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max no of partitions of an n x n square

Source: Israel Grosman Memorial Mathematical Olympiad 1997 p5

February 15, 2020
combinatoricscombinatorial geometry

Problem Statement

Consider partitions of an n×nn \times n square (composed of n2n^2 unit squares) into rectangles with one integer side and the other side equal to 11. What is the largest possible number of such partitions among which no two have an identical rectangle at the same place?
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