Q&A for How to Solve a Magic Square

Place the first number of the magic square in the center box of the top row. Then, use an up-one, right-one pattern to add the numbers.

Magic squares with numbers that start at 1 and are in consecutive order always have the same sum. A 3 x 3 magic square always has the sum of 15 and a 4 x 4 has a sum of 34.

Typically, you can't repeat digits in a magic square so making a 4 x 4 with the digits 0-9 isn't possible unless you repeat them.

In a normal magic square, you have numbers 1 to 9. To make them even numbers, just multiply each number by 2.

Just take any 3 x 3 magic square with 1 - 9 (magic number 15), and add 71 to each cell.

To solve a magic square with the same negative and positive integers, replace the problem you don't know how to solve with one you do know how to solve. In other words, replace the integers with the first n positive integers, where n is the number of integers. Solve the square, then replace the integers with the original integers in the problem you were given. So, if it's a 3x3 square with integers from -4 to 4, turn it into a regular 3x3 square, solve it, and replace 1 in the final solution with -4, replace 2 with -3, replace 3 with -2, etc.

It is an open problem in mathematics - in fact, for squares bigger than 6 x 6, there isn't even a formula counting how many magic squares exist.

You can't make the row sums equal the column sums unless the array is square.

Use a pencil/pen and a piece of paper and make 36 boxes into a square.

It's the same as any other math problem. All horizontal, diagonal & vertical lines must add up to the same number. Adding a negative number to a positive number is the same as subtraction, and adding a negative number to a negative number is the same as adding positive numbers, except that the answer is a negative. If all the numbers in the example Magic Square were negative, the answer for each equation would be -34.

You already know what the totals should be, since the entire top row is filled out! Reverse-engineer from the numbers already filled out. It is also possible that the starting number used is not in fact 1. Try to adjust for this as other answers describe - translate the values available into numbers that would go in that spot by adding or multiplying all numbers in the square uniformly. If the results of reverse-engineering yield an unsolvable scenario, you can consider transformation formulas that allow for re-arrangement of your basic solution.

Unfortunately, you've got 10 numbers there. The only way to use these numbers to solve a 3x3 magic square is by excluding either your highest or your lowest number. Once you have done so, assign the lowest remaining value to 1, the next lowest to 2, the next to 3, and so on an so forth until you assign the highest remaining value to 9. Solve the 3x3 as you normally would and then substitute 1-9 with their corresponding larger counterparts.

You can create 4X4 magic square for any number without using consecutive numbers. For example, the numbers 1, 4, 7, 10, 14, 17, 20, 23, 27, 30, 33, 36, 40, 43, 46 & 49 will produce a magic constant of 100.

Fill in all of the squares until you actually get a sum of the same number down, across, and diagonal.

Go to the previous square that was filled in and place the next number below it.

For an odd-numbered magic square put a 1 in the center box in the top row then keep adding numbers until the square is complete.