There is a set of figures made up of matches. Match puzzles with objects
We have all tried to solve puzzles with moving matches. Remember those? Simple, clear and quite interesting. We invite you to remember how this is done and solve these 10 exciting tasks. There will be no examples and math here, you can try to think over them together with the children. Each riddle comes with an answer. Here we go? 😉
1. Expand the fish
Exercise. Rearrange three matches so that the fish swims in the opposite direction. In other words, you need to rotate the fish 180 degrees horizontally.
Answer. To solve the problem, it is necessary to move the matches that make up the lower part of the tail and body, as well as the lower fin of the fish. Let's move 2 matches up, and one to the right, as shown in the diagram. Now the fish swims not to the right, but to the left.
2. Pick up the key
Exercise. In this problem, the shape of the key is composed of 10 matches. Move 4 matches to make three squares.
Answer. The task is solved quite simply. Four matches that form that part of the key handle must be moved to the key stem so that 3 squares are laid out in a row.
3. A glass with a cherry
Exercise. With the help of four matches, the shape of a glass is folded, inside of which there is a cherry. You need to move two matches so that the cherry is outside the glass. It is allowed to change the position of the glass in space, but its shape must remain unchanged.
Answer. The solution to this fairly well-known logical problem with 4 matches is based on the fact that we change the position of the glass by turning it over. The leftmost match goes down to the right, and the horizontal one moves to the right by half its length.
4. Seven squares
Exercise. Move 2 matches to form 7 squares.
Answer. To solve this rather complex problem, you need to think outside the box. We take any 2 matches that form the corner of the largest outer square and put them crosswise on top of each other in one of the small squares. So we get 3 squares 1 by 1 match and 4 squares with sides half the match.
5. Hexagonal star
Exercise. You see a star consisting of 2 large triangles and 6 small ones. By moving 2 matches, make sure that 6 triangles remain in the star.
Answer. Move the matches according to this scheme, and there will be 6 triangles.
6. Cheerful calf
Exercise. Move only two matches so that the calf is facing the other way. At the same time, he should remain cheerful, that is, his tail should remain directed upwards.
Answer. In order to look in the other direction, the calf simply needs to turn its head.
7. House of glasses
Exercise. Rearrange six matches so that two glasses make a house.
Answer. From the two extreme matches of each glass, you get a roof and a wall, and you just need to move the two matches at the bases of the glasses.
8. Libra
Exercise. The scales are made up of nine matches and are not in a state of equilibrium. It is required to shift five matches into them so that the scales are in balance.
Answer. Lower the right side of the scale so that it is level with the left. The match-base of the right side must remain motionless.
share Hello readers, friends! Today, the article is devoted to simple "toys" (they do not even need to be made, like others). And they are in every home.
For kids there are many puzzles with matches, but how to captivate a child with them and what games are better to start with? These games are a great way to develop spatial thinking and logic! My sons are very fond of such tasks. I'm sure you'll love them too - you just have to start right.
Many matchstick puzzles are aimed at school children or even adults. How about with preschoolers?
In general, any "adult" logic game can be adapted for children: divided into several tasks, reducing the number of permutation options. And when the child is already confident in coping with such simple options (and most importantly, he will enjoy these games - because he succeeds!), Then you can move on to more complex versions. Let's try to do the same with matches.
A few simple rules for playing with matches with children
- play with matches even children from 1.5 - 2 years old can, but on condition that they do not gnaw sulfur, and you make sure that the matches do not end up in the nose or ear
- be sure to prepare smooth flat surface. It can be a book, a smooth table or a board.
- start simple, even if your child is not a baby for a long time. Make sure the child understands what is shift 1 match, square, triangle. Let the child feel the joy of "victory"
Gleb and Mark play with matches
- don't show correct answer. Just postpone the task until the next time, and next time give an easier one.
- do not give tasks from the computer. Always give matches: it is important for children to try, they still have imaginative thinking is not developed enough to solve problems "in the mind"
- to make puzzles more interesting use small toys or pictures. You will understand how to do this by looking at our tasks.
Games and puzzles with matches I have divided it into three stages. Start with the first stage - it will be interesting even for younger students, and three-year-olds are usually completely delighted with these fairy tale games!
Stage 1: kids play
Kids 2-3 years old will hardly puzzle over the task of how to make a square ... .. They need games of a different kind, namely laying out figures, objects, and even better fairy tales from matches.
It was comfortable for us to play at a low coffee table (we have it set aside for children's creativity and games). So, pour a few packs of matches into the middle and start the story. For example, like this:
there lived a hedgehog
He had his own house
One day he met a snake
The snake lived in thick grass
Etc: tell us about how they became friends, met a horse, a man, tried to climb a tree and why the hedgehog did not succeed.
The child will definitely get involved if you don’t touch him, but it’s just interesting to create, tell and build. A little time will pass and you will already listen to fairy tales performed by the baby =)
Stage 2: keep playing and building
After a while (I think for children from 3-4 years old), when you tell a fairy tale and build from matches, ask the child to help you. Build SAME house, make a horse-girlfriend, chairs for all guests. Thanks to these tasks, the child will build "according to the model", which is very important for the development of spatial thinking. Without this stage, it will be very difficult to move on to the next - real tasks and puzzles.
Stage 3: start solving puzzles
Finally, we can move on to real puzzles. I collected simple puzzles that my 5 year old son could solve. I think your kids can do it too!
The easiest "preparatory" games
1. Fold 2 triangles out of 5 matches
2. Add one match to make 2 squares. (Harder option: Add one matchstick to make 3 quads)
3. Rearrange one match so that the hare's chair turns to the cabbage
4. How many squares are there? What about rectangles? Is a square a rectangle?
5. Add 2 matches to make 3 squares
6. Add one match to make 3 triangles
7. Turn the tracks in the opposite direction by rearranging 4 matches
8. There is a carrot in the basket. Move 2 matches so that the carrot lies under the basket
9. Make the letter H, the letter P, shifting one match
More difficult games
1. Move three matches so that the cancer crawls in the other direction
2. Turn the hut on chicken legs in the opposite direction
3. The wolf catches up with the hare. Move one match so that the wolf runs away from the hare
4. Move three matches so that the fish swims in the opposite direction
5. There is blue garbage in the scoop. Move 2 matches so that there is green debris in the scoop
6. Make 9 matches - 100 (Only if the child is familiar with this number)
7. Remove 3 matches to make a snowflake
8. Add three matches to make a wheel
9. The bunny is sitting on the roof. Hide it in the house by shifting three matches
10. Move 1 match so that the crocodile does not eat a bunny, but a carrot.
I will be glad if you like the games and matches become your favorite educational material =)
Sincerely, Nesyutina Ksenia
Join the conversation and leave a comment.
This is an educational article in mathematics, before starting classes, we recommend that you read the introductory part
It's a cramped, cramped house
One hundred sisters huddle in it.
Don't mess with your sisters
Thin…
We bring to your attention the next series of tasks for games with matches. Many of you are already familiar with the basic principles of working with this type of task. For those who meet them for the first time, we will briefly repeat the main points.
Match problems are traditionally problems of shifting or removing a certain number of matches. Usually, in the condition, we are offered some figure, from which, by shifting or removing the specified number of matches, we need to get a new figure that satisfies some required properties.
In all match problems, without exception, it is forbidden to bend or break matches, as well as to put them one on top of the other (assuming that this is one match).
If you need to remove or shift a certain number of matches, then by all means you need to remove or shift exactly as many matches as it is said - no more, no less.
One of the most fun ideas in matchstick puzzles is a non-standard way to change the "direction" of the figures involved in the match pattern. Surely you have already met the following problem:
Task 1.
The picture shows a cow. Move 2 matches so that the cow "looks" in the other direction.
Decision.
In order to show that the cow "looks" in the other direction, it is enough to turn the cow's head.
In addition to tasks similar to the previous one, there are also tasks in which you need to “reverse” the movement, shifting not all the matches of the figure. To do this, you need to guess which of the matches can participate in both directions. Let's take an example.
Task 2 .
The figure shows an arrow.
Move 3 matches so that the arrow flies in the opposite direction.
Decision.
Let's see what determines the direction of the arrow. An arrow is essentially two “ticks” connected by an “isthmus”. Each of the "ticks" can be easily "turned" in the opposite direction by shifting one match. After that, it is easy to find a solution to the original problem.
Answer:
Similar solution ideas have tasks for “transforming pictures”, when an image of one object is laid out in the figure, but you need to get an image of another.
Task 3.
In the picture of 10 matches, 2 glasses are laid out. Arrange 6 matches to make a house.
Decision.
To solve the problem, you need to notice the almost finished outlines of the house. We have highlighted them in gray in the figure.
After that, it remains only to “finish” the house.
(lower matches are shifted by half the length).
In this lesson, you will also be asked to remove or shift a certain number of matches to get from one set of geometric shapes - another set (a specified number of squares or triangles). Pay attention to the features of these figures specified in the condition: for example, squares are often required to be the same, and triangles are equilateral, that is, those in which all sides consist of the same number of matches. However, when not explicitly stated, any triangles and squares may be formed.
In these tasks, it is worth remembering the basic principle: no matter what set of geometric shapes you need to get, strictly prohibited the presence in the final picture of any "hanging matches". That is, matches that are not part of any of the geometric shapes required in the condition, matches that are simply superfluous, left over from the original figure. Even if these extra matches form a completely finished geometric figure, but not a word is said about it in the problem, they will still be considered “hanging”. Each match remaining on the table must be part of the figure required in the condition!
Task 4.
The lattice of matches forms 9 identical squares. Remove 4 matches so that exactly 5 squares remain.
Answer:
Pay attention to the complete absence of "hanging matches"! Indeed, each match is an integral part of a square. We got exactly five squares. The requirement of the task is fulfilled, and 4 matches are removed. So the problem is solved correctly.
Some problems have 2 or more solutions. For example, this problem has one more solution (see the figure below).
We see that by removing 4 matches in a different way, we again got exactly 5 squares. (Please note that this problem does not say that the squares must be exactly the same - we can count both small and large squares!) And also for any match, we can still specify at least one square in which it is a part . So, we got one more solution to our problem.
The lower figures show an example that is not a solution to the problem. Although, it would seem, all the conditions are met: we remove the gray matches, and we are left with 5 full squares. However, the matches highlighted in red will be "hanging", and their presence contradicts the basic principles of solving "Problems with matches".
Task 5.
Move 4 matches out of 16 so that you get exactly 3 squares.
Answer:
Possible options:
You will also meet in this task another type of task - a more creative one. In such tasks, it is required to build the figure described in the condition from a given number of matches. How to build it, and what the author means by, for example, "two rhombuses" - the child must guess for himself (although, of course, what a rhombus is - the child needs to be explained: this is a quadrangle, all sides of which consist of an equal number of matches). Such tasks require a little more practice, skill and spatial imagination than those described above.
Task 6.
From 10 matches, fold 3 squares.
Decision.
For 3 separate squares, we need 3 × 4 = 12 matches, while we only have 10. This means that our squares need to have common sides.
Answer 1:
Answer 2:
We see that this problem can again have 2 solutions.
The completion of the idea of folding the required number of geometric shapes is an exit into space. Of course, some of the problems discussed above can also be solved in space. But there was also a flat solution. In the next example, the flat case cannot be avoided. To make it convenient to solve such problems, you can offer the child to use plasticine to “fasten” matches or a magnetic set of sticks and balls.
Task 7.
From 12 matches, fold 6 squares.
Decision.
Let's count the number of matches needed. Each square has 4, total 6 squares. Total 4 × 6 = 24. But we have 12 matches. This means that each (!) match must be a side of two squares. Obviously, this is impossible on a plane. Let's go into space.
The solution to this problem will be a cube made of matches, with a side equal to one match. Indeed, the cube has 12 edges, and its faces (sides) form 6 squares.
(The “rear” matches are drawn in gray for better spatial perception of the picture.)
Also in the lesson you will meet tasks for non-trivial rearrangement: a match square may not look at all like we are used to. And maybe even have a side of half a match!
Task 8.
Move two matches out of nine so that you get three squares of the same size. It is impossible to bend, break and cross matches.
Answer:
The solution is "combined" squares.
In the figure, we can see 2 regular squares, as well as one in the middle, highlighted in blue. The numbers in the figure are in the lower left corner of each square.
Interestingly, we can place another square in this way by adding two matches, then another one ...
Above we have given examples of solutions to some problems. As you have already seen, the solution may well not be the only one. It all depends on the imagination of your child! Watch carefully that he does not violate the conditions, and if he comes up with an answer that does not match the one proposed by us, be glad that your student has found an original solution! If desired, as an exercise, you can invite the child to look for another solution to this problem.
We wish you success!
Test your knowledge!
For the smartest and most talented students, we hold a remote Internet Olympiad on the site. Immediately after passing the Olympiad, the results and a complete analysis of tasks for working on bugs are shown. Depending on the success of the Olympiad, electronic diplomas and commendations.
Each participant receives an email certificate participant.
Matches are not only a device for making fire, but also an opportunity to significantly diversify your leisure time. Everyone remembers how to do this, in whose soul a piece of a happy childhood still lives.
We offer to remember childhood and shift a few matches so that universal harmony reigns.
1. Remove two matches so that only two equilateral triangles remain
2. In the picture of matches, two rhombuses are laid out.
Move 2 matches so that you get 3 equal triangles.
3. In the drawing from matches, an incorrect equality is laid out 84 + 8 = 16.
Remove 3 matches so that the equality becomes true.
4. Move 3 matches so that you get 3 identical triangles.
5. In the drawing from matches, an incorrect equality is laid out 3 + 9 = 49.
Move 2 matches so that the equality becomes true.
6. In the picture of matches, 5 identical squares are laid out.
Move 3 matches so that you get only 4 identical squares.
7. In the drawing from matches, the wrong equality 2-7=5 is laid out.
Add 2 matches so that the equality becomes true.
8. In the picture of matches, 5 identical squares are laid out.
Move 3 matches so that you get only 4 squares.
9. In the drawing from matches, an incorrect equality is laid out 24-91 \u003d 120.
Move 1 match so that the equality is true.
10. Move 2 matches so that you get 3 triangles.
11. Move 3 matches to make 4 squares.
MBOU "Yunkurskaya secondary school named after V.I. Sergeev" Olekminsky district of the Republic of Sakha (Yakutia)
Collection of tasks and puzzles with matches
Compiled by: 
Soldatova T.P., teacher of mathematics
with. Yunkur 2016
Chapter 1
Correct the error in the equation by moving only one matchstick:
XI - V = IV
Move 1 matchstick to get the correct equation.
VIII + IV = XVII
Rearrange one match so that the example has the solution I + I = XII
III + I = I - I
VIII + IV = XVII
Using one extra match, achieve the correct equality
Move two matches so that the equality becomes true VI + X = III
In each of the three horizontal rows, shift one match so that six equalities (vertical and horizontal) are true
VI ∙ III = VII
V ∙ VIII = XXXIII
Make six out of five matches.
Make 8 out of 5 matches.
How to prove with matches that if you subtract 5 from 8, then nothing will remain?
Subtract 5 matches from 7 matches so that 5 are also left.
a) move one match, without touching the others, without touching the match representing the line of the fraction, so that a fraction equal to 1 is obtained.
b) turn this fraction into the number 1/3 without changing the number of these matches.
Add five more matches to the four matches laid out on the table so that you get one hundred.
In the drawing of matches, the number 57 is formed in Roman numeration.
By moving two of them without moving the rest, you get 0. Suggest 2 ways.
Prove that half of 12 is 7.
The riddle is a joke.
The son argued with his father that if you add eight to five, you can get one. And he won the argument. How did he do it?
Chapter 1
1. Six matches.
From six matches, build 4 regular triangles
2. Move two matches out of sixteen so that you get 6 squares.
3. Move 3 matches in this lattice in such a way that three squares are formed.
4. A figure similar to a children's toy “roly-poly” was folded out of matches.
You need to shift three matches so that this tumbler turns into a cube.
5. Move three matches out of twelve so that four identical squares out of three are obtained.
remove eight matches so that:
d) remove 3 matches so that 7 equal squares remain;
j) remove 6 matches so that you get 2 squares and 2 equal irregular hexagons;
14. This isosceles trapezoid is made up of ten matches.
Add five more such matches to it so that this trapezoid turns into four equal trapeziums.
15. Attach five matches to four matches so that you get one hundred:
We need to find two solutions.
16. Out of 12 matches, 4 identical squares are laid out. Move 2 matches to make 7 squares.
17. From 12 matches, you can make a figure of a cross, the area of \u200b\u200bwhich is equal to 5 "match" squares:
Fold from the same 12 matches one connected figure so that its area is equal to 4 "match" squares.
18. The figure shown in the figure is made of matches. Move two matches so that you get exactly four identical squares with a side length equal to the length of the match?
19. After shifting four matches, turn the ax into three equal triangles:
20. Move 6 matches to make 6 squares.
23. Eighteen matches form 6 identical squares adjacent to each other. Remove 2 matches so that 4 of the same squares remain.
26. In the figure shown in the figure, you need to shift 6 matches from one place to another in such a way that a figure is formed, made up of 6 identical quadrangles.
Chapter 1
Matches are arranged in three piles of 11, 7 and 6 matches.
It is necessary to decompose them into 3 piles so that each has 8 matches. This must be done in three moves, and you can only add as many matches as there are already in the pile.
There are two piles of matches. There are 7 matches in the first one, 5 in the second one. In one move, it is allowed to take any number of matches, but from one pile. The one who has nothing to take loses. Who wins when played correctly - the beginner or his partner? And how does he need to play?
There are 37 matches on the table. Each of the two players is allowed to take no more than 5 matches in turn. Whoever takes the last one wins. Who wins with the right strategy - the starter or the second player? What is the winning strategy?
From 18 matches, you need to add two quadrangles so that the area of one is greater than the area of \u200b\u200bthe other. Matches, as in all previous tasks, cannot be broken. Both quadrangles should lie apart, not adjacent to each other.
A cherry is placed in a "glass" made of matches:
It is necessary, having moved exactly two matches, to move the glass so that the cherry is outside.
A house is built from matches. Move two matches so that the house turns the other side.
The scales are made up of nine matches and are not in a state of equilibrium. Move five matches into them so that the scales are in balance.
In the picture you see a cow that has everything it needs: head, body, legs, horns and tail. The cow in the picture is looking to the left.
Move exactly two matches so that it faces to the right.
Arrange 6 matches so that each match is in contact with the other five.
The figure shows a fortress and a stone wall around it. Between the fortress and the wall is a moat filled with water, with hungry crocodiles in it. Show how, with the help of two matches, you can build a bridge between the fortress and the wall.
In the figure, with the help of 15.5 matches, a sad pig is laid out.
a) Make it fun by moving 3.5 matches.
b) Make the pig curious by removing one match and moving 2.5 matches.
Match cancer creeps up. Move three matches so that it crawls down.
Move 3 matches so that the arrow changes its direction to the opposite.
There are 6 small sections for rabbits in this picture. Can you build 6 rabbit hutches using only 12 matches?
Answers.
Chapter 1
X - VI = IV or XI - V = VI or XI - VI = V
VI = IX - III or VI = IV + II
Square root of 1
C - L = L or L + I = LI
In each of the three horizontal rows, shift one match so that six equalities (vertical and horizontal) are true
IV ∙ II = VIII
I V ∙ VIII = XXXII
39. a) the square root of unity
b) V
Let's draw the number VIII. Take away 5 matches from VIII and nothing remains
Let's draw the number XXVI with seven matches. We take 5 matches and leave V.
Place 6 matches as shown below:
a) _ I_ b) II
I - V I or V I - I
49. I + I = II or II + = II
50. IX - VIII = II
51. With the help of five and eight matches, he laid out the word "one".
Chapter 2
1. Six matches.
It is necessary to build a regular triangular pyramid.
2. Move two matches out of sixteen so that you get 6 squares.
3. Arrange 3 matches in this grid in such a way that three squares are formed.
4. Answer.
5. Move three matches out of twelve so that you get four identical squares out of three.
6. Move three matches out of twenty-four so that you get 14 squares out of
seven. Answer
7. Move four matches out of sixteen to make three squares
8. Move five matches in the figure shown in the figure so that three squares are obtained:
9. From 9 matches, make 6 squares.
10. Greek temple. This temple is built from eleven matches. It is required to shift four matches so that fifteen squares are obtained
11. The figure shown in the figure is made up of eight matches superimposed on each other. Remove 2 matches so that 3 squares remain.
12. In the figure shown in the figure:
remove eight matches so that:
a) there are only two squares left;
b) there are four equal squares left;
Option 1
Option 2
c) shift 12 matches so that 2 equal squares are formed;
e) remove 4 matches so that the remaining ones form one large and 4 small squares;
f) remove 4 matches so that the remaining ones form one large and 3 small squares;
g) remove 4 matches so that the remaining matches form 5 equal squares;
h) remove 6 matches so that the remaining matches form 5 equal squares;
i) remove 8 matches so that the remaining ones form 5 equal squares;
l) remove 6 matches so that 3 squares form from the remaining ones;
m) remove 8 matches so that 3 squares remain.
13. Spiral of matches. Of 35 matches, a figure resembling a "spiral" is laid out. Move 4 matches so that 3 squares are formed.
First solution:
Second solution:
16. Out of 12 matches, 4 identical squares are laid out. Move 2 matches to make 7 squares.
17. To make sure that the area of \u200b\u200bthis figure is 4, mentally supplement it to a triangle:
According to the Pythagorean theorem, this triangle is right-angled (the square of the length of its hypotenuse - 5 2 - is equal to the sum of the squares of the lengths of its legs - 3 2 + 4 2). This means that its area is equal to half the product of the lengths of its legs, that is, 6 "match" squares. And since the area of the shaded area is equal to 2 "match" squares, then the area of the figure we have constructed is exactly 4 "match" squares.
19. Axe.
20. Move 6 matches to make 6 squares. Answer:
21. Remove 17 matches so that 5 triangles remain
22. Remove 10 matches so that 4 equal squares are formed.
Option 1 Option 2.
3 option. 4 option
24. Move 4 matches so that 10 squares are formed.
25. Move 3 matches so that 3 equal squares are formed.
26. In the figure shown in the figure, you need to shift 6 matches from one place to another in such a way that a figure is formed, made up of 6 identical quadrangles.
27. In a figure made up of 17 matches, remove 5 matches without shifting the rest, so that only 3 squares remain.
28. From 12 matches you need to make a figure in which there would be three identical quadrangles and two identical triangles. How to do it?
29. On this puzzle, move 1 matchstick so that you get 4 identical triangles.
30. The figure shows the key.
a) Move 4 matches so that you get three squares.
b) Move 3 matches to get two rectangles.
c) Move 2 matches so that you get two rectangles.
31. From six matches, two of which are broken in half, it is required to make 3 equal squares.
32. There are 13 matches, each 5 cm long. You need to manage to lay out a meter from them.
Chapter 3
2. If played correctly, the novice player wins. His strategy: in his first move, he must equalize the number of matches in piles, i.e. take 2 matches from the first pile. Each next move must be "symmetrical" to the move of the second player, i.e. if "second" takes n matches from one heap, then "first" must also take n matches, but from another heap. Thus, if the "second" player can make a move, then the "first" player can also make a move. Since after each move the number of matches decreases, there will come a moment when the “second” cannot make a move (there will be no matches left in any of the heaps) and will lose.
3. On the first move, the beginner takes one match, and then each time supplements the number of matches taken by the opponent to six.
4. The area of the upper figure is formed by two squares, each with sides in one match. The lower quadrilateral is a parallelogram whose height is AB = 1.5 matches. The area of a parallelogram, according to the rules of geometry, is equal to its base multiplied by its height: 4 * 1.5 = 6, i.e. three times the area of the upper quadrangle.
8. Problem with a cow.
10. Fortress.
11. The problem of the pig.
12. Match cancer
References.
Krotov I.S. Gymnastics for the mind. - Moscow: CJSC "BAO-PRESS", LLC "ID" RIPOL classic ", 2005.
Nagibin F.F., Kanin E.S. Mathematical box: A manual for students in grades 4-8, middle school - 5th edition. - M .: Education, 1988. - 160 p.
Kovalenko V.G. Didactic games in mathematics lessons: Book. For the teacher.-M.-Enlightenment, 1990.
Nikolskaya I.L. Gymnastics for the mind: a book for primary school students, - M .: Exam Publishing House, 2013
Savin A.P. Entertaining mathematical problems.- M.: AST, 1995.
Troshin V.V. Entertaining tasks, exercises and games with matches in high school in the classroom and in extracurricular activities. Volgograd: Uchitel, 2008.
