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How many 3×3 magic squares exist?

How many 3×3 magic squares exist?

There are 8 possible magic squares for 3 X 3 matrix.

What is 3×3 magic square?

For a 3×3 magic square, there is actually only one normal solution and all of the puzzles are derived from rotations or reflections of that puzzle. The normal variations of these puzzles (the 3×3 puzzles that contain only 1-9) will have a magic constant of 15.

Is 15 a magic number?

The number 15 is called the magic number of the 3×3 square. You can also achieve 15, if you add the middle number 5 three times. The odd numbers 1,3,7, and 9 occur twice in the reductions, the even numbers 2,4,6,8 three times and the number 5 once.

How do you calculate a magic square?

Remember the equation: 54 (the target number) minus 34 (our original magic square total) = 20. And then you divide 20 by 4 to get 5 with no remainder! All you have to do is add 5 to each of the 16 numbers in your new grid and it will work.

How does magic square work?

A magic square is an n x n square with a whole number written inside each cell, so that the sum of the numbers in every row, in every column and in each of the main diagonals is equal. This number is called the magic number. The main diagonals are those that stretch from corner to corner.

How do you change a 3×3 magic square?

Another way to change a 3×3 magic square into another is by subtracting all the numbers from 10. So, for example, The reason there are only these 3×3 magic squares is simple enough. Each row must add up to 45 / 3, that is, 15.

Which is the magic square of order 3×3?

The first Magic Square Puzzle found has numbers from 1 to 9 which gives a Magic Constant of 15. The examples of Magic Square of Order 3×3 has been shown below: We can get the Standard or Secondary Magic Square of order 3×3 by adding some numbers to the above picture.

Is there a magic square to make 15?

This means 45 = 3 M so 15 = M. If a magic square exists, then each row, column and diagonal has to be 15. Suppose you use the numbers 1 and 2. You would need 12 in order to make 15. This is not possible since we are using the numbers 1 to 9. So we can’t combine 1 and 2 to make 15.

How is 45 equal to 3×3 magic square?

On the other hand, this is the same as adding the top row, the bottom row, and three times the middle number, so this is 15+15+middle+middle+middle. The only way to have 45 equal to 30 + 3 x middle, is if the middle number is 5. Once you know the middle is 5, you know that opposite numbers add to 10.