IMO 2022 Shortlist C7
Lucy starts by writing s integer-valued 2022-tuples on a blackboard. After doing that, she can take any two (not necessa...
Category: Combinatorics
Problem
Lucy starts by writing s integer-valued 2022-tuples on a blackboard. After doing that,
she can take any two (not necessarily distinct) tuples v “ pv1,...,v2022q and w “ pw1,...,w2022q
that she has already written, and apply one of the following operations to obtain a new tuple:
v w “ pv1 w1,...,v2022 ` w2022q
v _ w “ pmaxpv1,w1q,...,maxpv2022,w2022qq
and then write this tuple on the blackboard.
It turns out that, in this way, Lucy can write any integer-valued 2022-tuple on the blackboard
after finitely many steps. What is the smallest possible number s of tuples that she initially
wrote?
(Czech Republic)