foreman@winston.UUCP (Alastair Foreman) (03/14/86)
Here is an interesting puzzle, which I must confess I already know the
answer to, but would like to know the ELEGANT solution. I will post a
summary if there is sufficient response.
Puzzle:
Take a half a cup of tea, and a half a cup of coffee.
Take one tablespoon of the tea and mix it in with the coffee.
Take one tablespoon of the mixture and mix it back in with the tea.
The question is, which of the two cups (if either) contains more of
its original contents, and WHY.
Remember, I'm looking for simple, elegant solutions here....
enjoy
--
Alastair Foreman
New Media Technologies Ltd.
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Burnaby, B.C., Canada,
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(604) 291-7111ugfailau@sunybcs.UUCP (Fai Lau) (03/19/86)
> > Here is an interesting puzzle, which I must confess I already know the > answer to, but would like to know the ELEGANT solution. I will post a > summary if there is sufficient response. > > Puzzle: > > Take a half a cup of tea, and a half a cup of coffee. > Take one tablespoon of the tea and mix it in with the coffee. > Take one tablespoon of the mixture and mix it back in with the tea. > > The question is, which of the two cups (if either) contains more of > its original contents, and WHY. > > Remember, I'm looking for simple, elegant solutions here.... > The answer is neither one. Since the resulted volumns of both liquids haven't changed, and they are equal to begin with, whatever amount of original liquid one container loses must be replaced by the same amount of liquid which are originally found in the other container. So it follows that the other container loses the exact same amount of its original liquid. And the solution goes that the two containers eventually not only have the same amount of their original liquids, but the same amount of foreign liquids as well. +-----------------------------------------------------------------------------+ | Fai Lau | | ECE / CS SUNYAB | | BI: ugfailau@sunybcs | +-----------------------------------------------------------------------------+
mmar@sphinx.UChicago.UUCP (Mitchell Marks) (03/20/86)
In article <184@winston.UUCP> foreman@winston.UUCP (Alastair Foreman) writes: > >Here is an interesting puzzle, which I must confess I already know the >answer to, but would like to know the ELEGANT solution. I will post a >summary if there is sufficient response. > >Puzzle: > > Take a half a cup of tea, and a half a cup of coffee. > Take one tablespoon of the tea and mix it in with the coffee. > Take one tablespoon of the mixture and mix it back in with the tea. > > The question is, which of the two cups (if either) contains more of > its original contents, and WHY. > >Remember, I'm looking for simple, elegant solutions here.... > >enjoy > >-- If the amounts transferred are exactly equal, so that each container ends up with its original volume, then the amount of coffee in the tea and the amount of tea in the coffee have to be the same (or, as A.F. poses the question, the amount of coffee left in the cup that was originally pure coffee, and the amount of tea left in the cup that was originally pure tea, are the same.) Since coffee and tea aren't pure substances, and this should be a puzzle about logic, not physical chemistry and the geometry of molecules, let's make this two urns that start out with all red marbles in one and all blue marbles in the other. What you *don't* want to do is start asking how well it's stirred, and get into probabilities. The answer is independent of how well you stir. So we start out with R red marbles and B blue marbles in separate urns, (they can be different, it doesn't affect the answer); we transfer X red marbles into the blue urn, stir perhaps well or perhaps not, and transfer X marbles of the mixture back to the red urn. Now the red urn has R-X+X = R total marbles again. A certain number of them, Y, are blue, 0 <= Y <= X. So the red urn still has R-Y red marbles. It is missing Y of the original R red marbles. These red marbles have to be over in the blue urn; and they are the only red marbles in the blue urn. So the blue urn has B-Y blue marbles left. Each urn has Y marbles of the non-original color, and [original number] - Y of the original color marbles. And this holds regardless of the exact value of Y. We would bring in probability and discuss stirring only if we wanted to estimate Y -- but we don't need Y. -- -- Mitch Marks @ UChicago ...ihnp4!gargoyle!sphinx!mmar
dim@whuxlm.UUCP (McCooey David I) (03/20/86)
> Puzzle: > > Take a half a cup of tea, and a half a cup of coffee. > Take one tablespoon of the tea and mix it in with the coffee. > Take one tablespoon of the mixture and mix it back in with the tea. > > The question is, which of the two cups (if either) contains more of > its original contents, and WHY. > > Remember, I'm looking for simple, elegant solutions here.... > > enjoy Solution: (The cups contain EQUAL amounts of their original contents.) We begin with equal amounts of coffee and tea, right? We end up with a half cup of liquid in each cup, right? (this is the key...) The cups must therefore contain the SAME amount of their original contents, RIGHT? If, say, the tea cup ends up with more tea in it than the amount of coffee in the coffee cup, then there must be less coffee in the tea cup than the amount of tea in the coffee cup (because each cup ends up with the SAME amount of liquid). But this means that there is more tea (total) than coffee (total), which is impossible: | | | | |_______________| This |_______________| | COFFEE | situation | | |_______________| is | TEA | | | impossible |_______________| | | because | | | | there | | | TEA | is | COFFEE | | | more | | | | tea | | |_______________| |_______________| TEA CUP COFFEE CUP The nice thing about this problem is that it doesn't even matter how (badly) the tea is mixed in with the coffee, as long as the same amount of liquid is returned to the tea cup. Dave McCooey AT&T Bell Labs, Whippany ihnp4!whuxlk!dim
twb@mhuxh.UUCP (twb) (03/21/86)
> Puzzle: > > Take a half a cup of tea, and a half a cup of coffee. > Take one tablespoon of the tea and mix it in with the coffee. > Take one tablespoon of the mixture and mix it back in with the tea. > > The question is, which of the two cups (if either) contains more of > its original contents, and WHY. > > Remember, I'm looking for simple, elegant solutions here.... > 1. T represents Tea, C represents Coffee 2. Start with 8 tbl(=1/2cup) of each. 8T 8C 3. Coffee get 1T 7T 8C+1T 4. 1 tbl of the C mixture is 1/9T+8/9C 5. Put that into the T cup 7 1/9T+ 8/9C 7 1/9C+ 8/9T 6. Each cup has 7 1/9 tbl of the original contents and 8/9 tbl of the other liquid. QED Tom.