# What is the sum of a 3×3 magic square?

## 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 solve the 3×3 magic square puzzle?

Solving 3 x 3 Magic Squares

1. List the nine consecutive numbers in order.
2. Add them up then divide by three.
3. The very middle number in a consecutive number list is the number for the middle square.
4. Apply the rules in the magic square solution diagram.

### How do you solve sums of magic squares?

Fill in the remaining numbers using an up-one, right-one pattern. You will always fill in the numbers sequentially (1, 2, 3, 4, etc.) by moving up one row, then one column to the right. You’ll notice immediately that in order to place the number 2, you’ll move above the top row, off the magic square.

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 the formula of magic square?

The standard or normal magic square is defined as an arrangement of the first n2 natural numbers (or positive integers) into a square matrix so that the sum of the numbers in each column, row and diagonal is the same magic number. This magic number is determined by n and is equal to n(n2 + 1)/2.

What is the maximum number of 3×3 squares?

Grouping the top 3 rows, among the 6 columns, adjacent 3 columns can be selected in 4 ways which can give 3×3 box. Similarly when done for columns, we get 4 ways for 3×3 box. So, total number can be 4*4 = 16 boxes.

### How many squares are there in 3 * 3?

3×3. a 3×3 grid has 9 1×1 (3 * 3) squares 4 2×2 (2 * 2) squares and a single 3×3 square = 14.

What is the magic sum of a magic square of size 11?

The well-known magic square below has the property that the three numbers in each of the three rows, the three columns and the two diagonals all add up to the same number 15. This number is called the magic sum of the square….Age 11 to 16.

6 5 13
15 8 1
3 11 10

## How do you solve a 3×3 magic square with numbers?

Let’s now fill numbers from 24 to 32 in a 3 x 3 magic square. Sum of numbers in rows = 27 + 32 + 25 = 26 + 28 + 30 = 31 + 24 + 29 = 84 Sum of numbers in columns = 27 + 26 + 31 = 32 + 28 + 24 = 25 + 30 + 29 = 84 Using these tricks you can solve any 3 x 3 magic square with any sequence of 9 consecutive numbers.

How do you solve a magic square with a lower sum?

Any lower sum will force the use of either negative numbers or fractions (not whole numbers) to solve the magic square . What is the Franklin Square? Franklin’s square is a panmagic square with a magic constant of 260.

### What is the minimum number required to solve the magic square?

For a size 3×3, the minimum constant is 15, for 4×4 it is 34, for 5×5 it is 65, 6×6 it is 111, then 175, 260, Any lower sum will force the use of either negative numbers or fractions (not whole numbers) to solve the magic square .

How do you find magic sums?

Magic Sum = 3 * Middle Number. Then each opposite pair sums to twice the middle number, and the opposite pairs all consist of two numbers of the same parity, equidistant from the middle number. Every corner is half the sum of the two squares which are “knight’s move” away (the middle squares of the opposite sides), and falls halfway between them.