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What is a Magic Square? It is all about the math!

Updated on August 13, 2013

Magic Square

Magic Square
What is a Magic Square?
The Basics of Magic Square
How to solve the Magic Square?

Magic Square

I love math puzzles and one of my favorites is magic squares. Magic square are a neat math trick that you can teach students to create and challenge each other with.

A Magic square is an arrangement of integers in a square grid where all the numbers in any given row, column, or diagonal add up to the same sum.

The magic square dates back to early times in many cultures and has many different historical significance in several different cultures.

The Basics of a Magic Square

The most common magic square is a 3 by 3 square. This is an 3 sided square that have 32 spaces or 9 numbers.

The object of a magic square is to have all of the rows, columns, and diagonals add up to a common number. The common number for the rows, columns, and diagonals sums is called the Magic Constant or the Magic Sum.

My students always seems to forget about the diagonals also being part of the Magic Constant. So when you are solving make sure to take into account the diagonals.


How to Solve a Magic Square

The first thing to do when solving a magic square with missing elements is to add up the parts you do know.

I can see with the magic square on the right that the Magic Constant is 15.

By finding the Magic constant I can then use the numbers that I have to determine what parts I am missing.

I know that 4+5 = 9 and 8 + 1 = 9 so therefore the upper right corner must be 6. I place 6 into the missing box.

Now I only have one place left to determine.

4 + 9 = 13

7+6 = 13

8 +5 = 13

therefore the upper left corner is 2 since 13 + 2 = 15.


Try to see if you can solve the Magic Square at the bottom.

Your Turn to Solve

Solve this Magic Square
Solve this Magic Square | Source

Solve the Magic Square Above


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How to use these in the Classroom?

  • Create a magic square problem of the week
  • Have student create their own
  • Create the puzzle and switch with a neighbor
  • Fast finishers
  • Addition practice


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    • klanguedoc profile image

      Kevin Languedoc 5 years ago from Canada

      This is a fun game. It would make a cool app

    • kthix10 profile image
      Author

      kthix10 5 years ago from IL

      I agree, it would make a cool app. I have seen magic squares with a complete square when one number is wrong and you have to figure out which number is wrong and what the number should be

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