Exercise 1

Let $M$ be a $3\!\times\!3$ magic square with magic number $s$.

• Prove that the sum of $M$’s entries is $3s$.

• Prove that $s=3\cdot m_{2,2}$.

• Prove that $m_{2,2}$ is the average of the entries in its row, its column, and in each diagonal.

• Prove that $m_{2,2}$ is the median of $M$’s entries.