What is a magic square?

Magic squares have been more than people 2500 tied up for years. Actually, there is nothing magical about these squares, for they are nothing but addition tables, in which the numbers are cleverly arranged.

We draw a square with nine cells, as the picture shows. Now the numbers 1 to 9 in, a number in each field. But they should be arranged like this, that they always add up to the same sum, no matter, whether to cross a row, top down, or diagonally, i.e. added diagonally from one corner to the opposite.

We know, that the sum of all numbers of 1 to 9 = 45 is. We already have the formula for this on page 28 met. Let's share now 45 by 3, so we get 15. Therefore, each series of 3 numbers the same 15 being. Before we look at the solution below, everyone should try it themselves, to make a magic square.