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green or blue on each unit square of a 8x 8 table

Source: 2015 Saudi Arabia Pre-TST 1.4

September 12, 2020

tablecombinatoricsColoring

Problem Statement

We color each unit square of a

8\times 8

table into green or blue such that there are

a

green unit squares in each 3 \times 3 square and

b

green unit squares in each

2 \times 4

rectangle. Find all possible values of

(a, b)

.
(Le Anh Vinh)

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