A non-standard task in its argument about how to connect 9 points with 4 lines makes us break stereotypes and turn on creativity.
How to arrange the dots and pattern?
On a piece of paper, it is better if it is in a box, you need to draw 9 points. They should be arranged three in a row. The diagram will look like a small square, in the center of which there is a dot, and in the middle of each of the sides it also exists. It is better if this picture is placed away from the edges of the sheet. Such a placement of the box 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:
- It is forbidden to tear a pen or pencil from paper. The beginning of one must coincide with the end of the other.
- Lines can only be perfectly straight. No kinks are allowed.
- It is required to draw exactly 4 lines through all the drawn points.
Observing these rules, you need to connect 9 points with 4 lines. Very often, after only a couple of minutes of reflection on this drawing, a person begins to claim that this task has no answer.
The solution of the problem
The main thing is to forget everything that was taught at school. They give stereotypical ideas that will only interfere here.
The main reason that the task of how to connect 9 points with 4 lines does not solve in the following case: they end at the drawn points.
This is fundamentally wrong. Points are the ends of segments, and the problem explicitly refers to lines. This must be taken advantage of.
You can start from any vertex of the square. The main thing is precisely the angle, which specifically is not important. Let the points be marked on the left, moving to the right, and from 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.
- Guide the beam diagonally to points 5 and 9.
- The last one needs to be stopped - this is the end of the first line.
- Then there are two ways, they are both equivalent 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 there be the last option.
- The second line starts at point 9 and goes through 6 and 3. But on the last digit it does not end. It needs to be continued upward for another segment, as if another point were drawn there. Here will be the end of the second line.
- Now again the diagonal that goes through the numbers 2 and 4. It is easy to guess that the second number is not the end of the third line. It must be continued, as was the second. Thus ended the third line.
- It remains to draw the fourth through points 7 and 8, which should end in number 9.
On this task is completed and all conditions are met. To some, this figure resembles an umbrella, but someone claims that it is an arrow.
If you write down a shorter plan for how to connect 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 at 2 and 4, continue to ( 0), collapse to 7, 8 and 9. Here (0) the ends of segments that do not have numbers are indicated.
In conclusion
Now you can still puzzle over a more complex puzzle. There are already 16 points in it, located similarly to the task considered. And you need to connect them already with 6 lines.
If this task turned out to be 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 square order, like all subsequent ones, and 8 lines;
- 36 points on 10 lines that do not interrupt because the pen cannot be torn off the sheet;
- 49 points connected by 12 lines.