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RU-SPB 2020 Problem 101

  • Grade 10

Andryusha has 100100 stones of different weight and he can distinguish the stones by appearance, but does not know their weight. Every evening, Andryusha can put exactly 1010 stones on the table and at night the brownie will order them in increasing weight. But, if the drum also lives in the house then surely he will in the morning change the places of some 22 stones.Andryusha knows all about this but does not know if there is a drum in his house. Can he find out?

Dataset text AI-MO AoPS. Quoted with source.

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