The square was cut into $n^2$ rectangles with sides $a_i \times b_j, i , j= 1,..., n$. For what is the smallest $n$ in the set $\{a_1, b_1, ..., a_n, b_n\}$ all the numbers can be different?
Problem
Source: Sharygin 2005 VIII-X CR 11
Tags: combinatorial geometry, combinatorics, geometry, rectangle