November 2, 2000
Old Challenge. Suppose all that any voter in the US cares about is that different parties control the Presidency and the Congress. If there is no communication, how should each voter vote?
Answer. Jonathan Falk suggests that everyone should vote the President (s)he prefers and vote the opposite party for Congress. In such a close election as this year, however, that method could narrowly elect a Republican President for example without losing the Republican Congress. Joe Shipman suggests a more reliable method, based on the current division of control: everyone should vote Democratic for President and Republican for Congress.
Math Anagram. Joe Shipman asks for anagram math equations, such as
ELEVEN + TWO = TWELVE + ONE,
in which the letters on the left can be rearranged to yield the letters on the right.
New Challenge (reappeared on recent "Green Chicken" math competition between Middlebury, Simon's Rock, and Williams College).
1. What is the expected (average) length of the shorter piece of a meter stick with a random cut?
2. What is the expected length of the shortest of 3 pieces from 2 random cuts?
3. What is the expected length of the shortest of 4 pieces from 3 random cuts?
4. What is the expected length of the shortest of n pieces from n-1 random cuts?
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.