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 Solution (possibly too informal) by nikki)

Not to contradict the gist your solution, yet, given the problem statement, even though the minimum number of students one could have is 50, the maximum is not 150. Some students may be unable to speak English, French or Spanish. Some of these other students may also be multilingual.

Even though it is possible to have these additional students who speak none of the three "primary" languages, their number will have no impact on the solution as they can be added individually, in part or in whole to any of the five groups.

Posted by Dej Mar on 2008-09-30 08:07:04