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From: dim@whuxlm.UUCP (McCooey David I)
Newsgroups: net.puzzle
Subject: Re: Mixing Liquids
Message-ID: <911@whuxlm.UUCP>
Date: Thu, 20-Mar-86 10:57:44 EST
Article-I.D.: whuxlm.911
Posted: Thu Mar 20 10:57:44 1986
Date-Received: Sat, 22-Mar-86 02:19:29 EST
References: <1907@trwrba.UUCP> <184@winston.UUCP>
Organization: AT&T Bell Laboratories, Whippany
Lines: 50

> 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