IMO 2022 Shortlist C1
A ˘1-sequence is a sequence of 2022 numbers a1,...,a2022, each equal to either 1 or ´1. Determine the largest C so that,...
Category: Combinatorics
Problem
A ˘1-sequence is a sequence of 2022 numbers a1,...,a2022, each equal to either 1 or ´1. Determine the largest C so that, for any ˘1-sequence, there exists an integer k and indices 1 ď t1 ă ... ă tk ď 2022 so that ti1 ´ ti ď 2 for all i, and
k ÿ
i“1
ati
ě C.
(Czech Republic)