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MathNet 2006 — Part 04 Question 86

Math Olympiad Vault · MathNet 2006 — Part 04

Question 86

In a group of students, 50 students speak German, 50 students speak French and 50 students speak Spanish. Some students speak more than one language.
Prove that the students can be divided into 5 groups so that in each group exactly 10 students speak German, 10 French and 10 Spanish.