MathDB

3 \times 3

square is filled with numbers:

a, b, c, d, e, f, g, h, i

in the following way: https://cdn.artofproblemsolving.com/attachments/8/9/737c41e9d0dbfdc81be1b986b8e680290db55e.png Given that the square is magic (sums of the numbers in each row, column and each of two diagonals are the same), show that a)

2(a + c + g + i) = b + d + f + h + 4e

. (3) b)

2(a^3 + c^3 + g^3 + i^3) = b^3 + d^3 + f^3 + h^3 + 4e^3

. (3)

Problem Statement