MathDB

Regional Olympiad - FBH 2010 Grade 10 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2010

September 27, 2018

combinatoricsSets

Problem Statement

It is given set with

n^2

elements

(n \geq 2)

and family

\mathbb{F}

of subsets of set

A

, such that every one of them has

n

elements. Assume that every two sets from

\mathbb{F}

have at most one common element. Prove that

i)

Family

\mathbb{F}

has at most

n^2+n

elements

ii)

Upper bound can be reached for

n=3