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square was cut in n rectangles with sides a_i x b_j, min n for different a_i,b

Source: Sharygin 2005 VIII-X CR 11

August 18, 2019
combinatorial geometrycombinatoricsgeometryrectangle

Problem Statement

The square was cut into n2n^2 rectangles with sides ai×bj,i,j=1,...,na_i \times b_j, i , j= 1,..., n. For what is the smallest nn in the set {a1,b1,...,an,bn}\{a_1, b_1, ..., a_n, b_n\} all the numbers can be different?
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