Correct solutions were sent in from Bradley students Kenny Koch, Michelle McCluer, Nathan Pauli, Ray Kremer, Kyle Ambroso, Paul Leisher; a partial solution was submitted by Courtney Pelowski.   Correct solutions were also received from Cyril Terakopiantz, Tim Kelley (two solutions), Philippe Fondanaiche, William Troxel, Robert McQuaid, Aaron Kahn, Burkart Venzke, Anuradha Ratnaweera, William Webb, Tushar Sharma.  A extraspecial mention to Gregory Falcon for his most excellent solution!

The answer is 1/e.

The following presentation is due to Tim Kelley.

First, imagine a scenario similar to but not quite the same as the one described in the problem, where for some positive integer k you do the following:

Let 1/k cups leak from the bottom cup.  After this has happened, 
Let 1/k cups leak from the top cup. 
Repeat these steps k times.

After the first part of the first step, the bottom cup will have 1 - (1/k) = (k-1)/k cups of water remaining.  The addition of the wine from the top cup in the secod part of the first step will not change this amount.  Each succesive cycle of the two steps will result in the amount of water remaining being diminished by 1/k of what was there, so the amount remaining is, again, 1 - (1/k) of the previous amount.  This means that after n steps, you have [(k-1)/k]ⁿ cups of water remaining in the bottom cup.  Specifically, after all k steps are done, you'll have

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Page last updated 15 September 1999.