MathDB

The

1 \times 1

cells located around the perimeter of a

3 \times 3

square are filled with the numbers

1, 2, \ldots, 8

so that the sums along each of the four sides are equal. In the upper left corner cell is the number

8

, and in the upper left is the number

6

(see the figure below). https://i.ibb.co/bRmd12j/Kyiv-MO-2021-Round-1-8-2.png How many different ways to fill the remaining cells are there under these conditions?
Proposed by Mariia Rozhkova

Problem Statement