3

Part of 2007 Junior Tuymaada Olympiad

Problems(1)

dividing a 600x600 square in 4 types of cells

Source: Tuymaada Junior 2007 p3

600 \times 600

divided into figures of

4

cells of the forms in the figure: In the figures of the first two types in shaded cells The number

2 ^ k

is written, where

k

is the number of the column in which this cell. Prove that the sum of all the numbers written is divisible by

9

combinatoricscombinatorial geometrynumber theorydivisible