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Part of 2012 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

rectangle is divided into n^2 smaller by n - 1 horizontal and n-1 vertical

Source: Rioplatense Olympiad 2012 level 3 P2

9/4/2018
A rectangle is divided into n2n^2 smaller rectangle by n−1n - 1 horizontal lines and n−1n - 1 vertical lines. Between those rectangles there are exactly 56605660 which are not congruent. For what minimum value of nn is this possible?
combinatorial geometrycombinatoricsrectangleminimum