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MathNet 2009-part-03 — 175 problems (EN–VI) Question 4

Math Olympiad Vault · MathNet 2009-part-03 — 175 problems (EN–VI)

Question 4

The students of class $IV^{a}$ are members of the ecological, the literary or the mathematical club. Five students are members of all three clubs, and nine students are members of exactly two clubs. The ecological and literary clubs have 8 students in common, and the same number of students is in both the literary and the mathematical club. Also, 20 students are members of only one club, namely 5 each in the ecological and the mathematical club. How many students are there in class $IV^{a}$?