Q:

How do you solve a 3x3 magic square?

A:

Quick Answer

To solve a 3x3 magic square, determine the magic sum, which is the sum of each individual column, row and diagonal. Find the number for the center square and work outwards from there. To find out where to place each number, check if the placement of each number makes it possible to obtain the magic sum for the rest of the square.

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Full Answer

To determine the magic sum, add all the numbers from one to nine, which are the only numbers used in the square, and divide that total by three. The reason for dividing the total is because each magic sum is the sum of three out of nine squares. The sum of all the numbers from one to nine is 45, which divides by three to 15.

Using the magic sum of 15, you are able to find the number for the center square. Any number six or above doesn't work, because you must add nine and another number to it for one of the sums that results in a total greater than 15. Any number four or below also doesn't work, because you must add one and another number to it for one of the sums, which results in a total lesser than 15. The center square must have the number five.

Due to the possible combinations, nine and one can't go in any corners. Place these either above and below or to each side of the center. The only possible other combination for the nine is a two and a four, so place those around the nine. After doing so, the rest of the puzzle is simple to complete.

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