array of the digits 1,2,..., 9 in the shape of an X J
Source: 2021 Chile National Olympiad level 2 p2, level 1 p4
October 22, 2022
combinatorics
Problem Statement
A design is an array of the digits in the shape of an , for example,
https://cdn.artofproblemsolving.com/attachments/8/e/d371a2cd442cb7a8784e1cc7635344df722e20.png
We will say that a design is balanced if the sum of the numbers of each of the diagonals match. Determine the number of designs that are balanced.