Can you repeat numbers in a magic square?

As you can see all the rows add up to 15. Notice that each number from 1 to 9 is used once. If you could repeat numbers, many magic squares would become trivially easy, like a grid made entirely of 1s that added up to 3! This is the smallest sum possible using the numbers 1 to 16.

How do you make a magic square with numbers?

The method we use to construct a magic square of order 8 is the same as the method used for the 4 x 4. The only extra consideration is to include leading diagonals of each 4 x 4 ‘sub-square’. Let’s use the numbers 1, 2, 3, 4, …., 64, which give a magic sum of 260. Two ‘passes’ are required for the 64 numbers.

How do you solve a magic square of 15?

In a magic square you have to add 3 numbers again and again. Therefore the average sum of three numbers is 45:3=15. 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.

What’s the best way to solve a 3×3 magic square?

The only way to use these numbers to solve a 3×3 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.

How many 3×3 magic squares are there using each number exactly once?

Read about me, or email me. A magic square is a 3×3 grid where every row, column, and diagonal sum to the same number. How many magic squares are there using each the numbers 1 to 9 exactly once?

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.

What do you call a magic square of order n?

A magic square of order n is an arrangement of n^2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A magic square contains the integers from 1 to n^2. The constant sum in every row, column and diagonal is called the magic constant or magic sum, M.