How do you solve the 3×3 magic square puzzle?
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.
What is the sum of a 3×3 magic square?
The Magic 3×3 Square top You have 1+2+3+4+5+6+7+8+9=45. 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.
How do you make a 3 by 3 magic square?
3×3 Magic Square
- each row must add up to the same number,
- there are three rows, and.
- 1+2+3+4+5+6+7+8+9 is 45,
How many squares are in a 3×3 grid?
A 3×3 square board has 14 squares, the smaller 9 plus 4 2×2’s plus 1 3×3 one.
What is a magic square in maths?
Magic Squares are square grids with a special arrangement of numbers in them. These numbers are special because every row, column and diagonal adds up to the same number. So for the example below, 15 is the magic number. The “order” of a magic square tells how many rows or columns it has.
How do you code magic squares?
These are the characteristics for writing the code:
- Ask the user for an odd number.
- Create an n by n array.
- Follow these steps to create a magic square. a. Place a 1 in the middle of the first row. b. Subtract 1 from the row and add 1 to the column. i. If possible place the next number at that position.
- Print the array.
Can magic square have negative numbers?
A magic square is an arrangement like the one below where the vertical, horizontal and diagonal lines of numbers all add up to the same value. This ‘same value’ is called the sum of the magic square….Negative magic squares.
| 4 | 1 | 7 |
|---|---|---|
| 1 | 7 | 4 |
How to calculate magic squares for 3 x 3 matrix?
There are 8 possible magic squares for 3 X 3 matrix. There are two ways to approach this: So, compute all 8 magic squares by examining all permutations of integers 1, 2, 3, ….., 9 and for each one, check if it forms a magic square if the permutation is inserted into the square starting from the upper left hand corner.
Can a digit be converted to a magic square?
We can convert any digit a to any other digit b in the range [1, 9] at cost of |a – b|. Given s, convert it into a magic square at minimal cost. Print this cost on a new line. Note: The resulting magic square must contain distinct integers in the inclusive range [1, 9].
Which is the magic constant for a magic square?
We define a magic square to be an n x n matrix of distinct positive integers from 1 to n2 where the sum of any row, column, or diagonal of length n is always equal to the same number: the magic constant. You will be given a 3 x 3 matrix s of integers in the inclusive range [1, 9].
How to make a magic square in Excel?
Complete the formingMagicSquare function in the editor below. Each of the 3 lines contains three space-separated integers of row s[i]. If we change the bottom right value, s[2] [2], from 5 to 6 at a cost of |6 – 5| = 1 , s becomes a magic square at the minimum possible cost.