In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
Can you put the digits 1 to 9 in a square so that every row column and diagonal add to 15?
You can assemble the numbers 1 to 9 in a square, so that the sum of the rows, the columns, and the diagonals is 15. If you take the numbers 1 to 9, you have the standard square. A magic square remains magic, if you change each numbers by a constant c.
Which is the magic constant for a 3×3 square?
So, in the example of the 3×3 square: sum = 3 * [(9 + 1) / 2] sum = 3 * (10 / 2) sum = 3 * (5) sum = 15. The magic constant for a 3×3 square is 15. All rows, columns, and diagonals must add up to this number.
How many 3×3 magic squares are there in a puzzle?
So the first 3 rows sum to 3 M. On the other hand, if we sum up all 9 elements, we must have the sum of the numbers 1 to 9. 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.
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. Next, if you add the two diagonals and the middle column, you’ll get 15+15+15=45 again.
How to calculate the size of a magic square?
Example: Magic Square of size 3 ———————- 2 7 6 9 5 1 4 3 8 Steps: 1. position of number 1 = (3/2, 3-1) = (1, 2) 2. position of number 2 = (1-1, 2+1) = (0, 0) 3. position of number 3 = (0-1, 0+1) = (3-1, 1) = (2, 1) 4. position of number 4 = (2-1, 1+1) = (1, 2) Since, at this position, 1 is there.
