3

Part of 2017 Iran MO (2nd Round)

Problems(1)

Maximum number of black squares [Iran Second Round 2017, P3]

Source: Iran National Olympiad 2017, Second Round, Problem 3

n

be a natural number divisible by

3

n \times n

table and each square is colored either black or white. Suppose that for all

m \times m

sub-tables from the table (

m > 1

), the number of black squares is not more than white squares. Find the maximum number of black squares.