Magic Squares

Magic squares have been traced through history as known to Chinese mathematicians, Arab mathematicians, India and Egypt cultures. The first magic squares Magic squares have fascinated people for centuries, and historians have found them engraved in stone or metal and worn as necklaces. Early cultures believed that by wearing magic squares, it would ensure they had long life and kept them from getting sick.

Benjamin Franklin was well-known for creating and enjoying magic squares, and it was all the rage during his time. Here’s the deal: we’re going to arrange numbers in a way so that all the rows, columns, and even the diagonals add up to a single number (called a Magic Sum). In this video, I show you the first Magic Square published in Europe way back in 1514. Plus, I show you how to make your very own Magic Square. You can use it to test your friends.

Download Student Worksheet & Exercises

You can create a magic square that sums to any number by referencing the original “34” magic square. Ask a friend for a number larger than 34 (which is the smallest magic square you can create), and then follow these easy steps:

1. First take the number your friend gave you and subtract 34.
2. Divide your number from #1 by 4 and keep the remainder to use like this: the quotient is the first magic number and the quotient plus the remainder is the second magic number. For 67 the results are 8 and 9.
3. When you fill out a square in your new 4×4 magic square, peek at the 34-magic-square and see what’s already in the box. If it’s a 13, 14, 15, or 16, then add the second number to it and put it int he box. If not, add the first number to it.

Note that if your number is even (but not a multiple of 4) then you’ll have the same number for your first and second numbers. That’s okay!

Exercise

Find the value of the letters; A, B,C and D in the following upside-down magic square

18	A		61
D	81	98
91	B		88
C	68		96

1. A
2. B
3. C
4. D
5. What is the sum of elements of any diagonal in the first magical square published in 1514?
6. Find the element at the middle of a nine-element magic square.
7. Draw a nine-element magic square.

Find the values of b and c in the following magic square.

16		2
c	10	11	8
	6	7
		d	b

8. b
9. c
10. d