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Math and Arithmetic
Algebra

What are magic squares?

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2010-09-17 15:21:21
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, let�s 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.

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