The Magic of Math

Connect mathematical learning with other subjects, personal experiences,
current events, and personal interests
• See relationships between various kinds of problems and actual events
• Use mathematics as a way to understand other areas of the curriculum

In problem-solving situations involving whole numbers, select and
efficiently use appropriate computational procedures such as
• Recalling the basic facts of addition, subtraction, multiplication, and
division
• Using mental math

Just as scientific principles are instrumental in making magic tricks successful, so are the
concepts of mathematics. Especially in the field of “mental magic,” math is an important
factor in the success of many illusions. Mental magic is a type of magic performance that
usually requires no props and uses the thought processes of the audience to be successful.
Magic squares are a type of mental magic. The Chinese invented magic squares many
centuries ago. An example of a magic square appears below.
In a magic square, whether you add up, down, or across, you will always
come up with the same sum. This number is called the magic total. In this
case, you will always arrive at the number 15.





4+9+2=15
3+5+7=15
8+1+6=15
4+3+8=15
9+5+1=15
2+7+6=15
4+5+6=15
2+5+8=15

This example is an order three square since it has three rows and three columns. You can
make other order three squares by adding the same number to each number in the square
or by multiplying each number in the square by the same number. Here is an example:

+2 to each number in the square =






-
To make an order four magic square, enter the numbers 1-16 (or any other 16 consecutive
numbers) onto a 4x4 grid as shown. I’ll start with the number 5 for the sake of this
example.

Now: Switch the corners along the diagonals like this:

Also, switch the four center numbers along the diagonals:

Add the remaining numbers back into the square in their original positions.






Add all of the rows, columns, and diagonals and you will get the same number.
20+6+7+17=50
9+15+14+12=50
13+11+10+16=50
8+18+19+5=50
20+9+13+8=50
6+15+11+18=50
7+14+10+19=50
20+15+10+5=50
8+11+14+17=50

Also, the numbers in the center add up to 50: 15+14+11+10=50
Use the directions above to create your own 3x3 or 4x4 magic square. Check the square
by adding each row, column, and diagonal to make sure they add up to the same sum.

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