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....[Ludwik]my answer is that
there is more coffee in the tea than tea in the coffee.
...Oops, sorry, this is going down the wrong track. But I suppose it
illustrates my assertion that the wrong answers are very attractive.
Here's my analysis of the problem
1) The incisive qualitative analysis: There is a conservation law: In the
final state there are 2000 balls total (red+black) and 1000 balls in each
urn. Each red ball in the black urn displaces one black ball, which must
(by conservation) be in the other urn. Therefore there is _exactly_ the
same amount of coffee in the tea as tea in the coffee.
You don't even need to assume perfect mixing.
2) You can do numerical examples until you're convinced that the
concentrations always wind up the same. This alas loses some insights,
such as the (non)role of mixing....
Anybody else have thoughts on why this riddle is more challenging than it
looks?