MathDB

Problem 8 of First round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022

set theory

Problem Statement

A subset of the set

A={1,2,\dots ,n}

is called connected, if it consists of one number or a certain amount of consecutive numbers. Find the greatest

k

(defined as a function of

n

) for which there exists

k

different subsets

A_1,A_2,…,A_k

A

the intersection of each two of which is a connected set.