PROBLEM OF THE MONTH

April 2005




Congratulations to Jonathan Inbal and Clayton Bailey-Assan, who solved this problem!

In the plane, there are n blue points and n red points. Prove that one can always draw n disjoint segments, each connecting a blue point with a red point.

Hint: Start with n=2, and then try to work out the cases n=3,4,... Partial proofs (e.g. for n=5) will be considered.

Remark (thanks to Jonathan Inbal and Clayton Bailey-Assan). Some non-degeneracy assumptions are needed here. E.g. if there are only four points lying on the same line, then the statement is obviously wrong. But this is a degenerate case. You may assume, for example, that no triple of points is collinear.

This month's prize will be awarded to the best explained, correct solution.


Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to problem@math.sunysb.edu by the due date. Acceptable electronic formats are: PDF, Postscript, DVI, (La)TeX, or just plain text. Please include your name and phone number, or preferably your email address.

Closing date: May 10th at 12 pm.