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divide a 1 by 1 square into rectangles with the same circumference

Source: Dutch NMO 2014 p5

September 7, 2019

geometryrectanglecombinatoricscombinatorial geometrycircumradius

Problem Statement

We consider the ways to divide a

1

1

square into rectangles (of which the sides are parallel to those of the square). All rectangles must have the same circumference, but not necessarily the same shape. a) Is it possible to divide the square into 20 rectangles, each having a circumference of

2:5

? b) Is it possible to divide the square into 30 rectangles, each having a circumference of

2

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