Puzzle on how to connect 9 dots with 4 lines, and similar tasks

2024 Author: Sierra Becker | [email protected]. Last modified: 2024-02-26 03:46

Non-standard in its reasoning, the problem of how to connect 9 dots with 4 lines makes you break stereotypes and turn on creativity.

How to arrange the dots and pattern correctly?

On a sheet of paper, it is better if it is in a box, you need to draw 9 dots. They should be arranged three in a row. The diagram will look like a square, in the center of which there is a dot, and in the middle of each of the sides there is also one. It is better if this pattern is placed away from the edges of the sheet. This placement of the square will be required in order to correctly solve the problem of how to connect 9 points with 4 lines.

Problem condition

Requirements to be taken into account:

• It is forbidden to take a pen or pencil off the 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 drawn points.

Following these rules, you need to connect 9 dots with 4 lines. Very often, after a couple of minutes of thinking about this picture, a person begins to claim that this task does not have an answer.

Problem Solving

The main thing is to forget everything that was taught in school. They give stereotyped representations, which will only get in the way here.

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

This is fundamentally wrong. The points are the ends of the segments, and the problem explicitly refers to lines. This is what you should definitely use.

You can start from any vertex of the square. The main thing is the angle, which one specifically, it doesn’t matter. Let the points be marked on the left, moving to the right, and from above, moving down. That is, the first row contains 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 will need to do the following.

1. Travel the beam diagonally to points 5 and 9.
2. You need to stop at the last line - this 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 it doesn't end at the last digit. It needs to be continued up for another segment, as if another point was drawn there. This will be 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 aswas from the second. Thus ended the third line.
6. It remains to draw the fourth through points 7 and 8, which should end in the number 9.

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

If you write down a short plan of how to connect 9 points with 4 lines, you get the following: start at 1, continue at 5, turn at 9, draw at 6 and 3, extend to (0), turn to 2 and 4, continue to (0), turn to 7, 8 and 9. Here (0) are the ends of the segments that have no numbers.

As a conclusion

Now you can still puzzle over a more difficult problem. There are already 16 points in it, located similarly to the considered task. 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 the order of a square, like all subsequent ones, and 8 straight lines;
• 36 dots on 10 lines that do not break because the pen cannot be taken off the sheet;
• 49 dots connected by 12 lines.