Magic squares – one of the most ancient tasks in mathematics. To learn to solve them, it is necessary to understand the principle. Use the given decision algorithm which will help you to learn to cope with this cunning task.
It is required to you
- - paper;
- - handle or pencil;
- - eraser;
- - ruler.
Instruction
1. Draw a magic square on the sheet of paper. If your square is divided into 9 cages, in them to spread out numbers from 1 to 9 is necessary so that the sum number in each column, a line and diagonal made 15. It is better to draw a square on the squared paper sheet and to enter figures not the handle, but a pencil - so it will be easier for you to make changes, and you will not get confused in deletion of figures.
2. Write in all cages on figure 5. In this case, naturally, the rule of a magic square by which all parties, columns and diagonals have to be equal 15 will be observed.
3. In three cages leave figure 5. It can be, for example, the top left cage, average left and surely average. To two nearby the standing cages add figures 1 and 2 to the five, i.e. they have to turn into 6 and 7.
4. Now finish filling of a square. Place figures 1, 2, 3, 4, 8 and 9 on free cages. Remember that the sum of all parties, diagonals and columns has to be equal to 15.
5. There is also other way – use of symmetry. Draw a square of 5х5 cages. In this square a short flight of stairs write in a row number from 1 to 9. In the center there has to be figure 5.
6. Then "throw" figures 1 and 9 through figure 5 and write them near figure 5, i.e. unit has to rise to the right of the five, and the nine – at the left. Make the same with figures 3 and 7 (put the three under the five, and the seven – over it).
7. After you make it, you just will need to fill the cages which remained free.