Problem

Source: Mathematics Regional Olympiad of Mexico Center Zone 2015 P1

Tags: combinatorics



The first $360$ natural numbers are separated into $9$ blocks in such a way that the numbers in each block are consecutive. Then, the numbers in each block are added, obtaining $9$ numbers. Is it possible to fill a $3 \times 3$ 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.