Magic Squares

A magic square is a special grid filled with numbers. Every row, column, and diagonal adds up to the same number. This number is called the magic constant. Magic squares have fascinated people for thousands of years.

How They Work

The simplest magic square is 3 by 3. It uses the numbers 1 through 9. Each row, column, and diagonal adds up to 15. There is only one way to arrange the numbers to make it work, not counting rotations.

Bigger magic squares use more numbers. A 4 by 4 magic square uses numbers 1 through 16, and every line adds up to 34.

Magic Squares in History

The oldest known magic square comes from China and is over 4,000 years old. It is called the Lo Shu square. Legend says it appeared on the back of a turtle.

Magic squares have been studied in India, the Arab world, and Europe. The famous artist Albrecht Durer put a 4 by 4 magic square in one of his engravings in 1514.

Fun Facts

• Benjamin Franklin loved making magic squares and created some very large ones.
• The magic constant for a 3 by 3 square is always 15.
• There are 880 different 4 by 4 magic squares.

Did You Know?

In the magic square Albrecht Durer created, the two middle numbers in the bottom row are 15 and 14, which is the year he made it: 1514!