MathDB

3

Part of 2019 China Girls Math Olympiad

Problems(1)

An operation to change a sequence into another one

Source: China Girls Math Olympiad 2019 Day 1 P3

8/12/2019
For a sequence, one can perform the following operation: select three adjacent terms a,b,c,a,b,c, and change it into b,c,a.b,c,a. Determine all the possible positive integers n≥3,n\geq 3, such that after finite number of operation, the sequence 1,2,⋯ ,n1,2,\cdots, n can be changed into n,n−1,⋯ ,1n,n-1,\cdots,1 finally.
combinatorics