Math and Arithmetic
Algebra

# What are magic squares?

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###### 2010-09-17 15:21:21

answer Magic Square is an n x n matrix with each cell containing a number from 1 to n^2. You need to figure out where to place each number in the cells so that the sum of the vertical columns, horizontal rows, and main diagonal cells is the same. You can start out with a 3 x 3 matrix and build in complexity by working towards a 4 x 4 matrix and so on.

For example, letï¿½s take a look at a simple 3 x 3 matrix. On a piece of paper construct a matrix that has 3 columns and 3 rows. Next, we will need to figure out where to place the numbers from 1 to n^2 or 1 to 32 = 1 to 9 in this case. Trial and error is the common first method to employ when solving this puzzle. Verify that the sum of each vertical column, horizontal row, and main diagonal is the same. The main diagonal means the two diagonals that go through the corners of the matrix. answer an extra hint: In any (odd number) by (odd number) square, the number in the centre of the magic square is a third of the number you are attempting to make all hoizontals and verticals add to.

Also, the sum of numbers in each column, or each row, or each main diagonal is (n+n3)/2 where n is the number of cells along the side of the square. To construct a square, (which must have an odd number of cells along each side) start with 1 in the middle of the top row. The rule is to try and put the next number in the next cell diagonally higher to the right. If that is outside the square at the top, drop to the bottom of the square. If outside to the right, go to the left edge of the square. If the cell is already occupied, fall back to the cell immediately below the last number you entered.

## Related Questions

no the magic squares is a way different thing

Magic Squares - 1914 is rated/received certificates of: UK:U

swer in a 4x4 magic squares with 10-=25 numbers in each column?

While they may have been called magic squares, there is absolutely nothing magical about them. The arrangement of numbers in magic squares is all very rational.

Magic squares are grids of numbers that add up to the same number in each row, each column and both long diagonals. ■

Yes. Just add the same number to each square and see what happens. Also, there are magic squares of different sizes.

Seymour S. Block has written: 'Sudoku and magic squares' -- subject(s): Sudoku, Magic squares, Mathematical recreations

Benjamin Franklin would concoct magic squares when debates got rather tedious

Believe it or not, the Indian culture discovered magic squares first. However, many people tend to believe the Chinese invented this game.

math squares are a good an usefull tool but we may never now who made them lol

This is a game show now replaying on the retro channel.

There are many possible magic squares based on the periodic table. It is not one particular puzzle.

There is no such thing as a "magic number". You are probably thinking of magic squares where the sum of each row, column and major diagonal has the same "magic" value.

Magic squares have been a source of intrigue since the time of Pythagoras, and even before. You will find the following link useful.

The most commonly known word is ABRACADABRA which is actually a sequence of character used to make up one of a series of magic squares used in ceremonial magic.

once in china, a turtle arrived at a river bank and people noticed that it was having some designs on its back . these designs then turned into magic square

The name of the inventor is not known. But there is documentary evidence that magic squares were known in China by 650 BCE. These documents attribute the invention to a turtle!

Excluding rotations and reflections, there is only one 3x3 magic square.

because he was wants to show people that he was the most intelligent person in the world

The horizontal, vertical and diagonal numbers will all be the same sum when added together.

Magic squares are grids of numbers arranged in specific ways so that the rows and columns (and frequently, the major diagonals) add up to the same value. In the occult, magic squares are created of specific sizes and including specific ranges of numbers which are believed to have sympathy with specific spirits/gods/etc and are used to create sigils- a magical glyph of the entity's name.

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