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Guess the Largest Number

by

Professor Alan Taylor
Union College

January 17, 2005
4:30 pm
Blue House

Pastries and drinks will be served


Abstract:

Consider the following game. I give you a stack of one million blank index cards. On each one, you write any real number that you want (e.g., -17, pi, 22/7, 10-to-the-84th, etc.). I don't know anything about your choice of numbers, except that there are a million of them, and they're all distinct. The deck is then placed face down on a table, and I begin to turn the cards over, one by one. At some point, I stop turning cards and declare that the last card that I turned over contained the largest of all the numbers you wrote. If I'm wrong, I give you a dollar. If I'm right, you give me two dollars. Remarkably, there is a strategy whereby, in the long run, I come out ahead.


For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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