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MathNet 1968 — Part 01 Question 13

Math Olympiad Vault · MathNet 1968 — Part 01

Question 13

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.