A design $X$ is an array of the digits $1,2,..., 9$ in the shape of an $X$, for example, We will say that a design $X$ is balanced if the sum of the numbers of each of the diagonals match. Determine the number of designs $X$ that are balanced.
Source: 2021 Chile National Olympiad level 2 p2, level 1 p4
Tags: combinatorics
A design $X$ is an array of the digits $1,2,..., 9$ in the shape of an $X$, for example, We will say that a design $X$ is balanced if the sum of the numbers of each of the diagonals match. Determine the number of designs $X$ that are balanced.