Copyright © University of Cambridge. All rights reserved.

## 'Magic Constants' printed from http://nrich.maths.org/

This is a 4 x 4 Magic Square made from the numbers 1 to 16.

In a Magic Square all the rows, columns and diagonals add to the same number. This number is called the 'Magic Constant'.

Here are some questions about this Magic Square.

1/What is the Magic Constant of this Magic Square?

This particular square is especially 'magic' as some 2 x 2 squares within it also add to that number.

2/How many of these squares can you find?

3/What happens to the Magic Constant if you add 2 to each number in the square?

4/What happens if you double each number?

5/Can you make a square in which the Magic Constant is 17?

How did you do it?

6/Can you make a square in which the Magic Constant is 38?

How did you do it?

7/What other numbers under 100 can you make into the Magic Constant by changing all the numbers in the square in the same way?

8/Can some be made in more than one way?

9/Are there some numbers you really cannot make?