Originally posted by FabianFnasWell, as a simple minded person, I would use black and white marbles instead of paint. Since the buckets start with equal amounts, start with 100 black marbles in bucket A and 100 white marbles in bucket B.
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 n ...[text shortened]... em loses some of its interest.
So - how should the problem be formulated to be as intended?
Take a handful of black marbles from A and count them, then put them in bucket B.
Now remove exactly the number of marbles that were added to B and put them back in bucket A, without regard to the marble color.
You now have the same number or white marbles in bucket A as you have black marbles in bucket B.
Originally posted by RedDevil4LifeThe problem isn't the color, it's the stuff (paint) in the buckets. What's needed is a material that can be mixed, yet retains its identity (marbles work, as mwmiller mentioned).
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?
Originally posted by mwmillerNice analogy. Kind of puts it in black and white. 😛
Well, as a simple minded person, I would use black and white marbles instead of paint. Since the buckets start with equal amounts, start with 100 black marbles in bucket A and 100 white marbles in bucket B.
Take a handful of black marbles from A and count them, then put them in bucket B.
Now remove exactly the number of marbles that were added to B ...[text shortened]... You now have the same number or white marbles in bucket A as you have black marbles in bucket B.
Originally posted by mwmillerVery interesting, mwmiller, I might say! You certainly take us to a higher degree of understanding what’s it all about. 🙂 Those who can’t follow the mathematics about the problem can easy experiment with his marbles instead of real paint.
Well, as a simple minded person, I would use black and white marbles instead of paint. Since the buckets start with equal amounts, start with 100 black marbles in bucket A and 100 white marbles in bucket B.
Take a handful of black marbles from A and count them, then put them in bucket B.
Now remove exactly the number of marbles that were added to B ...[text shortened]... You now have the same number or white marbles in bucket A as you have black marbles in bucket B.
Now, the number of marbles doesn't matter, nor does the size of the buckets. Instead I can use of any object I choose as long they are distinguishable from each other.
Okay, I choose grains. White grains and black grains. A lot of them. Thousands, even millions of them, why not billions, even trillions of them? But then they has to be small. I put equal amounts of white grains in a bucket and equally much black grains in another and perform the experiment.
But I now see that the grains stick to the surface of the buckets electro statically so I use a solvent in order to handle the grains as a fluid. I use water or oil or something. The grains then solves into the medium into molecules and the two fluids appear to be black and white.
What do I get? Answer: Paint!
But when I blend the paint I get gray paint, not white paint with black in it, nor white paint with black in it. But I could use a microscope, perhaps an electron microscope or still better a mass-spectrograph to evaluate the number of black and white molecules.
And now we’re back to the original problem.
So there seems to be the same problem, either it is a known number of marbles or if it is an unknown and high number of color grains. I say – very interesting!
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Originally posted by FabianFnasYour original post did not present any 'unknown'.
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So there seems to be the same problem, either it is a known number of marbles or if it is an unknown and high number of color grains. I say – very interesting![/b]
It started with equal amounts, and the amount that was moved back and forth was equal.
Originally posted by mwmillerThe only amount presented was one unit of each, i.e. the same amount black as white paint.
Your original post did not present any 'unknown'.
It started with equal amounts, and the amount that was moved back and forth was equal.
If this amount was 1 litre, 1 gallon or 1 pint, doesn't matter.
But no unit was given, hence unknown.
Originally posted by FabianFnasI agree that the 'unit of measure' does not matter.
The only amount presented was one unit of each, i.e. the same amount black as white paint.
If this amount was 1 litre, 1 gallon or 1 pint, doesn't matter.
But no unit was given, hence unknown.
However, if you know that they are the same amount, and the amount moved back and forth is the same, then it is not unknown, because you know they are the same.