## How many solutions are there to a 3×3 magic square?

Answer To: How Many 3×3 Magic Squares Are There? There are 8 ways to make a 3×3 magic square. In fact, there is really only one pattern. Every other pattern is a rotation or reflection.

How do you solve a 3×3 Sudoku puzzle?

The nine 3×3 boxes in a sudoku puzzle are delineated by the bold lines. The basic premise of solving a sudoku puzzle is to place the numbers one through nine exactly once in each row, column and 3×3 box based on the starting numbers that are already filled in and any subsequent numbers you fill in.

How many squares are in a 3×3 square?

A 3×3 square board has 14 squares, the smaller 9 plus 4 2×2’s plus 1 3×3 one.

### What is empty square in Sudoku?

We define an Empty Rectangle as a rectangle that is inside a Square and the corners of which do not contain a particular Candidate. In this example, an Empty Rectangle for Candidate 1 is made of D4, D6, E4 and E6 in Square “5”. In Column “2” Candidate 1 must be the solution in either F2, or G2.

What is the magic constant for a 3×3 magic square?

The sum is referred to as the magic constant. For a 3×3 magic square, there is actually only one normal solution and all of the puzzles are derived from rotations or reflections of that puzzle. The normal variations of these puzzles (the 3×3 puzzles that contain only 1-9) will have a magic constant of 15.

Is there a parametric solution with a non-square magic sum?

The first known example with a non-square magic sum was constructed by Michael Schweitzer(Fig MS4of the M.I. article). It would be very interesting to find a parametric solution with a non-square magic sum, generating an infinite number of 3×3 squares.

#### 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.

How many cells are in a 3×3 magic square?

For example, a 3×3 magic square has nine cells and a normal 3×3 magic square will only contain the numbers 1-9 in it. Similarly, a 4×4 magic square with 16 cells contains only the values 1 through 16, and a 5×5 magic square only contians the values 1 through 25.