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## Main Question or Discussion Point

Given are two equally full cans containing two different but miscible fluids and one smaller, empty cup.

Take one cup of one of the liquids and pour its contents into the can containing the other liquid, similarly, take one cup of the resulting mixture and pour it back into the other can. This results in two mixtures of equal volume but of different concentrations.

Set this transfer equal to n = 1.

(You might have encountered this set-up in the form of a brain teaser, the tease being the relationship between the transferred liquids. The answer is equality.)

Now consider f(n), the concentration of one of the liquids in one of the cans after n transfers.

What is f(n)?

Take one cup of one of the liquids and pour its contents into the can containing the other liquid, similarly, take one cup of the resulting mixture and pour it back into the other can. This results in two mixtures of equal volume but of different concentrations.

Set this transfer equal to n = 1.

(You might have encountered this set-up in the form of a brain teaser, the tease being the relationship between the transferred liquids. The answer is equality.)

Now consider f(n), the concentration of one of the liquids in one of the cans after n transfers.

What is f(n)?

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