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

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

We start with:
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

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.

anyone have the answer to that?

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.

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!

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.

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.

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.