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MathNet 2016-part-05 — 184 problems (EN–VI) Question 41

Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)

Question 41

A group of tourists get on 10 buses in the outgoing trip. The same group of tourists get on 8 buses in the return trip. Assuming each bus carries at least 1 tourist, prove that there are at least 3 tourists such that each of them has taken a bus in the return trip that has more people than the bus he has taken in the outgoing trip.