A non-standard reasoning task on how to connect 9 points with 4 lines, forces to break stereotypes and turn on creativity.
How to properly position the points and drawing?
On a piece of paper, it is better if it is in the box,Need to draw 9 points. They should be located three in a row. The scheme will look like a small square, in the center of which there is a dot, and in the middle of each side it also exists. It is better if this picture is placed away from the edges of the sheet. Such an arrangement of the square will be required in order to correctly solve the problem of how to connect 9 points with 4 lines.
The task
Requirements that must be taken into account:
- Tearing a pen or pencil from the paper is prohibited. The beginning of one should coincide with the end of the other.
- Lines can only be perfectly straight. No kinks allowed.
- It is required to draw exactly 4 lines through all drawn points.
Following these rules, you need to connect 9 points with 4 lines. Very often, after a couple of minutes of thinking about this pattern, a person begins to say that there is no answer to this task.
The solution of the problem
The main thing is to forget everything that was taught in school. They give stereotypes that will only hinder here.
The main reason that the assignment is how to connect 9 points with 4 lines, does not solve in the following case: they end at drawn points.
This is fundamentally wrong. The points are the ends of the segments, and the problem explicitly speaks of lines. This must be used.
You can start from any vertex of the square.The main thing is the angle, which is specific, is not important. Let the points be marked on the left, moving to the right, and above, moving down. That is, in the first row are 1, 2 and 3, the second consists of 4, 5 and 6, and the third is formed by 7, 8 and 9.
Let the beginning be at the first point. Then, to connect 9 points with 4 lines, you need to do the following.
- Drive the beam diagonally to points 5 and 9.
- At the last you need to stop - this is the end of the first line.
- Then there are two ways, they are both equal and will lead to the same result. The first will go to the number 8, that is, to the left. The second - to the six or up. Let it be the last option.
- Вторая линия начинается в точке 9 и идет через 6 and 3. But on the last digit it does not end. It should be continued upwards for another segment, as if another point had been drawn there. Here will be the end of the second line.
- Now again the diagonal that will go throughnumbers 2 and 4. It is not difficult to guess that the second number is not the end of the third line. It must be continued, as was the second. So ended the third line.
- It remains to hold the fourth through points 7 and 8, which should end in figure 9.
This completes the task and all the conditions are met. To some, this figure resembles an umbrella, and someone claims that it is an arrow.
Если записать короче план того, как соединить 9 points with 4 lines, you get the following: start at 1, continue at 5, turn at 9, hold at 6 and 3, extend to (0), turn 2 and 4, continue to (0), turn to 7, 8 and 9. Here (0) are the ends of the segments that do not have numbers.
As a conclusion
Now you can still break your head over a more difficult task. There are already 16 points located in it, similar to the considered task. And you need to connect them with 6 lines.
If this task was too tough, then you can try to solve others, with the same requirements, but differing in the set of points and lines from the following list:
- 25 points in the order of the square, like all subsequent ones, and 8 lines;
- 36 points on 10 lines that are not interrupted, because the handle can not be torn from the sheet;
- 49 points connected by 12 lines.
