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dividing a 600x600 square in 4 types of cells

Source: Tuymaada Junior 2007 p3

May 12, 2019
combinatoricscombinatorial geometrynumber theorydivisible

Problem Statement

A square 600×600 600 \times 600 divided into figures of 44 cells of the forms in the figure: In the figures of the first two types in shaded cells The number 2k 2 ^ k is written, where k k is the number of the column in which this cell. Prove that the sum of all the numbers written is divisible by 99.
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