MathDB

We define the sets

A_1,A_2,...,A_{160}

such that

\left|A_{i} \right|=i

for all

i=1,2,...,160

. With the elements of these sets we create new sets

M_1,M_2,...M_n

by the following procedure: in the first step we choose some of the sets

A_1,A_2,...,A_{160}

and we remove from each of them the same number of elements. These elements that we removed are the elements of

M_1

. In the second step we repeat the same procedure in the sets that came of the implementation of the first step and so we define

M_2

. We continue similarly until there are no more elements in

A_1,A_2,...,A_{160}

, thus defining the sets

M_1,M_2,...,M_n

. Find the minimum value of

n

Problem Statement