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Puzzle 9 points. Few people can pass this test.

You probably love logical and creative tasks if you are reading this article. And, I must admit, this task is really quite complicated, although there are at least twelve (as smart people say) ways to solve it.

Condition

What do we see? We have nine dots arranged in the shape of a three by three square - three rows horizontally, three columns vertically. I don’t know what you thought when you read the title of the problem, but I’m willing to bet that when you saw the picture, you were a little puzzled. Most people, after thinking about a task for a few minutes, will be forced to admit that they have no idea how to do it.

Why is it not being decided?

And that’s why it’s a creative task, so it’s not easy to solve. Since childhood, we have been driven into a framework - this is the easiest way for the average person to be taught the minimum necessary for life and survival. We are taught minimal logic, but it is truly minimal and, as a rule, contains only one solution to each issue. But this option is supposedly one hundred percent, and creativity – well, that’s it... maybe it won’t be of any use. Let me guess - the shape of the dots immediately made you think of a square. But no, guys, this is the simplest solution - but there are only five lines, but you try to make four.

Solution

Throw away completely what is commonly called logic. Who said that you at least once drew the figure we needed in geometry at school? Where did you get the idea that the lines must end at one of the points?

From the top left point, draw a line down through the entire left column, but let the line continue further, not ending in the bottom row. Draw a similar line from the same point horizontally to the right. Now, from the same point, draw a line through the center point to the opposite one. You already guessed it, right? The last line should pass through the middle point of the bottom row and the middle point of the left column, connecting with the first two lines outside the square of dots.

It doesn’t matter from which corner of the square of dots you start drawing lines, but the result should be an umbrella. But admit it - you haven’t even thought about it.

Let's say right away that this is a tricky question. Or rather, the solution itself, like most similar problems, is not based on logic, but rather on creativity. M We are sure: desire and work, self-education and experience will help you achieve a new, non-trivial level of thinking.

The solution without further ado: how to connect nine dots using four lines?

This mystery has intrigued hundreds of thousands of people. The following conditions must be met: cross all nine points that form a square using straight lines (no more than four).

In this case, you cannot take your hand, or rather a pencil, off the sheet. The next line should begin where the previous one ended.At first glance, it is not so difficult, but in reality, each subsequent attempt often distances the inquisitive mind from a positive result.

The thing is that from childhood we were taught to think based on certain patterns and rules.First of all, logical thinking developed, on the principles of which our world is built. Yes, but not so.

Here you need to go beyond logic and stop thinking within the boundaries of the four sides of the square and its diagonals.

We analyze the problem based on knowledge about the object, but we should simply remember that a straight line is not necessarily limited by the boundaries of the form, that is, it is possible and necessary to go beyond the boundaries.

Let’s conditionally number each point from 1 to 9:

We draw the first line, starting from point 1 through 4, 7 and going beyond the boundaries of the figure.
Without lifting your hand from the sheet, we make a corner and strive for the point numbered 8 and 6 and go beyond the limits in the same way.
Next we turn and go through 3, 2, 1.
We turn through the corner of the square, going the rest of the way through points numbered 1, 5 and 9. It turns out to be a kind of arrow-cursor, which can be directed to any of the four corners at your request.

There is also a “hardcore” method for those who have spatial thinking.On a square piece of paper (sticky note), draw nine circles (as in the problem). Apply glue under the 7th and 8th points.

Take a cylindrical base. A tube of decorative cosmetics (lipstick or foundation) is ideal. Connect the place under 7 and 8 with the place under 2 and 3.

Draw one continuous line, starting from point No. 1 and going down in a spiral.When you return the leaf to its original form, you will see that three lines are drawn on it, covering all the points, which fits into the conditions of the puzzle.

“Advanced” individuals can solve it even without the help of glue, the main thing is to imagine the end result.

To solve this and similar puzzles, it is worth developing and discovering unusual approaches to the problem.Try the fun exercises below.

Tip: number the points directly on paper, this will make it easier to figure out the solution.

Games for home leisure

At one time, Steve Jobs, a man synonymous with the word “creativity,” emphasized that people who master the skill of creative thinking do not invent, but rather notice the connection between several things.

This is what makes it possible to synthesize something new.Therefore, first of all, it is worth “pumping up” such observation, over surrounding phenomena and things more often.

Game No. 1

We suggest the following exercise: look around and name as many things as possible that are in the same room with you and begin with the same letter, not excluding mental concepts.

For example, "m":

Furniture, zipper (on clothes), chalk (pet food)
Opinion, peacefulness, mannerism
Milk, materials (upholstery), T-shirt
Ointment, makeup, gauze, etc.

A simple version of the game: the letters “v”, “s”, “p”, “k”. If you are confident in your abilities, choose “t”, “a”, “d”.Don't limit yourself and your innate imagination.

If desired, you can find about 40+ words in one room. Experts find approximately 100 words in each room.

Game No. 2

The next game was very popular back in the 17th century. If you are offered to have fun with “nonsense”, do not rush to refuse; another name for it is “burime”.

To dive into the process, you will need a few sheets of paper, a pen, and a good company that doesn’t mind practicing collectively composing poetry. ZThe topic and limitations are specified in advance.

H Most often, obvious combinations of cognates, pronouns, verb forms and hackneyed platitudes (hello-dinner, love-carrot) are excluded. Sometimes a specific topic is discussed.

It happens like this: someone writes a line, and another complements the verse with the next one until a full-fledged work is obtained.

Game No. 3

This is for all ages, even the little ones.It develops spatial skills, which will certainly be useful in the adult future.

Place your child at a table and give him a black pencil and a piece of paper. Turn on some nice music and ask him to close his eyes.Let the child draw, interweave random lines among themselves, without thinking about accuracy.

Sometimes it is better to create several drawings in this way that overlap one another.Later, sit down with him and, using colored pencils, highlight shapes similar to animals, objects, and all kinds of images. Let the child himself be the source of ideas.

Choose entertainment that will help you kill time and benefit your memory.

Tip: puzzles with matches (sticks) will be an excellent workout for the mind. Such small puzzles will be interesting for both children and adults. They are available to everyone!

Exercises to develop creative thinking

Stand up. Take any book from the shelf. Blindly select a few words on two different pages.Now try to find everything in common that they might have. For example, the word “carpet” and “tree”: they both lie on the ground, their images are found in fairy tales (a flying carpet, a tree along which the learned cat walks), etc.

If you play with a child, choose simpler words: cat-dog, tomato-pear, table-chair.Write a dozen of any nouns on a piece of paper: “strawberry”, “fish”, “water”, etc. Now imagine that this sheet is the customer’s requirements, and you yourself are a builder-architect.

Build a house using these as basic requirements.For example, the wallpaper will be red “strawberry” in color, and the walls of the house will shine in the sun like fish scales. Let the house itself stand on the top of a mountain, where the sky is simply infinitely blue, like water, etc.

While sitting in a room, find an object within your sight that is familiar and interesting to you. For example, “apple”.

Books will come to your aid

Come up with five adjectives that go perfectly with the subject:

Green
Sour
Delicious
Soft
Juicy

Now we complicate the task and come up with five more adjectives, but those that are absolutely inappropriate in meaning: prickly, rough, plush, tin, slender.Some words are not so easy to work with, but that makes the task more interesting: well, train, wind, wall.

Take a pencil in your hands and draw a column of crosses in a checkered notebook.The width and height are arbitrary, just make sure they are far enough apart from each other.

Then we turn these crosses into small pictures, adding the necessary details (fish, crossed axes, sword, dragonfly, etc.).In the same way, draw the letter “o”, “t”, “v” and come up with new, interesting images. At an advanced level, you can turn sketches into short stories with action.

Make up a whole story! It's not as difficult as it might seem at first glance.

Use your computer wisely

Tip: read the words backwards: fairy tale - akzaks, bottle - aklytub, spoon - akzhol. This is certainly a useful activity that will help pass the time waiting in line or on public transport.

Online Games to Improve Creative Thinking

IQ-ball

You are a small, round, living ball with a suction cup flying out of your body.The goal is to get candy at each level, overcoming all kinds of obstacles. You will be hampered by fixed and moving elements, time limits, and inertia.

It is not possible to push off or cling with your paw from all surfaces. You will have to think quickly, the reach of the goal depends on this.

"Black cat"

In front of you is a field created from circles. A black cat sits in the middle of it. With a mouse click, you can fill a mini-area through which the cat can no longer pass.

One move is made by you, the next move is made by a cunning animal.Your task is to prevent him from running out of the edge of the playing field, because this means losing. Here you will have to use all your intellect and creative thinking, and most importantly, choose the right battle strategy.

In this case, we can advise you not to rush, but to think through your move in advance, mark the circles after one.In this case, you will always have time to block the path for the furry animal.

They are various images that you can easily find on the Internet.These are not just sketches, but pictures with inherent potential.

The same “doodle” can carry several meanings at the same time:

Facade
Wedge
Cloak
Diamond, etc.

The positive result of the game is the acceleration of thought processes, the diversified development of imagination and creativity. Such simple fun can captivate you for a long time.

"Memory Matrix"

Many adults and children are familiar with this game. In front of you is a field that is filled with squares for a few seconds.Then they disappear. Your task is to find these very figures “from memory”.

With each subsequent level the field grows and the task becomes more complicated. The game develops memory, creativity and the ability to quickly concentrate.

Advice: try playing Lines 98. At the same time, it develops logical thinking.

Tricky, developmental tasks

Draw a rectangular island on a piece of paper, in the middle of which countless treasures are hidden. It is surrounded by a moat of the same shape.

You are a jewel hunter who is beyond this land. The arsenal consists of only two planks, the length of each is slightly less than the width of the ditch.

It is impossible to jump over or fly over it, there is no rope to fasten the boards together, as well as nails, and each one individually is easy to fall into the abyss.

The goal is to get to the treasure. The answer to this riddle is based on the principles of geometry: “place” the first board on the corner of the ditch so that it does not fall through.

By doing this, you reduce the width of the moat, and the second board will freely reach the island with the treasure.Place a bold dot in the middle of the sheet. The goal is to drawThere is a regular circle around it, but so that the beginning of the line starts from the point itself.

Solution: fold the corner of the paper, put a dot in front of the corner itself, without lifting your hand, draw a line from the dot to the rest of the sheet, align the corner and continue moving until you draw a circle.

And finally, a simple question: why is it that only round pizza is made all over the world, but delivered in square boxes?

The contradiction here is only at first glance. And the answer is this: the pizza is round so that the corners do not burn, which inevitably happens when baking rectangular-shaped dishes.

In the case of a box, several factors are important:

This makes it easier to get food out of it
Square boxes are much cheaper and easier to produce than round ones.
The pizza seems more impressive in it

Advice: train your brain with small tasks at least several times a week and very soon you will feel that it has become much easier for you to find innovative solutions at work and in life, to think outside the strict framework of logical thinking.

Creativity is not a boring activity, and moreover, you can create with humor.Perhaps this problem is familiar to you. You may, like many others, think there is only one solution. So forget it and find something new.

Here they are - 9 magic points:

Task: Without lifting the pencil from the paper, draw 4 intersecting straight lines that touch all nine points only once.

We too often create boundaries that don't really exist. And we remain in them. We play by these rules. We use phantom criteria. We predict the development of a project based on trends and opportunities that have occurred in the past, without searching for and comparing new ones. We do not throw away the established paradigm without permission.

You could connect the dots with four lines extending beyond the square. Like this:

What do you think of the solution? Like? Doesn't it seem elegant and the only possible one to you? In fact, the most serious limitation in solving this problem is precisely the conclusion that there is only ONE answer. In reality, you can find several completely different solutions to this problem.

But how can we break the paradigm and find different results?

There is a technique called"forced departure"You need to forget about posing the problem and work on solving its distant version. This is the path to new paradigms, perspectives and results.

And the first modified task will be... the same 9 points

Task: this time draw 3 intersecting straight lines that should touch each point only 1 time. If you cannot find a solution, try to determine what frameworks, conclusions and criteria hinder you and stop your search.
Let's take a look together.

First, what do you see when you look at the dot area? I hope you have already given up the habit of drawing a square and other shapes. Now you may be blocked by seeing these dots on a piece of paper. In order to find several ways to solve the "3 lines" problem, you need to imagine these points in space. This is the only way 3 straight lines can leave a piece of paper.

Secondly, don't you think these lines should go through the center of each of the 9 points? This non-existent condition prevents you from thinking.

Third, how do you define the point itself? At school we were taught that dot- this is an element of geometric space, characterized only by position, belonging, and not by size or shape. But these circles, which in our problem are called dots, have both shape and size. Not entirely fair on our part, huh? Well, that's life. But in real life, dots vary greatly in size and shape. On billboards they grow to the size of a human head, and on a clown costume they shrink to the size of a pea. So add some reality to your dot ideas before you fall victim to another bad habit that interferes with creative thinking.

It's about using narrow definitions that limit the thinking process like a funnel. We get stuck in old paradigms.

Thanks to missing boundaries, refined assumptions, and expanded definitions, we found the following solution to the 3-line problem:

Mentally leave the sheet of paper. The first straight line passes tangent to the first point, intersects the second almost in the center and slightly touches the third point. Extend this line further, beyond the edge of the paper, until another line can do the same with the middle column of dots. The third straight line should behave similarly.

Here is a solution based on the postulate of non-Euclidean geometry that parallel lines intersect at infinity. The answer consists of three parallel lines, each touching a different row of points, and then all three lines connecting at infinity. Neat paradigm shift, right? It is possible that finding a solution will require leaving your comfort zone.

A habit that reduces creativity to zero: Often we identify a “fair” idea even before making a choice among several solutions. Don't let "decency" get in the way of your search.

The next problem is for 9 points.

Task: use 2 intersecting straight lines that will touch all 9 points only 1 time.

Impossible, you say? You could do with another revision of your unfounded assumptions, non-existent boundaries, far-fetched criteria, narrow definitions, thought funnels and patterns.

One block lies in the definition of the line you adhere to. From the school curriculum: line- this is an infinite number of points that are located on one line that has neither beginning nor end, i.e. have only one property - length. In real life, lines have width. Remember the flow of traffic on highways or a chain of trolleybuses in front of an intersection. Thus, again this time, the tendency towards ready-made terms led you to the conclusion that only thin lines can be used.
This is what happens if you expand the definitions - a solution consisting of one wide and one narrow line!

To find a solution to our last problem, try using the “forced withdrawal” technique.

Task: one straight line must touch all nine points.

In general, there are at least a hundred acceptable solutions. Some of them are included here to evoke new paradigms and thought funnels and whet the appetite for more.

Use one wide line that touches each point.
Pass a large 3-dimensional line through the nine dots from top to bottom so that it passes through the paper and touches each dot.
Fold the paper so that you can make one line that touches each point. (Did you assume that you were forbidden to fold the paper?)
Cut the paper so that each dot is on a separate piece. Place the particles in one line that will touch every point. (You thought you couldn't cut paper?)
Roll a piece of paper into a cone and draw a straight line that spirals around the surface of the cone and touches all nine points. (Has it ever occurred to you that you can do whatever you want with paper?)
Place a piece of paper with nine points on the Earth's equator and carefully draw a straight line around the Earth enough times so that it eventually touches each point. Or place the paper on the edge of the Universe and draw your straight circular line around the Universe until it touches every point. (Did you consider that you could use your imagination? Notice that we have expanded our nine-point mental funnel to a window overlooking the edge of the Universe).
Write "ONE" on top of the first row of dots, "STRAIGHT" above the middle row of dots, and "LINE" above the bottom row of dots. You touched the dots with the words "one straight line" (Did you think you couldn't use words?)
Draw a line on the thin edge of the paper. Look at the nine dots across this sideline.
Move the line like windshield wipers in a car, and you will touch all the points.
(Did you feel like you couldn't move the line, or that the line had to touch all the points at the same time?)
Cut a straight line into 1000 pieces and scatter them over nine points (Was it forbidden to cut lines?)
Cut so that one point is on a separate piece of paper. Line up the dots in a tower, one above the other. Click on all the points with a pencil. Not only have you touched all the points on the same line, but you have destroyed both the points and the problems. In one fell swoop.
Wait. Here's another food for thought. Imagine you are sitting at the table with your dots, and then the king of beasts comes in and swallows them all at once. Or how about nine people, each named Dot, eaten by one lion?
I can't resist making an even weirder decision. Change the points into clothespins and hang them on one straight clothesline. (Are you assuming that you can't convert points or lines to something else?)
Or you can turn the dots into tennis balls and play tennis with them until each one touches the tennis net, which is one straight line.
Or convert a straight line into a sunbeam and use a glass prism to break it into many colored lines that touch all nine points. Enough for now?

These puzzles can transform the creative atmosphere of your thinking.It doesn't take long to explain that this puzzle is a metaphor for the problems we face at work and in life. You can learn a lot from these 9 points.

Based on materials from the book"R&D CREATIVITY & INNOVATION HANDBOOK" A Practical Guide To Improve Creative Thinking & Innovation By

This is a rather difficult puzzle, because it is not so easy to figure out how to connect as many as 9 dots using just 4 lines without lifting your hands from the paper. There was a time that, after many fruitless attempts, I decided that this was simply impossible, but in fact the solution is very simple.

We start drawing from the lowest right point.

We solved this logical problem a long time ago at school, as far as I know, there is only one solution, without a variety of options. You need to take one point and, without lifting your pen, draw something like an arrow, as shown in the figure. This arrow can point in any direction you like)

Carolina has already given a clear example, but I will use your drawing to explain

You need to start from the point where the base of the red line will be. We draw the red diagonal. Without lifting your hand, draw a line corresponding to the blue one in the figure. Blue turns to purple. And the end will be a line similar to the green one. Everything is clear and simple. Four lines, the hand does not come off, all the points are connected to each other. The order of the lines is very important; it won’t work any other way. The only order of the blue and green lines can be swapped. Red is definitely the first one.

Connecting these points with one line without lifting your hand is not as difficult as it seems at first glance. To do this, you need to draw a triangle, the corners of which go beyond the points, you can start with a right angle, and when you return to a right angle, divide it in half by connecting the remaining points.

You can connect 9 points evenly separated from each other and having regular squares inside using a triangle that has 3 sides and a straight line from its vertex extending from its vertex.

Without looking up, these lines can be drawn as follows: from the corner, draw a straight line along the outside, connecting 4 points, then diagonally to the opposite point, 3 more points, then return to the starting point - the top, capturing 2 more points and go down at a right angle down and crossing the hypotenuse we finish the figure at the 9th point.

The condition is met, not a single point was crossed twice, the hand did not come off.

You can solve the problem in the second way, vice versa.

As far as I know, there is only one option (or rather, I know only one, it’s possible that our thinkers have come up with another way :-)). It is best seen in the picture, where all 9 points are connected by four straight lines.

Connecting 9 points with 4 straight lines is very simple. To do this, you need to draw lines beyond these points to create the desired angle. To clearly understand how nine dots are connected by four lines, watch this video.

If you have landed on this page, then you have probably already tried to solve the “9 dots test”, namely connecting nine dots with four straight lines without lifting your pen from a sheet of paper. If you couldn't solve this puzzle, don't despair. On this page you can find several solutions to this famous nine-point puzzle that has puzzled the minds of many thousands, if not millions, of people.

The task

Condition:

Condition: you need to connect the drawn nine dots with four straight lines without lifting your pen from the sheet of paper.

This task is not as simple as it might seem. To solve it you need to think outside the box and apply your creative thinking, otherwise nothing will work. If you try to act head-on and start connecting all the dots with standard lines, then you may spend a lot of time and still not solve the problem of nine dots. Our standard thinking, which we are taught in school, directs us to find a solution based on only six typical lines: the 4 sides of a square and its 2 diagonals. Most people think that the solution to the 9-dot puzzle should lie within this framework. But he's not there. You can’t even find it if you connect 2 more lines between the centers of the sides of the square:

In general, only 20 straight lines can be drawn between all nine points: 4 sides of the square; 2 diagonals; 6 lines connecting the centers of the sides of a large square; 8 lines connecting the centers of the sides of a large square with its corners. How to draw all the line segments connecting our 9 points is shown in the figure below:

But even using this diagram, it is impossible to find 4 lines that could connect all nine dots without lifting your hand.

The correct solution to the “9 points test”

The solution to this puzzle lies somewhat beyond our standard perception of the problem. In order to find the right approach yourself, remember that:

Only one straight line can be drawn through any 2 points.
A straight line is not a line segment and therefore we don't have to limit ourselves to our nine blue circles when drawing lines.

Thus, let's try to extend the lines beyond the square that limited us until recently. Here you can see that our search area has increased significantly. With a little effort you can come to one of the right decisions.

The sequence of connecting nine points with four lines:

To begin, draw a line connecting point No. 1 and point No. 7 through point No. 4. Don't stop moving and continue drawing approximately as much as from point No. 4 to point No. 7.
Next, move diagonally to the right and upward, connecting points No. 8 and No. 6. Do not stop at point No. 6 and continue the line to a mental straight line passing through the upper side of our square.
Draw a line from right to left sequentially through points No. 3, No. 2 and No. 1. Stop at point #1.
Now draw the final segment through points No. 1, No. 5 and No. 9. All 9 points are, indeed, connected by four lines, as required in the task conditions.

Other options. This method is not the only one; you can start from any corner and move in one of two directions. On the 4brain website there are at least 12 such options for solving the “9 points 4 lines” problem:

Just think, a problem that many cannot solve has 12 ways to solve it. Also see a simplified version of this problem: how to connect 4 points with three lines so that the lines close into a whole figure.

Get creative with this puzzle

Most people who solved this problem were never able to get beyond standard thinking, which in this test is expressed by a square formed by nine dots. We are comfortable looking at any life task directly, in the most simple way. On the other hand, a person can spend a lot of time and effort using a standard approach to find the right solution, when it is better to look for this solution by initially approaching the process creatively.

In our life, we often come across such problems about “nine points and four lines”, and in order to solve them, develop your creative thinking, including with the help of our training. After all, the problem of 9 points has other solutions (read more about this).