## Is there a 4×4 magic square?

The 4×4 magic square consists of 4 rows which multiplied by 4 columns is 16 cells. The 4×4 magic square must contain 16 different numbers. A pure magic 4×4 square contains the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 and 16.

**What is the formula of magic square?**

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 do you see 4×4?**

16

Ask the students how many squares are there in a 4×4 grid of squares. Many will answer 16.

### What is a 4 by 4 square?

A standard foursquare area is one large square, 10′ x 10′ divided into four smaller squares (5′ x 5′), and each box is labeled A, B, C, D or 1, 2, 3, 4. The box labeled A or 1 contains a smaller service box (1.5′ x 1.5′) located in the far outside corner of the square.

**How many squares are there in a 4×4 grid?**

After they have had a chance to think about and have yelled out some more answers ask them how many squares there are in a 1×1 grid (1) and in a 2×2 grid (the 4 small squares and the 1 big square = 5) and a 3×3 grid (9 small squares, 4 of the 2×2, and 1 big one = 14). So the total for a 4×4 is 16 + 9 + 4 + 1 = 30.

**How do you solve a magic square step by step?**

Here are the steps:

- List the numbers in order from least to greatest on a sheet of paper.
- Add all nine of the numbers on your list up to get the total.
- Divide the total from Step 2 by 3.
- 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.

#### How do you calculate the number of squares?

A number n squared is written as n² and n² = n × n. If n is an integer then n² is a perfect square. For example, 3 squared is written as 3² and 3² = 3 × 3 = 9.

**What is the magic number of a 4×4 magic square?**

The 4 x 4 Magic Square to the left is the “basic” 4 x 4 Magic Square. It uses the numbers 1 to 16 inclusive, and its “Magic Total” is 34, as predicted by the formula shown on another page.

**Can I create magic squares that add up to any number?**

However, Magic Squares can be created that add up to any “Magic Total” you like, provided that you know the right formula. If you want to see a 4 x 4 Magic Square that adds up to a number greater than zero and less than 1,000, enter it in the box below and press the Calculate button:

## How do you make a 3×3 magic square?

The numbers in the Red Squares form the 3×3 magic Square. The numbers beside the Red Squares show the totals for each row. The horizontal and vertical totals are to the right and below in green squares. The other, blue, squares show the diagonal totals – including all of the “broken diagonals”. You can make your own Magic Square in two ways.

**How do you find the structure of a magic square?**

By moving your Mouse over a Blue Arrow and waiting, you can observe the numbers in the Magic Square. This reveals the underlying structure of a 4×4 Pan-Magic Square – one in which all of the diagonals are magic. This method only produces pan-magic squares.