What is a Magic Square?

A magic square is an array of numbers where the sum of each row, each column and both diagonals are the same. This sum is called the 'magic sum'. Usually magic squares consist of positive numbers where each number only appear once and in sequence starting with number '1'. This is called a 'normal' magic square. However, several other variants of magic squares exist.

Magic squares of different sizes exist. A magic square with three rows and three columns, i.e. includes nine numbers, is called a magic square of order 3.

A magic square of order 1 is trivial, since it consists of only one number.

Normal magic squares of any order is possible to construct, except for order 2.

This means that a magic square of order three (a 3x3 array) is the smallest of interest.

Shown below, are my handmade wooden coasters with a pattern similar to an ordinary die, see product page. The coasters can be re-arranged into a 3x3 magic square.

Which is the 'magic sum' for a normal magic square of order 3?

The numbers in a normal 3x3 magic square are 1, 2, 3, 4, 5, 6, 7, 8 and 9. The sum of these number are 45.

We know that the sum of each row is equal to the 'magic sum', here called 'M'. Then the sum of all three rows is then 3*M. This is also equal to the sum of all included numbers, i.e. 3*M = 45.

Conclusion: The magic sum M for a normal 3x3 magic square then has to be 15!

A challenge for you and your friends

It is a challenge for your friends, children and yourself to arrange the nine coasters into a 3x3 magic square. 

The magic square coasters are also an excellent way to get your party guests to collaborate and get to know each other a bit better.