6

Part of 2022 Austrian MO National Competition

Problems(1)

square 1000x1000 divides into 31 square tiles

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

(a) Prove that a square with sides

1000

31

squares tiles, at least one of which has a side length less than

1

.
(b) Show that a corresponding decomposition into

30

squares is also possible.
(Walther Janous)

combinatoricstilesTiling