## Frank Morgan's Math Chat |

March 2, 2000

**WINNING ANSWER** (Joe Shipman). In the United States, instead of always
starting in Iowa and New Hampshire, a year before the primaries start
choose five congressional districts at random to have a primary the last
week in January and five more the first week in February. This preserves
the advantage of starting small, so that the best-funded candidates don't
have such a huge advantage,
but avoids the distortions caused by always using the same two relatively
atypical states.

An additional idea along these lines is to spread the remaining primaries out evenly over the next 4-5 months to avoid the "Super Tuesday" advantage candidates with early funding get, but there would be a problem in getting states' party organizations to cooperate.

**NEW CHALLENGE.** You can find three equidistant points in the plane
(vertices of any equilateral triangle). Likewise, you can find four
equidistant points on a round sphere (so that the shortest path on the
surface of the sphere between any two of them has the same length). Can you
find five or more equidistant points on other surfaces?

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.