Math and Arithmetic
Algebra

# What are magic squares?

777879 ###### 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 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. 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. 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! 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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