March 2, 2000
OLD CHALLENGE. Propose a new system for selecting Presidential candidates.
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.
Copyright 2000, Frank Morgan.