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Magic Constants

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

Magic square : 15, 10, 3, 6; 4, 5, 16, 9; 14, 11, 2, 7; 1, 8, 13, 12.

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?