PROBLEM OF THE MONTH
March 2006
Congratulations to this month winners Say Cheong, Itamar Gal,
Clayton Bailey-Assam and Amghibech Said!
Solution by Itamar Gal: [pdf]
There are three colleges in a town.
Each college has n students.
Any student of any college knows n+1 students
of the other two colleges.
Prove that it is possible to choose a student
from each of the three colleges so that all three
students would know each other.
Hint: solve this problem for small n first
(take n=2,3,4).
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: April 10th at 12 pm.