# Black and white paint

FabianFnas
Posers and Puzzles 26 Oct '06 08:38
1. 26 Oct '06 08:38
Assume you have two buckets, one with black paint, one with exactly the same amount of white paint. They are not filled up entirely, they have enough free space to perform following actions:

(1) Pour some of the black paint over to the bucket with the white paint. (Stir the bucket if you want or don't stir it.)
(2) Then pour back exactly the same amount of the black and white mixture back to the first bucket. (Stir again but you don't have to.)

Now - this is the question:
Is there more white paint in the black paint as there is black paint in the white paint?
2. 26 Oct '06 09:14
I think it should be equal as however much black paint goes back to its origional bucket stops that amount of white paint getting into the black bucket.

Let b be the amount of black paint transfered and w the amount of white paint transfered. T is the total amount transfered. The numbers represent transactins 1 and 2.

T1 = b1 ---> T1 black paint in white bucket

T1 = T2 = b2 + w2 ---> T1 - b2 black paint in white bucket
w2 white paint in black bucket

and T1 - b2 = w2

there fore there is the same amount of white paint in the black bucket as there is black paint in the white bucket.

Sorry if this is not explained very well.
3. 26 Oct '06 12:18
The answer is simple. It is equal.
In words - When pouring the paint the second time(i.e. When pouring the mixture into the "black bucket"ðŸ˜‰ the amount of white paint that comes out of the "white bucket", obviously, equals the amount of white paint that goes in the "black bucket",
and amount of black paint that remains in the "white bucket" equals the amount of black paint that is missing from the "black bucket".
And Since the total paint in each bucket is equal at the end; then the amount of black paint missing from the "black bucket" equals the amount of white paint in that bucket,
and the amount of white paint missing from the "white bucket" equals the amount of black paint in that bucket,
thus the amount of white paint in the "black bucket" and the amount of black paint in the "white bucket" are equal.
4. 26 Oct '06 12:27
It has to be equal as if it wasnt the puzzle could easily be resolved by a multitude of counterexamples showing how it was not equal. To be a good puzzle therefore the amounts have to be equal.
5. 26 Oct '06 12:331 edit
And here is the proof in maths terms:
Let black paint be b.
Let white paint be w.
Let the total amount of initial paint in a bucket be t.

therefore: black bucket = tb and
white bucket = tw

Let the amount of paint poured out first be x.

black bucket = tb - xb

white bucket = tw + xb

Let the amount of white paint in mixture be y and black paint be z, such that y + z = x (i)

black bucket = tb - xb + (yw + zb)
black bucket = tb - xb + yw + zb
black bucket = (t - x + z)b + yw

white bucket = tw + xb - (yw + zb)
white bucket = tw + xb - yw - zb
white bucket = (t - y)w + (x - z)b

BUT from (i): y = x - z

therefore :
black bucket = (t - y)b + yw

white bucket = (t - y)w + yb

Thus the amount of black paint in the white bucket = the amount of white paint in the black bucket.
6. mwmiller
RHP Member No.16
26 Oct '06 12:37
once black paint is added to the white, it becomes gray and there is now no more white paint. When you add the gray paint to the remaining black paint, it also becomes gray and there is now no black or white paint.
7. 26 Oct '06 12:39
Originally posted by mwmiller
once black paint is added to the white, it becomes gray and there is now no more white paint. When you add the gray paint to the remaining black paint, it also becomes gray and there is now no black or white paint.
This is the thinking of simple minded people
8. mwmiller
RHP Member No.16
26 Oct '06 12:46
Originally posted by RedDevil4Life
This is the thinking of simple minded people
True, but is my answer correct?
9. 26 Oct '06 12:48
Originally posted by mwmiller
True, but is my answer correct?
You have not read the previous posts have you?
10. 26 Oct '06 13:03
Originally posted by RedDevil4Life
You have not read the previous posts have you?
I bet he did. But his answer is correct. The puzzle should have been reworded to avoid this complication.
11. 26 Oct '06 13:16
Originally posted by Mephisto2
I bet he did. But his answer is correct. The puzzle should have been reworded to avoid this complication.
I am not the one that started this thread, but if I am correct this has nothing to do with the colour of the paint.
12. 26 Oct '06 13:21
Originally posted by RedDevil4Life
I am not the one that started this thread, but if I am correct this has nothing to do with the colour of the paint.
It has ALL to do with the colour of the paint. But to be fair, even in this case, the answer is: equal (because there is no white or black paint anymore).
13. 26 Oct '06 13:31
Originally posted by Mephisto2
It has ALL to do with the colour of the paint. But to be fair, even in this case, the answer is: equal (because there is no white or black paint anymore).
There is still both white and black paint, it is just not seen.
14. 26 Oct '06 13:32
Originally posted by RedDevil4Life
I am not the one that started this thread, but if I am correct this has nothing to do with the colour of the paint.
I am the one started this thread, and yes, the puzzle should be formulated so this confusion wouldn't be.

The solution to the problem is as we've heard earlier:
There is as much white paint in the black bucket as black paint in the white bucket.

If a mixture of black and white paint is no longer white paint in black or black paint in white so we no have shades of gray instead the problem loses some of its interest.

So - how should the problem be formulated to be as intended?
15. 26 Oct '06 13:42
Dont mention colour. Just say paint in bucket 1 and paint in bucket 2.
Then: Buckets 1 and 2 are of the same size and have equal amounts of paint in them. If you were to throw some of the paint of bucket 1 into bucket 2. then throw the same amount paint as thrown before of the mixture into bucket 2. Will the amount of bucket 1's initial paint in bucket 2 be less than the amount of bucket 2's initial paint in bucket 1?