I think I got the correct answer…
http://www.fotolusion.com
January 31, 2010 at 12:03 pm |
I first opened an Excel sheet, but closed it soon. Trying to figure it out in my head. Envying the smarter ones.
January 31, 2010 at 1:33 pm |
I first opened an Excel sheet too.
January 31, 2010 at 3:01 pm |
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January 31, 2010 at 3:26 pm |
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.
January 31, 2010 at 5:52 pm |
I believe I have it.
January 31, 2010 at 6:45 pm |
This is Puzzle 408, in Henry E. Dudeney’s “536 Puzzles & Curious Problems.”
January 31, 2010 at 6:47 pm |
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
January 31, 2010 at 8:37 pm |
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.
January 31, 2010 at 8:55 pm |
Loved the puzzle!
Intuitively solved within a second. Proof took a minute.
January 31, 2010 at 11:12 pm |
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.
February 1, 2010 at 12:31 am |
Visualization works for me too and, in about 10 seconds. Look forward to more. .K.
February 3, 2010 at 5:05 pm |
Took me about a min
July 4, 2010 at 4:24 pm |
i got in 4 second