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Junior Balkan Mathematical Olympiad 2021- P4

Source: JBMO 2021

July 1, 2021
JuniorBalkanSetsmaximumcombinatorics

Problem Statement

Let MM be a subset of the set of 20212021 integers {1,2,3,...,2021}\{1, 2, 3, ..., 2021\} such that for any three elements (not necessarily distinct) a,b,ca, b, c of MM we have ∣a+b−c∣>10|a + b - c | > 10. Determine the largest possible number of elements of MM.
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