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Speaking Volumes (Posted on 2004-11-10) Difficulty: 3 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 3.1667 (6 votes)

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re(2): Solution (yes, too informal) | Comment 5 of 18 |
(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
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