## Frank Morgan's Math Chat |

September 7, 2000

Math Chat invites readers to submit further examples of questionable mathematics.

**Old Challenge** (Al Zimmermann). For some reason you need a standard fair die
(with the numbers from 1 to 6 on the six faces). All you have is an unfair
"loaded" die. How can you use the loaded die to fairly choose random
numbers from 1 to 6?

**Answer **(José Cañizo and Arthur Pasternak). Roll the die three times. If you
don't get three different numbers, start over. When you get three different
numbers, the highest roll H, the middle roll M, and the lowest roll L can
occur in six, equally likely patterns: HML, HLM, MHL, MLH, LHM, and LMH,
which can be associated with the numbers from 1 to 6.

**New Challenge.** In the September ACBL Bridge Bulletin, Noreen Wurdemann of
the Bahamas reports that the two bridge hands below were dealt out at her
club. She says that she is "100% certain there was no hanky-panky." What is
the probability of this happening among say 28 boards? somewhere in the
world in a year? in a century? How do you explain this report?

Send answers, comments, and new questions by email to
Frank.Morgan@williams.edu, to be eligible for* Flatland *and other book
awards. Winning answers will appear in the next Math Chat. Math Chat
appears on the first and third Thursdays of each month. Prof. Morgan's
homepage is at www.williams.edu/Mathematics/fmorgan.

THE MATH CHAT BOOK, including a $1000 Math Chat Book QUEST, questions and answers, and a list of past challenge winners, is now available from the MAA (800-331-1622).

Copyright 2000, Frank Morgan.