School-Safe Puzzle Games

## Red Wine and White Wine Brain Teaser

You have a bucket of red wine and a bucket of white wine. You take a cup of red wine and pour it into the bucket of white wine. After thoroughly mixing, you then take a cup of this mixture and pour it back into the red wine bucket.

Is there more red wine in the white wine or is there more white wine in the red wine?

Feel free to post your answer in the comments section; however, you should really try to solve it yourself first before scrolling down.

### 37 Comments to “Red Wine and White Wine Brain Teaser”

1. Gabrielle Bricknell | Guest

why of course there is more red wine in the white wine, considering the second mix was not pure!

2. Kathy Z | Guest

it would be equal.

for example, lets say in each bucket there is 30 oz
you take 10oz (probably not a real cup) of red wine and pour it into the white wine and mix thoroughly.
red wine bucket=20oz
white wine bucket=30 oz of white wine, 10 oz of red wine
if you take 10oz now from the white wine bucket, you might , by random, be taking 2oz of red wine and 8oz of white wine.
pour that into the red wine bucket and now you have
red wine bucket=22 oz of red wine, 8 oz of white wine
white wine bucket=22oz of white wine, 8 oz of red wine

thats the best way i can explain it, but i dont even know if its right. hopefully =]

3. david | Guest

i agree with kathy, my first guess was that there would be equal amounts.

4. John Hartnett | Guest

I agree with kathy and david. The way I thought about it was semi-sort of-pseudo algebra. check me please, because I do not know if I have this right.

forget wine, call them “x” and “y”. the cup of red wine call “x2”, the cup of the red/white mix call “y2”.

x-x2+y2 = y+x2-y2

they’re equivalent, yes? No?

5. doug | Guest

it doesnt seem right at all, my first instict was the same as gabrielle’s, but when i consider it like this, i see it differently…..

consider each bucket contains 10 cups of wine, and one full cup of red is mixed in with the white. you now 11 cups of wine, 10 of which are white (91%)

after mixing thouroughly, you have a solution that will yield this same 91% ratio regardless of the sample size you take, be it an ounce, a cup, or a quart.

one cup of this solution to be poured back into the red wine bucket is only 91% white wine, while 9% red.. the red wine bucket now has 9 full cups of red wine +9% of 1 cup, while the original white wine bucket has 10 cups of white wine -91% of one cup…

so…this leaves each bucket with 91% of one cup of the foreign wine…its important to remember that there is some red wine being transfered back to its original bucket, so even though you do indeed transfer LESS white wine in the process, the red wine that you bring back with it makes it even.

i think…..

6. RLP | Profile

Very similar I believe to what Doug mentions above, a helpful way I’ve found to conceptualize the problem is to imagine 2 buckets: one filled with 1000 blue marbles, and a second bucket filled with 1000 white marbles.

If a cup can hold 200 marbles, imagine scooping 200 out of the blue bucket and pouring them into the white bucket.

There are now 1200 marbles in the white bucket (200 blue, 1000 white). After mixing thoroughly, when you take 200 out (a cup), 40 will be blue, 160 white.

Therefore, 160 blue marbels will be left in the white bucket, and you’ll be putting 160 white marbels in the blue bucket.

So in the end, there are just as many white marbels in the blue bucket as there are blue marbels in the white bucket.

Many people (myself included) initially get this problem wrong relying just on intuition.

7. IQ-101 | Guest

Explanation:

Mentally paint the red-wine bucket red, the white-wine bucket white for easier identificaion.

Consider the situation after one cup of red wine is added to the white bucket.

Focus on the amount of white wine lost from the white bucket when one cup of the mixture is taken out and transferred to the red bucket.

The amount of “lost” white wine must be the same as the NET amount of red wine added in the white bucket, because the white bucket begins and ends with one bucketful of wine.

So this amount of “lost” white wine (from the white bucket) becomes the “added” white wine in the red bucket.

So the amount of “added” white wine in the red bucket is the same as
the amount “lost” white wine from the white bucket, which is in turn equal to
the amount of “added” red wine in the white bucket.

The key is that each bucket has the same amount of wine before and after the two mixings, namely, one bucketful of total wine.

P.S.:

Once you gets it, you wonder how it can be otherwise.

IQ-111

=================

Explanation:

Once you gets it, it’s very simple.

I’ll try an intuitive explanation, i.e. no numbers.

To easier identify the buckets, mentally paint the red-wine bucket red, the white-wine bucket white.

Consider the situation after one cup of red wine is added to the white bucket.

Focus on the amount of white wine lost from the white bucket when one cup of the mixture is taken out and transferred to the red bucket.

The amount of “lost” white wine must be the same as the NET amount of red wine added in the white bucket, because the white bucket begins and ends with one bucketful of wine.

But this very same amount of “lost” white wine becomes the “added” white wine in the red bucket.

Putting the last two sentences together, the amount of white wine in the red bucket is equal to the amount of white wine lost from the white bucket, which is in turn equal to the amount of red wine in the white bucket.

In effect, the “lost” white wine becomes the key to understanding.
In the white bucket, it corresponds to the net amount of red wine added.
In the red bucket, it corresponds to the amount of white wine added.

I did some paper and pencil calculation and came to the same answer.

In fact I tried an intuitive argument first. Getting nowhere and getting tired, late at night, I forced myself to do some paper and pencil calculation and came up with equal amounts. Went to bed. The next morning, the intuitive argument became clearer and clearer to me. To the point that I asked myself how it can be otherwise.

It’s a very good IQ problem. I like it much.

8. Arthur | Guest

Take r (for red) and w (for white) as constants. a is a variable.
With r=w.

We begin with:
1) ar and aw (equal amounts of wine in both)

2) (a-1)r and aw + r (take one unit out of red wine and put into the white wine)
Now we he have a-1 units of red wine in one bucket.
In the other we have a units of white wine and 1 unit of red wine: total a+1 units

After mixing, take 1 unit out of the bucket with a+1 units and put it into the bucket with a-1 units:
3) (a-1)r + (aw+r)/(a+1) and aw+r – (aw+r)/(a+1)

Write out the algebra:
4) ((a-1)r(a+1) + (aw+r))/(a+1) and ((aw+r)(a+1)-(aw+r))/(a+1)

5) ((a^2-1)r+(aw+r))/(a+1) and ((aw+r)(a+1-1))/(a+1)

6) (a^2r-r +aw+r)/(a+1) and ((aw+r)a)/(a+1)

7) (a^2r+aw)/(a+1) and (a^2w+ar)/(a+1)

As you can see in the numerator: the amount of white wine in the red wine bucket equals the amount of red wine in the white wine bucket.

9. OZ | Guest

well you see there is no need for any math equations in this question.. it is actually a trick question.. the correct answer is that there is more RED wine in the white wine.. after you mix the red wine in it changes the color of the WHITE wine to RED .. when you put the WHITE wine in the red it doesnt change the color because the red is a darker color. also its already red from mixing it. I know this because in the first part of the question it says that it was MIXED… all of the other ppl that thought they were being smart with there math equations YOU ALL ARE WRONG
-email me if you think that i am wrong
emosborne@comporium.net

10. siddu | Guest

those who are saying equal
Assume that one cup of wine is removed from white bucket and then a cup of red wine is added and then the removed cup of white wine is added to the red bucket is this and as per the question both contains equally??????

No

The white bucket contains more red than white in red bucket no mathematics required think logically. Because we are carrying some of red back to the red bucket if you some numerics it may looks equal but theoretically they are not equal.

as per as color is concerned i completely agree with OZ

11. Leonard | Guest

The reason why it is counter-intuitive is probably because (assuming 1 bucket = 5 cups) when 1 cup goes from the white bucket to the red bucket, 1 cup of white mixes with 5 cups of red. However, taking 1 cup back from the (mixed) red bucket to the white bucket, it is mixed back with only 4 cups of white (as compared to 5 cups of red on the initial mixture). So although the second cup contained a “watered-down” mixture (non-pure red), it’s impact is larger than the first cup (pure white) which ultimately balances out.

12. MJ | Guest

Forgive me if I am just reiterating what has already been pointed out on this one… But I didn’t understand this either at first and this is how I put it to myself in terms I could understand. You have a glass of white wine and a glass of red wine. You put a cup of red in with the white and mix it thoroughly. You then take a cup of the mixture, which ideally, with a perfectly, evenly-blended mixture, would be equal parts red and white wine and mix it in with the red wine. You are essentially putting back in half of the red wine what you just took out moments ago. After you mix it back in, bottom line is that the glass of white wine will have half a cup of red wine in it, and the glass of red wine will have half a cup of white wine in it. This is assuming that this was a perfect blend, of course, but theoretically the above would be your result.
As far as the color goes, try this… Take a very light shade of food coloring (perhaps a diluted blue or reddish/pink color). Mix a drop into a glass of clear spring water. Of course you are going to see a change in the color of the water. Now, take that same amount of the same food coloring and mix it into a dark beverage, such as Pepsi, Coke, coffee, etc. You’re not going to see a change in the color of those beverages, but that doesn’t mean they have any less food coloring in them than the water does.

13. Abhijit | Guest

Both the red wine bucket and the whtite wine bucket contain more of the opposite wine . Because after thorough mixing , the whole red wine cannot be taken back , and a portion remains in the white wine bucket and vice versa .

14. Ian Peder | Guest

They are equal.
Any red wine missing from the red wine bucket will have been replaced by an equal quantity of white wine since the final volumes in each bucket are the same as they started out.
This is true regardless of how much wine was in each original bucket possibly even different quantities.

If the question had been which one is most “polluted” then this cannot be answered without knowing the repective ratios of each bucket contents.

15. Mac | Guest

They are equal.
this is a simple scientific riddle. it is about the mass of each substance. sort of like oil and water.
Lats say the red wine (being less dense) is the oil, and the White wine is the water. You pour a cup of oil into the bucket of water. No matter how much you stir, the oil rises to the top. Taking a cup of the substance in the mixed bucket, you would get a cup purely full of oil, thus pouring exactly 1 cup of oil into the bucket it originally came from. Therefore, you have the exact same about of red and white wine in their original buckets.

16. Ian | Guest

I really like siddu’s anwser of it being a trick question.
look at it and take it into concideration.
but if they were different colors, it would be equal.

17. Kip | Guest

i like this answer the best so far, they are equal, here is my explanation its a little complicated but just bear with me and try to follow it, ok? here it goes.. magic

18. taires | Guest

ok this is very easy lets say that we have 90red wine and 90white wine

we take 10red and put it in the white so now the white wine bucket has 90white + 10red … right?.

when we take the mixed wine in the cup we will have 9white and 1 red ( we have to respect the proportions ) leaving 81 white wine and 9 red wine.

when we add it to the red wine .. the red wine bucket will have 80red+1red+9white=81red and 9 white

so yes they are equal

19. bob | Guest

it would be pink when you mixed the two wines. so… pink doesn’t affect red so more red.

20. bob L. head | Guest

equal

21. Sundeep Singh | Guest

I find RK’s analogy of red and black marbles to be very effective!!
It really becomes very easy, if you think of marbles as molecules and then do te maths:
1000 molecules of red wine : 1000 molecules of white whine
take 250 molecules of red wine and pour into white wine
–> 750 molecules of red wine : 1000 molecules of white wine+250 molecules of red wine (1000:250 –> 4:1 ratio)
Now take 250 molecules of white wine (mixture) and pour it into red wine.
Now 250 molecules of mixture (4:1) => (200 white + 50 red) molecules
Therefore final mixture is:
(800 red+200 white) : (800 white + 200 red)

22. Russ Johnson | Guest

Okay, if you read the question carefully, it never says that the red wine poured into the white wine was actually taken from the bucket of red wine. For all we know, it could have come from another source. If that is true, then there is more red wine when the two buckets are mixed. On the other hand, if you think that the cup of red wine was taken from the bucket of red wine, then there would be equal amounts of red and white wine. By the way, you can’t change the type of wine by changing the color since each type of wine comes from different grapes so I would think that argument about the liquid turning red means “red wine” would not be logical. That is just my opinion.

23. veliah | Profile

Leading off Russ’ answer on the assumpion that the added red wine comes from an outside source, poured into the white busket, mixed, then a cup of the mixture poured back into the red bucket, then there would be more red wine in the white.

Explaination: when you add the cup of red to thw white, by the nature of spacial dispersion ((Objects in a container allways attempt to evenly and equally fill said container unless acted on upon an outside force)) The red wine even disperses into the white wine, meaning that the cup you remove from the mixture would naturally have a large amount of white wine and a very miniscule amount of red wine. this added to the red bucket puts slightly less than a full cup of white wine into the red and a tiny amount of additional red into the red. Truth is, none of this really matters, because we’re assuming the extra wine came from an outside sourse, which means the white bucket has a bucketfull, and the red bucket has a bucket full plus a cup, you can better understand what I’m getting at by assining a numerical value to each bucket and the cup value. Lets assume each bucket starts out holding 10 cups. If this is true then this is what you have at the beginning:

(W will denote white wine, R will denote red)
white bucket = 10W
red bucket = 10R
cup = 1R

We mix the cup into the white bucket, getting this:

White bucket = 10W 1R
Red Bucket = 10R

Mix throughly, and take a cup of the white bucket mixture (not yet adding it) to get this:

White bucket: 9.1 W .9R
red bucket: 10R
Cup: .9W .1R

Following? Next add the cup to the red bucket to get this:

White Bucket = 9.1 W .9R = 10 cups total
Red Bucket = .9W 10.1R = 11 Cups total

if you notice, each bucket has .9 of a cup of the opisite wine in it. HOWEVER, the Red Bucket also had the extra cup. From here, its basic math, get the percentage of each bucket compisiotn. ((percentage is figured by taking the portion you want to figure the percentage of and dividing it by the whole, for instance, 5 beads out of a totall of 100 beads, 5 divided by 100 is .05, or the decimial equivilant of 5 %)) This being the case, it works out like this:

White Bucket = .9 divided by 10 is .09 or 9% red wine in the white
Red Bucket = .9 divided by 11 is .081 repeating, or 8.2% white wine in red

In this case, it is easy to see there is moreRed wine in the white.

Using this same method you can also come to the solution assuming the red wine was taken from the red bucket, and not an outside source. In this case, the wine totals end up being the same! ((Without all the unneeded algebra I might add))

Explination:

Lets use the same 10 cup model, assuming each bucket starts off with 10 cups of each respective wine in it. If so, we start with this:

White Bucket = 10W
Red Bucket = 10R
Cup =nothing

take a cup from the red bucket and add to the white, you get this dilution ratio:

White Bucket = 10W 1R
Red Bucket = 9R
Cup = Empty again

Mix the white bucket and add a cup of the mixture to the red bucket:

White bucket = 9.1 W .9 R
Red Bucket = 9.1 R .9 W

Do the math and you come to the obvious answer:

White Bucket = .9 divided by 10 = .09 or 9%
Red Bucket = .9 Divided by 10 = .09 or 9%

The trick about this whole thing is RATIO. When the cup of red is mixed with 10 cups of white, it is a 10 to 1 Ratio of white to red
(Or 10:1 White/Red) Because the one cup of red with evenly disperse in the 10 cups of white, for every cup thereafter you pull out of the mixed bucket will have a 10:1 ratio just like is source)

The great thing about this riddle truly is that the wording leaves it open to two possible answers, meaning that to just say one or the other would technically by incorrect because of a lack of critical details, in order to correctly answer this riddle, you’d have to explain both possibilities.

^^

24. nitemare | Profile

ok i think. they will be exactly the same

heres my reasoning.

if you have 16oz in each lets say.
you take 1 cup (8oz) of red add to white.
you will have 8oz of red in red bucket and then 8oz red 16oz white in the white bucket. you mix well as it says… you will have a 24oz mixture of 2/3 white 1/3 red.
take 8oz of that out. it will contain 1/3 red 2/3 white. or 2.667 oz red 5.333oz white.
add this to the 8oz of red wine in the red bucket.
so now the red bucket has 10.667oz red 5.333oz white.
the white bucket will have 5.333oz white 10.667oz red.
exactly the same.

25. ian pedder | Profile

Why is everyone assuming that the buckets hold identical amounts? The problem doesn’t say this.

Previous answers 7 and 14 seem to sum it up perfectly.

However, if we are now saying that the original cup of red wine may not have come from the original bucket of red wine (as Russ has noted (22)) then we cannot possible say for sure without knowing the relative sizes of each starting quantity in each bucket and the size of the cup used in the transfer.

Quite frankly, with all this talk of buckets of wine it is no wonder there is a drink problem.

26. brye0909 | Profile

I think:

since the given problem states WINE and not MARBLES nor VARIABLES, mixing is manifested.

A little RED in WHITE = reddishwhite (white is dominant)
A little REDDISHWHITE in RED = littleWHITISHred (RED is dominant!)

That’s all folks!

27. clem | Profile

Its easy theres more RED it never said you got the red from the bottle, it said a glass of red. It didnt specify from the bottle of red there fore there would be more red.
e.g.
30oz of red in a bottle
30oz of white in a bottle
10oz of red in a glass
add it up theres more red

28. avunduk | Profile

There more red wine in the white wine.

29. andymoor | Profile

is everybody here being serious?

Ive had a few glasses of red and white wine, but surely it depends on the size of the bucket and the mug?

The question wasnt to find an equation to figure out the solution to the amount of red and white dependent on the size of the each bucket, size of the mug, wind speed and humidity. It was to see if there is more red or white….

and the answer = we need more detail, surely? too many varying factors. and im 29 years old and not studied science since 16 but my scientist wide just told me the answer was “red” even though she is constantly telling me about her “scientific ways”…. just scientists often overlook so many simple factors that are more relevant than may initially seem.

30. andymoor | Profile

some people just didnt read the question.. id didnt say you should empty the “bucket” of mixed wine!
It said to take a “cup” of mixed wine into the other “bucket”
?????
seems surreal to me, i only went on the net to see if it actually does increase any kind of hangover symptoms to drink red and white wine in one session.

anyone have the answer to that?

31. bilbao | Profile

Original source:
W. W. Rouse Ball in ‘Mathematical Recreations And Problems Of Past And Present Times’, 3rd edition (1896)

Is there more red wine in the white wine or is there more white wine in the red wine?

Answer: There will always be equal proportions of each in each.

This problem assumes each bucket contains equal amounts of wine, and equal amounts are poured into the other. To make this easier to illustrate, let’s say for example that:

* Red bucket: 9 cups of pure red wine.
* White bucket: 9 cups of pure white wine.
* We’ll pour exactly 1 cup from one bucket into the other.

1. Pour 1 cup of red wine into the bucket of white wine, and mix thoroughly. You now have:

* Red bucket: 8 cups of pure red wine.
* White bucket: 10 cups of unpure wine (9 cups of pure white wine and 1 cup of pure red wine).

Any 1 cup in the white wine bucket (thoroughly mixed) will now contain:

* .9 cup white wine and .1 cup red wine.

2. Pour 1 unpure cup from the white wine bucket back into the red wine bucket. You now have added back:

* .9 cup white wine.
* .1 cup red wine.

Since the red wine bucket had 8 cups, you now have 8.1 cups red wine and .9 cup white wine.

The opposite will always be true. You will now have 8.1 cups white wine and .9 cup red wine in the white wine bucket.

It balances out, because you’re adding impure wine back into less pure wine. That’s the secret.

33. syker | Profile

The answer is both. There is now more white wine in the red bucket and more red wine in the white bucketfrom when you started

34. hex | PUZZLE MASTER | Profile

Latest comments on the front page are useful indeed. This is how i located this nice puzzle.
The answer is of course that they are equal.

L = wine volume in each bucket
C = cup volume
R1 and W1 = red and white volumes in red wine bucket
R2 and W2 = red and white volumes in white wine bucket

R1 = L
W1 = 0
R2 = 0
W2 = L

Transfer one cup from bucket 1 to bucket 2:
R1 = L – C
W1 = 0
R2 = C
W2 = L
R2%=C/(L+C)
W2%=L/(L+C)

Transfer one cup from bucket 2 to bucket 1:
The cup will contain C*C/(L+C) red wine and L*C/(L+C) white wine
R1 = L*L/(L+C)
W1 = L*C/(L+C)
R2 = L*C/(L+C)
W2 = L*L/(L+C)

As we can see, R1=W2 and R2=W1

35. bilbao | Profile

Hi Hex, some time ago I scanned the whole smartkit puzzle collection and I found really outstanding puzzles that are unfairly forgotten in older posts. I guess you love math puzzles, so you may want to try i.e. ‘what to do with a camel hair’ or ‘fox chase’.

36. hex | PUZZLE MASTER | Profile

@bilbao, thanks for the tip.

I have just posted my answer to the camel hair puzzle. Will look next at the fox puzzle.

37. desi_soulja | Profile

they are equal
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