You will need
- - a pen or pencil;
- - eraser;
- - the range.
Draw the magic square on a sheet of paper. If your square is divided into 9 cells, they need to decompose the numbers 1 to 9 so that the sum of the numbers in each column, row and diagonal equal to 15. It is better to draw a square on paper and write the numbers don't pen, and a pencil - so it's easier to make changes and you don't miss strikeout numbers.
Write all cells to the digit 5. In this case, of course, the rule of the magic square in which all sides, columns, and diagonal must equal 15, will be observed.
Three cells Express the number 5. This can be, for example, the top-left cell, middle left and sure average. In two adjacent cells add to the fives figures 1 and 2, i.e. they have to become 6 and 7.
Now finish filling the square. Put in empty squares of the numbers 1, 2, 3, 4, 8, and 9. Remember that the sum of all sides, diagonals and columns must be equal to 15.
There is another method – use of symmetry. Draw a square of 5x5 cells. Inside this square, visitors can write consecutive numbers from 1 to 9. In the center should be a number 5.
Then "throw" the numbers 1 and 9 using the number 5 and write them next to the number 5, i.e. the unit should stand to the right of the five and nine on the left. Do the same with numbers 3 and 7 (put the top three under five, and a seven – over it).
Once you do, you will simply fill the remaining free cells.
If you are a beginner in dealing with magic squares, then practice first in solving the most simple problems of this kind. Because learning to solve squares of 3rd and 5th order, you can move on to more complex magic squares, for example, 10-th and 15-th order.
If you choose the square in which some values are already known, use the equations with the unknown.
Advice 2: How to learn math
Mathematics is one of the most fundamental Sciences. Without having the main mathematical knowledge it is impossible to count on success in any other technical field. Without mathematics it is impossible to solve physical and chemical problems, to write programs and manage complex technology. So how do you quickly and efficiently learn mathematics?
You will need
- Handbook of elementary mathematics, collection of problems,
First you need to take reference on mathematics and appreciate its spaces. All sections of mathematics which are unclear, need to repeat (or to learn). If you have spaces in all sections, then it is desirable to disassemble these sections in order. Next you need to proceed to the analysis of the theory. You clearly need to understand basic things and be able to do the drawings describing a particular branch of mathematics (graphs, drawings).
The solution of problems from the collection is one of the most important means of learning mathematics. Only practice can bring you dividends in the form of knowledge. In the beginning it is necessary to understand the examples from the directory, then go to resolve similar problems. If the job seems simple, it is still run - a branch of mathematics which is taken from the example unconsciously will seem simple and you will be better able to solve more complex problems.
Distance education is a great way to improve your knowledge. There are portals which will help you completely free of charge excellent teachers. The most important thing is to write down specific questions and examples that cause you difficulty. The perfect project e - learning www.cde.ruthe joint portal of Moscow state University and MIPT. In order to learn it, you need to pass a simple registration procedure and configure the software, which can be found on the website.
Video lectures a good tool for those who want to learn math fast. Find lectures on mathematics on the site of the North-Western Technical University. When viewing, try to make notes in a notebook to structure their knowledge.
Try to vary the learning process. See the math cartoons and comics - this will make it easy to refer to book knowledge.