Question 98
Let $A_1, A_2, \dots, A_{160}$ be set such that $|A_i|=i$, $i=1, 2, \dots, 160$. Using the elements of these sets we construct new sets $M_1, M_2, \dots, M_n$ with the following procedure: At the first step we choose some of the sets $A_1, A_2, \dots, A_{160}$ and we subtract from each of them the same number of elements. All these elements are the elements of the set $M_1$. At the second step we repeat the same procedure to the remaining sets after the application of the first step and we define the set $M_2$. We continue in this way until all sets $A_1, A_2, \dots, A_{160}$ become the empty set and we define the sets $M_3, \dots, M_n$. Find the minimal value of $n$.