In a group of students, 50 speak English, 50 speak French and 50 speak Spanish. Some students speak more than one language. Prove it is possible to divide the students into 5 groups (not necessarily equal), so that in each group 10 speak English, 10 speak French and 10 speak Spanish.

(In reply to re: Solution (yes, too informal) by Tristan)

In each of the 5 groups to be formed, take 5 from each of the subsets you mention.  That is, each of the new groups has 5 people who speak Spanish and English, 5 people who speak English and French, and 5 people who speak French and Spanish.

It is not a counterexample.

Posted by Charlie on 2004-11-11 14:34:17