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1

Part of 2015 Regional Olympiad of Mexico Center Zone

Problems(1)

magic square 3x3 from one 9 element block of first 360 naturals

Source: Mathematics Regional Olympiad of Mexico Center Zone 2015 P1

11/12/2021
The first 360360 natural numbers are separated into 99 blocks in such a way that the numbers in each block are consecutive. Then, the numbers in each block are added, obtaining 99 numbers. Is it possible to fill a 3×33 \times 3 grid and form a magic square with these numbers?
Note: In a magic square, the sum of the numbers written in any column, diagonal or row of the grid is the same.
combinatorics