IMO 2023 Shortlist A5
Let a1,a2,...,a2023 be positive integers such that • a1,a2,...,a2023 is a permutation of 1,2,...,2023, and • |a1 ´ a2|,|...
Category: Algebra
Problem
Let a1,a2,...,a2023 be positive integers such that • a1,a2,...,a2023 is a permutation of 1,2,...,2023, and • |a1 ´ a2|,|a2 ´ a3|,...,|a2022 ´ a2023| is a permutation of 1,2,...,2022. Prove that max ` a1,a2023 ˘ ě 507. (Australia) 4 Chiba, Japan, 2nd–13th July 2023