9 dots puzzle: how to connect 9 dots with 4 lines?
There are many ways to spend your free time — from watching films and blogs to drawing and doing sports. Some people prefer to develop their logical thinking when they have spare hours (or even minutes). What can help you to do it is crossword puzzles, conundrums, or logic puzzles.
You have probably heard about one of the most popular puzzle called “4 lines 9 dots”. We challenge you to try to solve it by yourself, but if your efforts are not quite successful, we will reveal some secret methods just for you.
What are the conditions?
So, imagine there are three equal rows that consist of three dots each. What you have to do is to draw four straight lines to connect all of the dots. However, the challenge is to avoid lifting the pencil off the paper. You can start from any position you want, but the main requirement is to draw everything with a pencil stuck to the sheet. A place where one line finishes is a starting point for the next one. Also, you can not go through the same track more than once.
Now try to do it in your notebook — draw nine dots and connect them, keeping in mind the requirement above. Do not hesitate to use your creative thinking skills — it is the main clue to solve this problem.
How to solve the 9 dots puzzle?
First of all, we need to consider several things before we solve the problem. Everyone knows that a square has four sides and two diagonal lines. However, this information will only confuse us in this case. There are not less than twenty lines that we can draw, connecting nine dots:
- four sides of the square;
- two diagonal lines;
- six lines that connect sides’ central dots with each other;
- eight lines that connect sides’ central dots with angles.
Do not forget that two dots can be connected only with one line. Also, bear in mind that a straight line is endless from both sides, so there is no need to limit yourself with these nine dots only.
All in all, how do we solve this problem? There is the most well-known way to do it:
- Step 1. Draw a straight line down from the very first dot (in other words, draw a left side of the square), but make it a bit longer, as if there was the fourth dot below;
- Step 2. From this point, you lead the next line to the last dot of the second column and then to the second dot of the third column. And again, draw a longer line, imagine that there is one more dot in this direction;
- Step 3. Now you need to draw a straight line from right to left, crossing the top row of the square;
- Step 4. The last step is to draw a diagonal line from the very first dot to the last one, going through the center of the square.
So, the problem is solved! You have not broken any rules — four lines connect nine dots, and you have drawn them without taking your pencil off the paper. The point is that no one told you to stay in the frames of the square — and that is the most important clue here. This principle works no matter what angle you choose to be the starting point.
Are there any creative solutions of the 9 dots 4 lines puzzle?
Nowadays there are 12 different solutions to this problem, thanks to the people who managed to come up with their unusual ideas.
For example, some of them can draw a line so wide that it will cover all nine dots at once. There was not a word about it in the task! Others manage to connect the dots using three lines — they draw a zigzag line that goes through each row. Another unusual solution can be achieved with manipulations with a pen. There is a requirement that we cannot take it off the paper, so we need to rotate it on the side and draw three parallel lines. It is pretty weird, but it works!
What lessons can we learn from this puzzle?
To begin with, it encourages us to look beyond the problem definition. We analyze it and realize what is allowed and what is prohibited in this task. Then we can think of other meanings of what we have just read. It is also important to define if the task is correct — in other cases, there is no solution at all.
Secondly, it helps us to start thinking “out of the box”. When we see any frames, we need to wonder if there is a possibility to enlarge them or even get rid of them. Sometimes such changes can lead to the right solution.
Finally, it makes us realize that hard work does not necessarily mean the right direction. If your solution is wrong, it will not become right no matter how many times you repeat it. When you feel that the right path is somewhere close, do not run in circles. Think of some other, simpler ways to find it. Anyways, all the great things are simple.
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