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All-Soviet-Union Mathematical Olympiad

Geometry Difficulty 6.0 AIME, harder Prove it Soviet Union

Problem:

Does there exist a rectangle which can be dissected into 15 congruent polygons which are not rectangles? Can a square be dissected into 15 congruent polygons which are not rectangles?

Solution

Solution:

yes, yes

By stretching vertically we get a square.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.