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# How many solutions does a 4×4 magic square have?

## How many solutions does a 4×4 magic square have?

Unlike 3×3 magic squares where there is only one basic solution to the puzzle, a 4×4 magic square has exactly 880 distinct normal solutions.

## How do you solve a magic square game?

Magic Square Solution

1. List the numbers in order from least to greatest on a sheet of paper.
2. Add all nine of the numbers on your list up to get the total.
3. Divide the total from Step 2 by 3.
4. Go back to your list of numbers and the number in the very middle of that list will be placed in the center of the magic square.

What is the sum of a 4×4 magic square?

The magic square is magic, because the sum of the numbers of each row, each column and both diagonals always give the same result. The sum can be calculated as follows, the (even) size of the square divided by 2 multiplied by the lowest plus the highest number: 4 / 2 x (1 + 16) = 34.

What is magic square formula?

To solve an odd-numbered magic square, start by using the formula n[(n^2+1)/2] to calculate the magic constant, or the number that all rows, columns, and diagonals must add up to. For example, in a 3 by 3 square where n=3, the magic constant is 15.

### How many squares are in 4×4?

So the total for a 4×4 is 16 + 9 + 4 + 1 = 30.

How many squares do you see in a 4×4 square *?

A 4×4 grid will have: 16 1×1 squares; 9 2×2 squares (as there are 3 squares in each of the top 3 rows that can be an upper right hand corner of a 3×3 square), 4 3×3 squares, and 1 4×4 square. So an n x n grid will have ∑k2 total squares. In this case 16 + 9 + 4 + 1 = 30.

How do you solve missing numbers in magic squares?

Add the unused numbers to the open boxes in the magic square so that the rows, columns, and diagonals add up to 15. In the first row: 6 + 8 = 14, the missing number to total 15 is 1. In the third row: 2 + 4 = 6, the missing number to total 15 is 9. In the first column: 6+2 = 8, the missing number to total 15 is 7.

#### What is a Parker square?

The semi-magic square was devised by Matt Parker in an attempt to create an elusive 3×3 square meeting two criteria: – 9 unique square numbers. – Adding to the same value along all rows, columns and diagonals.

#### What are the rules of magic square?

Magic Squares’ Rules. The game board consists of two squares, each with nine checkboxes arranged in three rows. A checkbox may be either checked or unchecked. In the left square, the checkboxes behave as one would expect of a regular checkbox – clicking on it toggles its state. In the right square the behavior is different.

How to create a magic square?

Start in the middle of the top row,and let n = 1;

• Insert n into the current grid position;
• If n = N 2 the grid is complete so stop. Otherwise increment n;
• Move diagonally up and right,wrapping to the first column or last row if the move leads outside the grid.