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(2): Solution (???) by nikki)

To Charlie:
I think you misread.  I changed the problem to make 50 groups, not 5 groups.

To Nikki:
Yes, I did make a new problem statement.  I might not have read your solution carefully enough, but it seems your proof would apply to the new case I created.  In other words, the same proof could be used to prove my new problem statement.  But since a counterexample exists for my new problem statement, your proof must be invalid.

That does not mean that there is a counterexample in the original problem.  I doubt there is.

Posted by Tristan on 2004-11-11 18:26:52