Question

place the numbers 0 to 8, in the magic square so that sum of the numbers in each row, column,and diagonal is the same number, 12

Answer 1

`\begin{array}{ccc}1&6&5\\8&4&0\\3&2&7\end{array}`

Explanation:

A magic square can be made by putting the average number in the middle spot. Here, there are 3 numbers in each row, column, or diagonal that total 12, so their average is 12/3 = 4.

There are only 2 pairs of numbers that total 12: (8+4) and (7+5). These must be in the same row and column as the digit 0. If 0 were on a diagonal, we would need three pairs of numbers that total 12, so 0 cannot be on a diagonal.

Our square has 4 in the middle and 0 in a side spot, so it could look like ...

`\begin{array}{ccc}1&6&5\\8&4&0\\3&2&7\end{array}`