Magic squares

Hello, and welcome to Myriora Maths! In a magic square, every row, every column and both diagonals add up to the same number. Can you put the numbers one to nine in a three by three square, and make it magic?

First, find the magic total. One plus two, all the way to nine, is forty-five. The three rows use every number once, and each row has the same total. So each row is forty-five divided by three: fifteen.

Which number goes in the middle? The centre square is in four lines: a row, a column, and both diagonals. Five, the middle number, pairs up the others perfectly: one and nine, two and eight, three and seven, four and six. Each pair adds to ten, and ten plus five is fifteen!

Now fill it in. Put two in a corner, and eight in the opposite corner. Put six and four in the other two corners. Then each gap is fifteen, take away the other two numbers in its line. Along the top: fifteen take away two and six is seven. The other gaps work the same way: nine, one and three.

Let's check. Every row, every column and both diagonals add to fifteen. It's magic!

A common mistake is thinking the magic total is always fifteen. That's only for the numbers one to nine! For other numbers, add them all up, and divide by three.

Your turn! A magic square uses the numbers three to eleven. What is the magic total? And which number goes in the middle? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! Three plus four, all the way to eleven, is sixty-three. Sixty-three divided by three is twenty-one. The middle number of three to eleven is seven, so seven goes in the centre. Seven is a third of twenty-one, just like five is a third of fifteen.

Quick review. To find the magic total, add all the numbers, and divide by three. The middle number goes in the centre. Then fill each gap with the total, take away the other two. See you next time!