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Problem of the Week 889

Putnam Probabilities

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Some friends were sitting around a table and each of them estimated the probability that he or she would score 20 or more on the Putnam competition. It turned out that all the probabilities were different.

Alice then observed that her probability of breaking 20 was equal to the probability that at least one of her friends present would not break 20. Bob then observed that this statement was true for everyone sitting at the table. How many people were sitting around the table?

Source: Mathematics and Informatics Quarterly; 4/98 Vol 8 p. 179

This is the last POW of the semester. The POWs will start again in September, of course. I am now in Colorado for the summer working on various projects. In July, I teach my annual Rocky Mountain Mathematica course (a few spots still available).

If you do send me problems to consider, do send solutions as well, as I get quite a few suggestions and cannot work them all out myself.

© Copyright 1999 Stan Wagon. Reproduced with permission.

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27 April 1999