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square 1000x1000 divides into 31 square tiles

Source: 2022 Austrian Federal Competition For Advanced Students, Part 2 p6

October 5, 2022
combinatoricstilesTiling

Problem Statement

(a) Prove that a square with sides 10001000 divided into 3131 squares tiles, at least one of which has a side length less than 11.
(b) Show that a corresponding decomposition into 3030 squares is also possible.
(Walther Janous)
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