A magic square is the arrangement of consecutive integers such that sums of the numbers in each row, column, and the two main diagonals are the same number. This sum is called the “magic constant”. In the "Xugu Zhaiqi Suanfa" 《续古摘奇算法》, the Chinese mathematician Yang Hui (杨辉, c. 1238 – 1298 AD) gave solutions to magic squares from to .
Determine the “magic constant” of the magic square.
【Solution】
Let represent the “magic constant” of a magic square. The “magic constant” is determined as follows: add all the numbers in the magic square together; then divide by the number of rows (or columns).
or
The formula for calculating the sum of consecutive positive integers is
