Magic constants

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Age
7 to 11
Challenge level
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Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



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

Magic Constants

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?