Urban math game kangaroo job. Mathematical competition-game “Kangaroo - mathematics for everyone

March 16, 2017 Grades 3-4 The time allotted for solving problems is 75 minutes!

Tasks worth 3 points

№1. Kenga made up five addition examples. What is the largest amount?

(A) 2+0+1+7 (B) 2+0+17 (C) 20+17 (D) 20+1+7 (E) 201+7

№2. Yarik marked with arrows on the diagram the path from the house to the lake. How many arrows did he draw wrong?

(A) 3 (B) 4 (C) 5 (D) 7 (E) 10

№3. The number 100 is multiplied by 1.5 times, and the result is halved. What happened?

(A) 150 (B) 100 (C) 75 (D) 50 (E) 25

№4. The picture on the left shows beads. Which picture shows the same beads?

№5. Zhenya made six three-digit numbers from the numbers 2.5 and 7 (the numbers in each number are different). She then arranged the numbers in ascending order. What is the third number?

(A) 257 (B) 527 (C) 572 (D) 752 (D) 725

№6. The figure shows three squares divided into cells. On the extreme squares, some of the cells are shaded, and the rest are transparent. Both of these squares were superimposed on middle square so that their upper left corners match. Which of the figurines is visible?

№7. What is the most small number white cells in the figure should be painted over so that there are more shaded cells than white ones?

(A) 1 (B) 2 (C) 3 (D) 4 (E)5

№8. Masha drew 30 geometric shapes in this order: triangle, circle, square, rhombus, then again triangle, circle, square, rhombus and so on. How many triangles did Masha draw?

(A) 5 (B) 6 (C) 7 (D) 8 (E)9

№9. From the front, the house looks like the picture on the left. Behind this house there is a door and two windows. What does he look like from behind?

№10. It's 2017 now. In how many years will the next year be without the digit 0?

(A) 100 (B) 95 (C) 94 (D) 84 (E)83

Tasks, evaluating 4 points

№11. Balls are sold in packs of 5, 10 or 25 pieces each. Anya wants to buy exactly 70 balloons. What is the smallest number of packages she will have to buy?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

№12. Misha folded a square sheet of paper and poked a hole in it. Then he unfolded the sheet and saw what is shown in the figure on the left. What might the fold lines look like?

№13. Three turtles are sitting on a path in dots A, AT and With(see picture). They decided to gather at one point and find the sum of their distances. What is the smallest amount they could get?

(A) 8 m (B) 10 m (C) 12 m (D) 13 m (E) 18 m

№14. Between numbers 1 6 3 1 7 two characters must be inserted + and two characters × so that you get the best results. What is it equal to?

(A) 16 (B) 18 (C) 26 (D) 28 (E) 126

№15. The strip in the figure is made up of 10 squares with a side of 1. How many of the same squares must be attached to it on the right so that the perimeter of the strip becomes twice as large?

(A) 9 (B) 10 (C) 11 (D) 12 (E) 20

№16. Sasha marked a cell in the checkered square. It turned out that in its column this cell is fourth from the bottom and fifth from the top. In addition, in its line, this cell is the sixth from the left. Which one is right?

(A) second (B) third (C) fourth (D) fifth (E) sixth

№17. Fedya cut out two identical figures from a 4 × 3 rectangle. What kind of figurine could he not get?

№18. Each of the three boys guessed two numbers from 1 to 10. All six numbers turned out to be different. Andrey's sum of numbers is 4, Borya's is 7, Vitya's is 10. Then one of Vitya's numbers is

(A) 1 (B) 2 (C) 3 (D) 5 (E)6

№19. Numbers are placed in the cells of a 4 × 4 square. Sonya found a 2 × 2 square in which the sum of the numbers is the largest. What is this amount?

(A) 11 (B) 12 (C) 13 (D) 14 (E) 15

№20. Dima rode a bicycle along the paths of the park. He entered the park at the gate BUT. During the walk, he turned right three times, left four times and turned around once. Through which gate did he leave?

(A) A (B) B (C) C (D) D (E) the answer depends on the order of rotations

Tasks worth 5 points

№21. Several children took part in the run. The number of Misha who came running before three times more number those who ran after him. And the number of those who came running before Sasha is two times less than the number of those who came running after her. How many children could participate in the race?

(A) 21 (B) 5 (C) 6 (D) 7 (E) 11

№22. In some of the filled cells, one flower is hidden. Each white cell contains the number of cells with flowers that have a common side or vertex with it. How many flowers are hidden?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 11

№23. A three-digit number is called surprising if among the six digits that it and the number following it are written, there are exactly three ones and exactly one nine. How many amazing numbers are there?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

№24. Each face of the cube is divided into nine squares (see figure). What is the most big number squares can be colored so that no two colored squares have common side?

(A) 16 (B) 18 (C) 20 (D) 22 (E) 30

№25. A stack of cards with holes is strung on a thread (see picture on the left). Each card is white on one side and shaded on the other. Vasya laid out the cards on the table. What could have happened to him?

№26. From the airport to the bus station every three minutes there is a bus that travels 1 hour. 2 minutes after the departure of the bus, a car left the airport and drove to the bus station for 35 minutes. How many buses did he overtake?

(A) 12 (B) 11 (C) 10 (D) 8 (E) 7

Constructions and logical reasoning.

Task 19. winding coast (5 points) .
In the picture - an island on which a palm tree grows and several frogs sit. island restricted coastline. How many frogs are on the ISLAND?

Answer options:
BUT: 5; B: 6; AT: 7; G: 8; D: 10;

Decision
When solving this task on a computer, you can use the Fill tool. Now it is clearly seen that 6 frogs are sitting on the island.

You could do something similar to this fill with a pencil on a sheet of conditions. But there is another interesting way to determine whether a point is inside or outside a closed non-self-intersecting curve.

Let's connect this point (frog) with a point that we know for sure is outside the curve. If the connecting line has an odd number of intersections with the curve, then our point lies inside (i.e. on the island), and if it is even, then outside (on the water)

Correct answer: B 6

Task 20. Numbers on balls (5 points) .
Mudragelik has 10 balls, numbered from 0 to 9. He divided these balls among his three friends. Lasunchik got three balls, Krasunchik - four, Sonk about- three. Then Mudragelik asked each of his friends to multiply the numbers on the received balls. Lasunchik received a product equal to 0, Krasunchik - 72, and Sonyk about- 90. All the kangaroos correctly multiplied the numbers. What is the sum of the numbers on the balls Lasunchik got?

Answer options:
BUT: 11; B: 12; AT: 13; G: 14; D: 15;

Decision
It is clear that among the three balls that Lasunchik received, there is the number 0. It remains to find 2 more numbers. Krasunchik has as many as 4 balls, so it will be easier to first find which three numbers from 1 to 9 need to be multiplied to get 90, like Sonya a? 90 = 9x10 = 9x2x5. This will the only way represent 90 as a product of the numbers on the balls. After all, if Sonka a one of the balls was with one, then it would be required to break 90 into the product of two factors less than 10, which is impossible.

So Lasunchik has 0 and two other balls, Sonk a balls 2, 5, 9.
Four Krasunchik's balls give in the product 72. Let's first break 72 into the product of two factors, so that then each of these factors can be divided by 2 more:
72 = 1x72 = 2x36 = 3x24 = 4x18 = 6x12 = 8x9

From these options, we immediately exclude:
1x72 - because we can't split 1 into 2 different multipliers
2x36 - because 2 breaks only as 1x2, but Krasunchik definitely doesn’t have a ball with the number 2
8x9 - because 9 is broken like 1x9 (you can’t break it like 3x3, since there are no two balls with triples), and Krasunchik doesn’t have a nine either

Remaining options:
3x24 - splits into 4 multipliers as 1x3x4x6
4x18 - split into 4 multipliers as 1x4x3x6, that is, the same as the first option
6x12 - breaks like 1x6x3x4 (because, remember, there is no ball with a deuce).

So, for a set of Krasunchik's balls, there is only one option. He has balls 1, 3, 4, 6.

For Lasunchik, in addition to the ball with the number 0, there are balls 7 and 8. Their sum is 15

Correct answer: D 15

Task 21. Ropes (5 points) .
Three ropes are attached to the board as shown in the picture. You can attach three more to them and get a solid loop. Which of the ropes given in the answers will make it possible to do this?
According to groups "Kangaroo" VKontakte, only 14.6% of the participants of the Mathematical Olympiad from the third and fourth grades solved this problem correctly.

Answer options:
BUT: ; B: ; AT: ; G: ; D: ;

Decision
This problem can be solved by mentally applying the picture to the picture and carefully checking the connections. And you can do a little better. Let's renumber the ropes and write down the line 123132 - these are the ends of the loops on the figure given in the condition. Now, above the ends of the ropes in the answer options, we also sign these numbers.

Now it is easy to see that in the variant BUT rope 2 connects to itself. In the variant B rope 1 connects to itself. But in the variant AT all the ropes are connected to each other in one large loop.

Correct answer: B
Task 22. Elixir Recipe (5 points) .
To prepare an elixir, you need to mix five types of aromatic herbs, the mass of which is determined by the balance of the scales shown in the figure (we neglect the mass of the scales themselves). The healer knows that 5 grams of sage should be put into the elixir. How many grams of chamomile should he take?

Answer options:
BUT: 10 g; B: 20 g; AT: 30 g; G: 40 g; D: 50 g;

Decision
Basil should be taken as much as sage, that is, also 5 grams. There is as much mint as sage and basil together (we do not take into account the weight of the scales themselves). So, mint should be taken 10 grams. Melissa should be taken as much as mint, sage and basil, that is, 20g. And chamomile - as much as all the previous herbs, 40 g.

Correct answer: G 40g

Task 23. Unseen Beasts (5 points) .
Tom drew a pig, a shark, and a rhinoceros on the cards and cut each card as shown. Now he can stack different "animals" by connecting one head, one middle and one back. How many different fantasy creatures can Tom collect?

Answer options:
BUT: 3; B: 9; AT: 15; G: 27; D: 20;

Decision
This is classic problem to combinatorics. the good thing is that they can (and should) be solved not mechanically by applying the rules for calculating the number of permutations and combinations, but by reasoning. How much different options is for the head of an animal? Three options. And for the middle part? Also three. There are three options for the tail. This means that there will be 3x3x3 = 27 different options in total. We multiply these options because any body and any tail can be attached to each head, so that each segment of the animal increases the combination options exactly 3 times.

By the way, the condition contains the word "fantastic". But after all, by combining any heads, torsos and tails, we will get real pigs, sharks and rhinos. So the correct answer should have been 24 fantasy animals and three real ones. However, apparently fearing different interpretations of the condition, the authors did not include option 24 in their answers. Therefore, we choose the answer D, 27. And who knows, what if the drawings also depict a fantastic talking pig, a fantastic flying shark and a fantastic rhinoceros who proved Fermat's theorem? :)

Correct answer: G 27

Task 24. Kangaroo bakers (5 points) .
Mudragelik, Lasunchik, Krasunchik, Khitrun and Sonko baked cakes on Saturday and Sunday. During this time, Mudragelik baked 48 cakes, Lasunchik - 49, Krasunchik - 50, Khitrun - 51, Sonko - 52. It turned out that on Sunday each kangaroo baked more cakes than on Saturday. One of them baked twice as much, one - 3 times, one - 4 times, one - 5 times, and one - 6 times.
Which kangaroo baked the most cakes on Saturday?

Answer options:
BUT: Mudragelik; B: Lasunchik; AT: Krasunchik; G: Khitrun; D: Sonko;

Decision
Let's first think about what information the fact that someone baked exactly 2 times more cakes on Sunday than on Saturday gives us? If on Saturday the kangaroo baked some cakes, then on Sunday - so many and so many more. This means that in just two days he baked three times (1 + 2 = 3) more cakes than on Saturday.

So what? And the fact that, for example, he could not bake 49 or cakes, since these .

It turns out that the one who baked three times more cakes on Sunday than on Saturday, their total number should be whitened by 4 = 1 + 3. Some people have 5, some have 6 and some have 7.

The principle of solving this problem emerges. Here we have five numbers: 48, 49, 50, 51, 52. 2 numbers (48 and 51) are divisible by 3 of them and 2 numbers are also divisible by 4 (48 and 52). But only one number, 50, is divisible by 5. It turns out that the one who baked 50 pies on Sunday baked 4 times more of them than on Saturday.

Only one number is also divisible by 6, this is 48. It turns out that the kangaroo, who baked only 48 cakes, baked them like this: 8 on Saturday and 40 on Sunday. Well, then it's simple. We get that:
Mudragelik baked 48 cakes: 8 on Saturday and 40 on Sunday (5 times more)
Lasunchik baked 49 cakes: 7 on Saturday and 42 on Sunday (6 times more)
Krasunchik baked 50 cakes: 10 on Saturday and 40 on Sunday (4 times more)
Khitrun baked 51 cakes: 17 on Saturday and 34 on Sunday (2 times more)
Sonko baked 52 cakes: 13 on Saturday and 39 on Sunday (3 times more)

It turns out that Hitrun baked the most cakes on Saturday.

Correct answer: G Khitrun

The Kangaroo competition has been held since 1994. It originated in Australia at the initiative of the famous Australian mathematician and teacher Peter Halloran. The competition is designed for the most ordinary schoolchildren and therefore quickly won the sympathy of both children and teachers. The tasks of the competition are designed so that each student finds interesting and accessible questions for himself. After all the main objective of this competition is to interest the children, instill in them confidence in their abilities, and the motto is “Mathematics for all”.

Now about 5 million schoolchildren around the world participate in it. In Russia, the number of participants exceeded 1.6 million people. AT Udmurt Republic 15-25 thousand schoolchildren participate in Kangaroo every year.

In Udmurtia, the competition is held by the Center educational technologies"Another School"

If you are in another region of the Russian Federation, please contact the central organizing committee of the competition - mathkang.ru

Competition procedure

The competition takes place in test form in one step without any pre-selection. The competition is held at the school. Participants are given tasks containing 30 tasks, where each task is accompanied by five possible answers.

All work is given 1 hour 15 minutes of pure time. Then the answer forms are submitted and sent to the Organizing Committee for centralized verification and processing.

After verification, each school that took part in the competition receives a final report indicating the points received and the place of each student in general list. All participants are given certificates, and the winners in parallel receive diplomas and prizes, the best ones are invited to math camps.

Documents for organizers

Technical documentation:

Instructions for conducting a competition for teachers.

The form of the list of participants in the competition "KANGAROO" for school organizers.

Form of Notification of the informed consent of the participants of the competition (their legal representatives) to the processing of personal data (to be filled in by the school). Their filling is necessary due to the fact that the personal data of the contest participants are automatically processed using computer technology.

For organizers who wish to additionally secure themselves for the validity of collecting the fee from the participants, we offer the form of the Minutes of the meeting of the parent community, by the decision of which the powers of the school organizer will also be confirmed by the parents. This is especially true for those who plan to act as an individual.

Millions of children in many countries of the world no longer need to be explained what "Kangaroo", is a massive international mathematical contest-game under the motto - " Math for everyone!".

The main goal of the competition is to involve as many children as possible in the solution math problems, to show each student that thinking about a problem can be a lively, exciting, and even fun affair. This goal is achieved quite successfully: for example, in 2009 more than 5.5 million children from 46 countries participated in the competition. And the number of participants in the competition in Russia exceeded 1.8 million!

Of course, the name of the competition is associated with distant Australia. But why? After all, mass mathematical competitions have been held in many countries for more than a decade, and Europe, in which the new competition was born, is so far from Australia! The fact is that in the early 80s of the twentieth century, the famous Australian mathematician and teacher Peter Halloran (1931 - 1994) came up with two very significant innovations that significantly changed the traditional school olympiads. He divided all the problems of the Olympiad into three categories of difficulty, and simple tasks should be accessible to literally every student. And besides, the tasks were offered in the form of a multiple-choice test, focused on computer processing results The presence of simple but entertaining questions ensured a wide interest in the competition, and a computer check made it possible to quickly process a large number of works.

The new form of competition was so successful that in the mid-80s, about 500,000 Australian schoolchildren participated in it. In 1991 the group French mathematicians, based on the Australian experience, held a similar competition in France. In honor of the Australian colleagues, the competition was named "Kangaroo". To emphasize the entertainingness of the tasks, they began to call it a contest-game. And one more difference - participation in the competition has become paid. The fee is very small, but as a result, the competition ceased to depend on sponsors, and a significant part of the participants began to receive prizes.

In the first year, about 120,000 French schoolchildren took part in this game, and soon the number of participants grew to 600,000. This began the rapid spread of the competition across countries and continents. Now about 40 countries of Europe, Asia and America participate in it, and in Europe it is much easier to list countries that do not participate in the competition than those where it has been held for many years.

In Russia, the Kangaroo competition was first held in 1994 and since then the number of its participants has been growing rapidly. The competition is included in the program "Productive game contests» Institute for Productive Learning under the guidance of Academician of the Russian Academy of Education M.I. Bashmakov and is supported by Russian Academy education, the St. Petersburg Mathematical Society and the Russian State Pedagogical University them. A.I. Herzen. The Kangaroo Plus Testing Technology Center took over the direct organizational work.

In our country, a clear structure of mathematical Olympiads has long been established, covering all regions and accessible to every student interested in mathematics. However, these Olympiads, starting from the regional and ending with the All-Russian, are aimed at highlighting the most capable and gifted from the students who are already passionate about mathematics. The role of such Olympiads in shaping the scientific elite of our country is enormous, but the vast majority of schoolchildren remain aloof from them. After all, the problems that are offered there, as a rule, are designed for those who are already interested in mathematics and are familiar with mathematical ideas and methods that go beyond school curriculum. Therefore, the Kangaroo contest, addressed to the most ordinary schoolchildren, quickly won the sympathy of both children and teachers.

The tasks of the competition are designed so that every student, even those who do not like mathematics, or even are afraid of it, will find interesting and accessible questions for themselves. After all, the main goal of this competition is to interest the children, instill in them confidence in their abilities, and its motto is “Mathematics for All”.

Experience has shown that children are happy to solve competition problems that successfully fill the vacuum between standard and often boring examples from a school textbook and difficult, demanding special knowledge and preparation, tasks of city and regional mathematical Olympiads.

We present tasks and answers to the competition "Kangaroo-2015" for 2 classes.
The answers to the tasks Kangaroo 2015 are after the questions.

Tasks worth 3 points
1. What letter is missing in the pictures on the right to form the word KANGAROO?

Answer options:
(A) D (B) F (C) K (D) N (E) R

2. After Sam climbed the third step of the stairs, he began to walk through one step. On what step will he be after three such steps?
Answer options:
(A) 5 (B) 6 (C) 7 (D) 9 (E) 11

3. The picture shows a pond and some ducks. How many of these ducks are swimming in the pond?

Answer options:

4. Sasha walked twice as long as she did her homework. She spent 50 minutes on the lessons. How long did she walk?
Answer options:
(A) 1 hour (B) 1 hour 30 minutes (C) 1 hour 40 minutes (D) 2 hours (E) 2 hours 30 minutes

5. Masha drew five portraits of her favorite nesting dolls, but she made a mistake in one drawing. In which?

6. What is the number indicated by the square?

Answer options:
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

7. Which of the figures (A) - (D) cannot be made up of the two bars shown on the right?

8. Seryozha conceived a number, added 8 to it, subtracted 5 from the result and got 3. What number did he conceive?
Answer options:
(A) 5 (B) 3 (C) 2 (D) 1 (E) 0

9. Some of these kangaroos have a neighbor who looks in the same direction as him. How many kangaroos have such a neighbor?


Answer options:

10. If yesterday was Tuesday, then the day after tomorrow will be
Answer options:
(A) Friday (B) Saturday (C) Sunday (D) Wednesday (E) Thursday

Tasks worth 4 points

11. What is the smallest number of figurines that must be removed to leave figurines of the same type?

Answer options:
(A) 9 (B) 8 (C) 6 (D) 5 (E) 4

12. There were 6 square chips in a row. Between each two neighboring chips, Sonya placed a round chip. Then Yarik put a triangular chip between each neighboring chips in the new row. How many chips did Yarik put in?
Answer options:
(A) 7 (B) 8 (C) 9 (D) 10 (E) 11

13. The arrows in the figure indicate the results of operations with numbers. The numbers 1, 2, 3, 4 and 5 must be placed one by one in the squares so that all the results are correct. What number will be in the shaded box?

Answer options:
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

14. Petya drew a line on a sheet of paper without lifting the pencil from the paper. Then he cut this sheet into two parts. Top part shown in the figure on the right. What might it look like Bottom part this sheet?

15. Little Fedya writes out numbers from 1 to 100. But he does not know the number 5 and skips all the numbers that contain it. How many numbers will he write?
Answer options:
(A) 65 (B) 70 (C) 72 (D) 81 (E) 90

16. The pattern on the tiled wall consisted of circles. One of the tiles fell out. Which?

17. Petya arranged 11 identical pebbles into four piles so that all the piles had different number pebbles. How many pebbles are in the largest pile?
Answer options:
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

18. On the right is the same cube in different provisions. It is known that a kangaroo is painted on one of its faces. What figure is drawn opposite this face?

19. The Goat has seven kids. Five of them already have horns, four have spots on the skin, and one has neither horns nor spots. How many kids have both horns and skin spots?
Answer options:
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

20. Bone has white and black dice. He built 6 towers of 5 cubes in such a way that the colors of the cubes alternate in each tower. The figure shows what it looks like from above. How many black dice did Kostya use?

Answer options:
(A) 4 (B) 10 (C) 12 (D) 16 (E) 20

Tasks worth 5 points

21. In 16 years, Dorothy will be 5 times older than she was 4 years ago. In how many years will she be 16?
Answer options:
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

22. Sasha pasted five round stickers with numbers one after the other on a piece of paper (see picture). In what order could she stick them on?

Answer options:
(A) 1, 2, 3, 4, 5 (B) 5, 4, 3, 2, 1 (C) 4, 5, 2, 1, 3 (D) 2, 3, 4, 1, 5 (D) ) 4, 1, 3, 2, 5

23. The figure shows a front, left and top view of a structure made of cubes. What is the maximum number of cubes that can be in such a construction?

Answer options:
(A) 28 (B) 32 (C) 34 (D) 39 (E) 48

24. How many exist three-digit numbers, for which any two adjacent digits differ by 2?
Answer options:
(A) 22 (B) 23 (C) 24 (D) 25 (E) 26

25. Vasya, Tolya, Fedya and Kolya were asked if they would go to the cinema.
Vasya said: "If Kolya does not go, then I will go."
Tolya said: "If Fedya goes, then I will not go, but if he does not go, then I will go."
Fedya said: “If Kolya doesn’t go, then I won’t go either.”
Kolya said: "I will go only with Fedya and Tolya."
Which of the guys went to the movies?
Answer options:

BUT) Fedya, Kolya and Tolya (B) Kolya and Fedya (C) Vasya and Tolya (D) only Vasya (D) only Tolya

Answers Kangaroo 2015 - Grade 2:
1. A
2. G
3. In
4. In
5. D
6. D
7. B
8. D
9. G
10. A
11. A
12. G
13. D
14. D
15. G
16. In
17. B
18. A
19. In
20. G
21. B
22. 22
23. B
24. D
25. In