A puzzle about how to connect 9 points with 4 lines, and similar tasks to it

Unconventional in its reasoning problem on how to connect 9 points in 4 lines, makes it necessary to break stereotypes and include creativity.

How to correctly arrange the points and drawing?

On a sheet of paper, better if it is in the cell, you need to draw 9 points. They should be arranged three in a row. The diagram will look like a square, in the center of which there is a point, and in the middle of each side, too, it is available. It is better if this figure is placed away from the edges of the sheet. This placement of a square is 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 prohibited to tear off a pen or pencil from paper. The beginning of one must coincide with the end of the other.
• The lines can only be perfectly straight. No excesses are allowed.
• It is required to draw exactly 4 lines through all the drawn points.

Observing these rules, you need to connect 9 points in 4 lines. Very often, after a couple of minutes of reflection on this drawing, a person begins to assert that there is no answer for this task.

The solution of the problem

The main thing is to forget everything that was taught in school. There they give stereotyped ideas, which are only a hindrance.

The main reason that the task of how to connect 9 points with 4 lines is not solved in the following case: they end in drawn points.

This is fundamentally wrong. Points are the ends of segments, and the task clearly speaks of lines. This and must definitely take advantage.

You can start from any vertex of the square. The main thing is the angle, which is specific, it is not important. Let the designated points be left, moving to the right, and from above, moving down. That is, in the first row there 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 origin be at the first point. Then, to connect 9 points with 4 lines, you will need to do the following.

1. Lead the beam diagonally to points 5 and 9.
2. The last one needs to stop is the end of the first line.
3. 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 it be the last option.
4. The second line starts at point 9 and goes through 6 and 3. But on the last digit it does not end. It must be continued upwards to such a length, as if there was another point drawn there. Here is the end of the second line.
5. Now again, the diagonal, which will pass 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 it was with the second. So ended the third line.
6. It remains to hold the fourth through the points 7 and 8, which should end in the figure 9.

On this task is completed and all conditions are met. For some, this figure resembles an umbrella, and someone claims that it is an arrow.

If you record a shorter plan for how to connect 9 points with 4 lines, you will get the following: start at 1, continue at 5, turn at 9, hold at 6 and 3, extend to (0), turn to 2 and 4, continue to ( 0), collapse to 7, 8 and 9. Here (0) denotes the ends of segments that do not have digits.

As a conclusion

Now you can still break your head over a more complex task. It already has 16 points, located similar to the task considered. And you need to connect them already 6 lines.

If this task turned out to be on the teeth, you can try to solve others, with the same requirements, but differing in a set of points and lines, from the following list:

• 25 points in the order of the square, like all the subsequent ones, and 8 straight lines;
• 36 points per 10 lines, which do not interrupt, because the handle can not be torn from the sheet;
• 49 points connected by 12 lines.