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Re: physics/pedagogy of coffee-mixing



John Denker wrote:

Suppose you have a cup of coffee and a cup of tea. In step 1,
you transfer one spoonful of liquid from the coffee-cup to the
tea-cup. In step 2, you transfer one spoonful of liquid from
the tea-cup back to the coffee-cup. Question: Is there more
tea in the coffee, or more coffee in the tea?

I never heard this question. So let me show how I would answer.
Model each cup as an urn with 1000 balls, black for the coffee and
red for the tea. Suppose one spoonful means 10 balls and that good
mixing occurs after the first transfer. Also that volumes of coffee
and tea balls are identical. Pure water balls are white and can be
ignored in this problem.

After the first transfer we have 990 black balls in one cup and a
mixture of 1010 balls in another. What happens after the second
transfer? It is unlikely that the second spoon will contain more
than one or two black balls. On that basis my answer is that
there is more coffee in the tea than tea in the coffee.

I know of several ways of analyzing this problem, some of
which lead to the right answer, and some of which don't.

To which category does my answer belong? Please summarize
these "several ways", if you can.

So the questions for today are
*) Why do people have a hard time with this riddle?
*) What can be learned from this family of mistakes?
*) In what other circumstances might people be tempted to
make similar mistakes? What are the warning signs?

I would like to know mistakes before trying to answer.
Ludwik Kowalski