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Dissecting a rectangle into similar non-congruent ones

Source: 42nd International Tournament of Towns, Senior A-Level P5, Fall 2020

February 18, 2023
combinatoricscombinatorial geometryTournament of Towns

Problem Statement

Does there exist a rectangle which can be cut into a hundred rectangles such that all of them are similar to the original one but no two are congruent?
Mikhail Murashkin