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Maximum good numbers in a circle

Source: IMOC 2021 C1

August 11, 2021
combinatoricsIMOC

Problem Statement

The numbers 1,2,⋯ ,20211,2,\cdots,2021 are arranged in a circle. For any 1≤i≤20211 \le i \le 2021, if i,i+1,i+2i,i+1,i+2 are three consecutive numbers in some order such that i+1i+1 is not in the middle, then ii is said to be a good number. Indices are taken mod 20212021. What is the maximum possible number of good numbers?
CSJL
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