Kangaroo Olympiad tasks. International Mathematical Competition-game "Kangaroo
We present tasks and answers to the Kangaroo-2015 contest for 2 classes.
Answers to kangaroo 2015 tasks are after questions.
Tasks measured in 3 points
1. What letter is missing in the pictures to the right to make the word kangaroo?
Replies options:
(A) g (b) e (c) to (g) n (e) p
2. After Sam climbed the third step of the stairs, he began to walk through one step. What step does he turn out to be after three such steps?
Replies options:
(A) 5 (b) 6 (c) 7 (g) 9 (e) 11
3. The figure shows a pond and several ducks. How many of these ducks are swimming in a pond? 
Replies options:
4. Sasha walked twice as long as she did lessons. She spent 50 minutes for her lessons. How much time she walked?
Replies options:
(A) 1 hour (b) 1 hour 30 minutes (c) 1 hour 40 minutes (g) 2 hours (e) 2 hours 30 minutes
5. Masha drew five portraits of her beloved nesting, but in one drawing she was mistaken. In which? 
6. What is the number indicated by the square?
Replies options:
(A) 2 (b) 3 (c) 4 (g) 5 (e) 6
7. What of the figures (a) - (e) cannot be made up of two bars depicted on the right? 
8. Seryozha was conceived by the number, added to it 8, from the result took 5 and received 3. What number did he think?
Replies options:
(A) 5 (b) 3 (c) 2 (g) 1 (e) 0
9. Some of these kangaroo have a neighbor who looks into one side with him. How many kangaroo have such a neighbor? 
Replies options:
10. If yesterday was Tuesday, then the day after tomorrow
Replies options:
(A) Friday (b) Saturday (c) Sunday (d) Wednesday (e) Thursday
Tasks measured in 4 points
11. What is the smallest number of figure figures have to be removed to remain the figures of one species? 
Replies options:
(A) 9 (b) 8 (c) 6 (g) 5 (e) 4
12. In the row lay 6 square chips. Between each two adjacent chips, Sonya laid a round chip. Then Yarik between each neighboring chips in the new row put on a triangular chie. How many chips put Yarik?
Replies options:
(A) 7 (b) 8 (c) 9 (g) 10 (e) 11
13. Arrogors in the figure indicate the results of actions with numbers. Numbers 1, 2, 3, 4 and 5 must be placed one in squares so that all the results are correct. What number will fall into the shaded square? 
Replies options:
(A) 1 (b) 2 (c) 3 (g) 4 (e) 5
14. Petya drew a line on a sheet of paper, without taking a pencil from paper. Then he cut this sheet into two parts. The upper part is shown in the drawing on the right. How can the lower part of this sheet look like? 
15. The kid Fedya discharges numbers from 1 to 100. But he does not know the figure 5 and skips all the numbers that contain it. How many numbers will he write down?
Replies options:
(A) 65 (b) 70 (c) 72 (g) 81 (e) 90
16. Pattern on the wall laid out with tiles, consisted of circles. One of the tiles fell out. What? 
17. Peter decomposed 11 identical pebbles for four piles so that all the bunchings turned out to be a different number of pebbles. How many pebbles in the biggest cummy?
Replies options:
(A) 4 (b) 5 (c) 6 (g) 7 (e) 8
18. The same cube is depicted on the right in different positions. It is known that Kangaroo was drawn on one of his faces. What figure is drawn opposite this face? 
19. At the goats seven kids. The five of them already have horns, four have stains on the skin, and one does not have any rozen, nor stains. How many goats are also horns, and spots on the skin?
Replies options:
(A) 1 (b) 2 (c) 3 (g) 4 (e) 5
20. The bone has white and black cubes. He built 6 towers in 5 cubes so that in each tower the color of the cubes alternate. The figure shows how it looks at the top of it. How many black cubes used Kostya?
Replies options:
(A) 4 (b) 10 (c) 12 (g) 16 (e) 20
Tasks measured in 5 points
21. After 16 years, Dorothy will be 5 times older than it was 4 years ago. Through how old will it be 16?
Replies options:
(A) 6 (b) 7 (c) 8 (g) 9 (e) 10
22. Sasha stressed on a sheet of paper one after another five round stickers with numbers (see Figure). In what order she could stick them? 
Replies options:
(A) 1, 2, 3, 4, 5 (b) 5, 4, 3, 2, 1 (c) 4, 5, 2, 1, 3 (g) 2, 3, 4, 1, 5 (d ) 4, 1, 3, 2, 5
23. The figure shows the front view, on the left and above the design folded from cubes. What the largest number of cubes can be in such a design? 
Replies options:
(A) 28 (b) 32 (c) 34 (g) 39 (e) 48
24. How many three-digit numbers exist, which any two neighboring numbers differ in 2?
Replies options:
(A) 22 (b) 23 (c) 24 (g) 25 (e) 26
25. Vasya, Tol, Fedy and Kolya asked if they would go to the movies.
Vasya said: "If Kohl does not go, then I will go."
Tolya said: "If Fedya goes, I will not go, and if he does not go, then I will go."
Fedya said: "If Kohl does not go, then I will not go."
Kolya said: "I'll go only with Fedya and Tolley."
Which of the guys went to the movies?
Replies options:
BUT)Fedya, Kolya and Tolya (b) Kolya and Fedya (c) Vasya and Tolya (d) Only Vasya (D) only toly
Answers Kangaroo 2015 - 2 class:
1. A.
2. G.
3. B.
4. B.
5. D.
6. D.
7. B.
8. D.
9. G.
10. A.
11.A.
12. G.
13. D.
14. D.
15. G.
16. B.
17. B.
18. A.
19. B.
20. G.
21. B.
22. 22
23. B.
24. D.
25. B.
The international mathematical contest "Kangaroo" -2012 ended. We present the attention of schoolchildren on 3-4 classes and their parents the opportunity to verify their tasks with the answers to the Kangaroo contest.
Questions are grouped by complexity (by points). Answers to tasks are after questions.
Tasks measured in 3 points
1. Sasha draws on a poster of the Word of the Kangaroo. The same letters he draws in one color, and different letters - different colors. How many different colors will it need?
Options:
(A) 6 (b) 7 (c) 8 (g) 9 (e) 10
2. One alarm clock is in a hurry for 25 minutes and shows 7 hours 50 minutes. What time does another alarm clock show, which is 15 minutes behind?
Options:
(A) 7 hours 10 min (b) 7 hours 25 min (c) 7 hours 35 min (g) 7 hours 40 min (e) 8 hour
3. Only on one of these five pictures, the area of \u200b\u200bthe painted part is not equal to the area of \u200b\u200bthe white part. What?
Options:
4. Three balloons stand for 12 rubles more than one ball. How much is one ball?
Options:
(A) 4rub. (B) 6 rubles. (B) 8 rubles. (D) 10 rubles. (E) 12 rubles.
5. On what of the drawings of the cell A2, B1 and SZ are painted?
Options:
6. 3 Kitten, 4 duckling, 2 goes and several puppies study at school for animals. When the teacher recalculated the paws of all his students, it turned out 44. How many puppies study at school?
Options:
(A) 6 (b) 5 (c) 4 (g) 3 (e) 2
7. What is not seven?
Options:
(A) Number of days in the week (b) half a dozen (d) number of rainbow colors
(B) the number of letters in the word Kangaroo (D) number of this task
8. Tiles of two species were laid out on the wall in a checkerboard order. Several tiles fell from the wall (see Figure). How many striped tiles fell? 
Options:
(A) 9 (b) 8 (c) 7 (g) 6 (e) 5
9. Petya conceived a number, added to him 3, the amount multiplied by 50, again added 3, multiplied the result by 4 and received 2012. What number was looking for Petya?
Options:
(A) 11 (b) 9 (c) 8 (g) 7 (e) 5
10. In February 2012, a small kangaroo was born in the zoo. Today, March 15, it turns 20 days. What day did he born?
Options:
(A) February 19 (b) February 21 (B) February 23 (d) February 24 (e) February 26
Tasks measured in 4 points
11. On a sheet of paper Vasya paste one after another 5 identical squares. Visible parts of these squares in the picture are marked with letters. In what order Vasya stressed squares? 
Options:
(A) a, b, in, g, d (b) b, g, in, d, a (c) a, d, b, b, g (g) g, d, b, in, a (d ) G, b, in, d, and
12. Bloch jumps along a long staircase. It can jump or 3 steps up, or on 4 steps down. For what the smallest number of jumps does she move from the ground on the 22nd step?
Options:
(A) 7 (b) 9 (c) 10 (g) 12 (e) 15
13. Fedya laid out the right chain of seven dominoes (the number of points in the neighboring squares of two different dominoes is always the same). On all the dominals together there were 33 points. Then Fedya took two dominoes from the resulting chain (see Figure). How many points were in a square in which the question mark is? 
Options:
(A) 2 (b) 3 (c) 4 (g) 5 (e) 6
14. A year before the birth of Kati her parents together were 40 years old. How many years now are Kate, if after 2 years she and her parents will be together for 90 years?
Options:
(A) 15 (b) 14 (c) 13 (g) 8 (e) 7
15. Four-grader Masha and her brother First-grader Misha solved the tasks of the Kangaroo competition for 3-4 classes. As a result, it turned out that Misha received not 0 points, and Masha was not 100 points. What is the largest number of points Masha could overtake Misha?
Options:
(A) 92 (b) 94 (c) 95 (g) 96 (e) 97
16. The "correctly" ride strange clocks are confused by the arrows (hour, minute and second). At 12:55:30 pm arrows were located as shown in the figure. What will this watch shown at 20 o'clock 12 minutes? 
Options:
17. Five men from one family went fishing: Grandfather, 2 of his son and 2 grandson. Their name is: Boris Grigorievich, Grigory Viktorovich, Andrei Dmitrievich, Viktor Borisovich, and Dmitry Grigorievich. How was the grandfather in childhood?
Options:
(A) Andryusha (b) Boria (c) Vitya (d) Grisha (D) Dima
18. The parallelepiped consists of four parts. Each part consists of 4 cubes of the same color (see Figure). What form does a white part?
Options:
19. In football, the team gets 3 points for victory, for a draw - 1 point, and for the defeat - 0 points. The team played 38 matches and received 80 points. What is the largest number of times this team could lose?
Options:
(A) 12 (b) 11 (c) 10 (g) 9 (e) 8
20. To a five-digit number, the amount of numbers of which is 2, added a two-digit number. It turned out a five-digit number again, the amount of numbers of which is equal to 2. What number turned out?
Options:
(A) 20000 (b) 11000 (c) 10100 (g) 10010 (D) 10001
Tasks measured in 5 points
21. Near Venice are three islands: Murano, Burano and Torchello. You can visit Torchello only by visiting the road and Murano and Burano. Each of the 15 tourists visited at least one island. At the same time, 5 people visited Torchello, 13 people visited Murano and 9 people - on Burano. How many tourists visited exactly two islands?
Options:
(A) 2 (b) 3 (c) 4 (g) 5 (e) 9
22. Paper cube was cut and unfolded. Which of the figures 1-5 could turn out?
Options:
(A) all (b) only 1, 2, 4 (c) only 1, 2, 4, 5
(D) only 1, 4, 5 (e) only 1,2,3
23. Nikita chose two three digits, which coincide the amounts of numbers. From a larger number, he took away the smaller. What is the biggest number could Nikita get?
Options:
(A) 792 (b) 801 (c) 810 (g) 890 (e) 900
24. At noon from the capital to the city, the sword and the merchant came out. At the same time, on the same road, the squad of the guards came out. An hour later, the guards met the fracture, after another 2 hours they met a merchant, and after 3 hours the guards arrived in the capital. How many times is the fastest of the merchant goes?
Options:
(A) 2 (b) 3 (c) 4 (g) 5 (e) 6
25. How many squares formed by the dedicated lines are shown in the figure? 
Options:
(A) 43 (b) 58 (c) 62 (g) 63 (e) 66
26. In the equality of Ken \u003d GU * RU different letters marked different nonzero numbers, and letters are the same numbers!
Find E if it is known that the number "Ken" is the smallest possible.
Options:
(A) 2 (b) 5 (c) 6 (g) 8 (e) 9
Answers to the "Kangaroo" contest -2012 for 3-4 grade:
Designs and logical arguments.
Task 19. Winding coast (5 points)
.
The picture is an island on which a palm tree grows and several frogs are sitting. The island is limited by the coastline. How many frogs are sitting on the island?
Response options:
BUT: 5; B: 6; IN: 7; G: 8; D: 10;
Decision
When solving this task, you can use the "Fill" tool on the computer. Now it is clearly seen that 6 frogs are sitting on the island.
It was possible to make something like this pouring and a pencil on the leafle of conditions. But there is another interesting way that allows you to determine whether the point is inside a closed non-saving curve or outside.
Connect this point (frog) with a point about which we know exactly that it is outside the curve. If the connecting line will have an odd number of intersections with a curve, then our point lies inside (i.e. on the island), and if one is clear - then outside (on the water)
Correct answer: b 6
Task 20. Numbers on balls (5 points)
.
Musbande 10 goals numbered from 0 to 9. He divided these balls between three her friends. Lasunchik got three goals, the stubchik - four, Sonyk about - three. Then Mudragelik asked each of their friends to multiply the numbers on the balls received. Lasunchik got a product, equal to 0, the tutor - 72, and Sonyk about - 90. All kengurites correctly changed the numbers. What is the amount of numbers on those balls that the lasschik got?
Response options:
BUT: 11; B: 12; IN: 13; G: 14; D: 15;
Decision
It is clear that among the three goals who received a lasschik, there is a number 0. It remains to find 2 more numbers. The tunter has 4 balls, so it will be easier to first find which three numbers from 1 to 9 need to multiply to get 90 like Sonk but? 90 \u003d 9x10 \u003d 9x2x5. This will be the only way to present 90 in the form of a product of numbers on the balls. After all, if Sonyk but One of the balls was with a unit, then you would need 90 into the work of two factors, smaller than 10, which is impossible.
So, the Lasunchik has 0 and two other balls, Sononk but Balls 2, 5, 9.
Four crust balls are given in the work 72. Give first 72 in the work of two multipliers, so that later each of these factors break another 2:
72 \u003d 1x72 \u003d 2x36 \u003d 3x24 \u003d 4x18 \u003d 6x12 \u003d 8x9
From these options immediately shut down:
1x72 - because 1 we will not dismiss in 2 different factors
2x36 - because 2 is divided only as 1x2, but the ball with a number 2 does not exactly have a crust
8x9 - because 9 is broken as 1x9 (it is not broken as 3x3, since there are no two balls with three), and there are no nails at the tutor
Options remain:
3x24 - splits in 4 multipliers as 1x3x4x6
4x18 - divided into 4 multipliers as 1x4x3x6, that is, as well as the first option
6x12 - divided as 1x6x3x4 (after all, we remind, there is no ball with a twos).
So, for the set of the balls of the stubble is the only option. He has balls 1, 3, 4, 6.
For a lasschik, besides the ball with a number 0, there are balls 7 and 8. Their amount is equal to 15
Proper answer: d 15
Task 21. Rope (5 points)
.
Three ropes are attached to the board as shown in the figure. You can attach three more and get a whole loop. Which of the rods given in the answers will make it possible to do this?
According to kangaroo Groups VKontakte This task was correctly solved by only 14.6% of the participants in the Mathematical Olympiad from the third and fourth classes.
Response options:
BUT: ; B: ; IN: ; G: ; D: ;
Decision
This task can be solved, mentally appling the picture to the picture and carefully checking the connections. And you can go a little more optimal. I reset the rope and write down the line 123132 is the endings of the loops on this in the condition of the figure. Now over the ends of the rods in the options of answers, too, together these numbers.
Now it's easy to see that in the variant BUT Rope 2 is connected to himself. In the embodiment B. The brainstitch is connected with it 1. But in the version IN All rings are connected to one larger loop.
Correct answer: in
Task 22. Recipe Elixira (5 points)
.
To prepare the elixir, it is necessary to mix five types of fragrant herbs, the mass of which is determined by the balance of the scales depicted in the figure (we neglect the weight of the scales). The badge knows that the elixir needs to put 5 grams of sage. How many chamomile grams can he take?
Response options:
BUT: 10 g; B: 20 g; IN: 30 g; G: 40 g; D: 50 g;
Decision
Basilica must be taken as much as Sage, that is, also 5 grams. Mint is so much as sage and basilica together (we do not consider the mass of the scales themselves). So, mint need to take 10 grams. Melissa must be taken as much as mint, sage and basilica, that is, 20g. And chamomile - as much as all previous herbs, 40 g.
Correct answer: g 40g
Task 23. Unprecedented beasts (5 points)
.
Tom painted a pig, shark and rhino and cut each card as shown in the figure. Now he can add different "animals", connecting one head, one middle and one back. How many different fantastic creatures can collect tom?
Response options:
BUT: 3; B: 9; IN: 15; G: 27; D: 20;
Decision
This is a classic problem on the combinatorics. That is good that they can (and necessary) decide not to mechanically apply the rules for calculating the amounts of permutations and a combination, but arguing. How many different options are for the head of the animal? Three options. And for the middle part? Also three. There are three options for the tail. So, all different options will be 3x3x3 \u003d 27. Moving these options because any body can be joined and any tail, so that each animal segment increases the combinations options exactly 3 times.
By the way, the condition is the word "fantastic." But after all, combining any heads, torso and tails, we will receive both real pigs, shark and rhino. So the correct answer was to be 24 fantastic animals and three real. However, apparently, fearing various interpretations of the condition, the authors did not include the 24nd responses option. Therefore, we choose the answer g, 27. Yes, and who knows, suddenly in the drawings also depicts a fantastic speaking pig, a fantastic flying shark and a fantastic rhino, which has proven the farm theorem? :)
Correct answer: g27
Task 24. Kenguryata-bakery (5 points)
.
Monda, the lasunchik, the stubborn, Khitrun and Sonko baked pastries on Saturday and Sunday. During this time, the Monda Lasunik is 49, the lasunchik - 49, the stubchik - 50, Khitrun - 51, Sonyko - 52. It turned out that on Sunday every kengurian spit cupcakes more than on Saturday. One of them is twice as much, one - 3 times, one - 4 times, one - 5 times, and one - 6 times.
Which of the kengury is a spit at Saturday most of the cakes?
Response options:
BUT: Mondaheelik; B: Lasunchik; IN: Strike; G: Hitrune; D: Sonyko;
Decision
Let's first think about what information does it give us the fact that someone is a spit on Sunday the cakes exactly 2 times more than on Saturday? If on Saturday the kengurian spit some cakes, then on Sunday - so much and so much. So, in just two days it is a spit three (1 + 2 \u003d 3) more cakes than on Saturday.
So what? And the fact that, for example, 49 or cakes he could not lose, as these.
It turns out that someone on Sunday a hole is three times more cakes than on Saturday, their total number should make 4 \u003d 1 + 3. Someone else has 5, at someone at 6 and someone at 7.
The principle of solving this problem is identified. Here we have five numbers: 48, 49, 50, 51, 52. On 3 of them, 2 numbers (48 and 51) are divided into 4 - also 2 numbers (48 and 52). But on the 5th only one number, 50. It comes out, one who is a dish of 50 pies, on Sunday a spit 4 times more than on Saturday.
Only one number is also divided by only one number, it is 48. It turns out, the kengurren, which is a dish of only 48 cakes, their peaks: 8 on Saturday and 40 on Sunday. Well, then just. We get that:
Monda Speake 48 Cakes: 8 on Saturday and 40 on Sunday (5 times more)
Lasunchik Spit 49 Cakes: 7 on Saturday and 42 on Sunday (6 times more)
The stubchik is a dish of 50 cakes: 10 on Saturday and 40 on Sunday (4 times more)
Hitrun Spy 51 Cake: 17 on Saturday and 34 on Sunday (2 times more)
Sonya Skeok 52 Cakes: 13 on Saturday and 39 on Sunday (3 times more)
It turns out, on Saturday, the most cake spit hectrun.
Correct answer: g Hitrune
TASKS
International Competition
"Kangaroo"
2010 3 - 4 classes
Tasks measured in 3 points
1. What can be obtained from the word if you erase some letters?
2. Children measured the length of the track. Ani had 17 steps, Natasha 15, Denis 14, from Vanya 13 and Tanya 12. Which of these children has the longest step?
(A) Anya (b) Natasha (c) Denis (D) Vanya (D) Tanya
3. What is the digit encrypted by the icon if +12 \u003d + + +?
(A) 2 (b) 3 (c) 4 (g) 5 (e) 6
4. The labyrinth is designed so that the cat can get to milk, and the mouse is to cheese, but they cannot meet. What part of the labyrinth is closed by a square?
5. Eva staples 100 legs. Yesterday she bought and put 16 pairs of new shoes. Despite this, 14 legs remained bass. How many legs were shods before she bought shoes?
(A) 27 (b) 40 (c) 54 (g) 70 (e) 77
6. The figure shows how digit 4 is reflected in two mirrors. What will be visible on the place of the question of the question, if instead of the number 4 take the number 6? 
7. The lesson began at 11:45 and lasted 40 minutes. Exactly in the middle of the lesson Vasya
sneeze. At what point did it happen?
(A) 12: 00 (b) 12: 05 (B) 12: 10 (g) 12: 15 (e) 12: 20
8. For all November 2009, the sun shone the sun in St. Petersburg
13 hours. How many hours during this month in the city was not
Sun?
(A) 287 (b) 347 (c) 683 (g) 707 (e) 731
9. Syoma discharged all three-digits, in which the average digit is 5, and the amount of the first and last is 7. How many numbers did he write?
(A) 2 (b) 4 (c) 7 (g) 8 (e) 10
10. Models for sale machines of three types: 15 rubles, 21 rubles. And 28 rubles, and a set of three such machines costs 56 rubles. Mom promised to buy all three models. How many rubles can be saved if you buy a set, and not all three cars separately?
(A) 2 (b) 3 (c) 4 (g) 7 (e) 8
Tasks measured in 4 points
11. Fly has 6 paws, spider - 8. Two flies and three spiders together have
as much paws, how much 10 parrots and
(A) 2 cats (b) 3 proteins (c) 4 dogs (d) 5 hares (e) 6 foxes
12. Ira, Katya, Anya, Olya and Lena learn in the same school. Two girls learn
In 3 and class, three - in 3 b. Olya studies not with Katya and not together
With Lena, Anya studies not with Ira and not with Katya. Which girls study in 3 and class?
(A) Anya and Olya (b) Ira and Lena (c) Ira and Olya
(D) Ira and Katya (D) Katya and Lena
13. The design in the figure weighs 128 grams and is in equilibrium (the weight of horizontal planks and vertical threads is not taken into account). How much is the asterisk weigh?
(A) 6 g (b) 7 g (c) 8 g (d) 16 g (e) 20 g
14. Carl and Clara live in a multi-storey building. Clara lives on 12 floors
higher than Karl. One day, Karl went to visit Clare. After having passed half the way, he was on the 8th floor. What floor lives Clara?
(A) 12 (b) 14 (c) 16 (g) 20 (e) 24
15. Production 60 × 60 × 24 × 7 equals
(A) the number of minutes in seven weeks (b) number of hours in sixty days
(C) the number of seconds in seven hours (d) number of seconds in one week
(E) the number of minutes in twenty four weeks
16. Figure on the right shows a ceramic tile. What picture can not be made of four such tiles?
17. Two years ago, Kotam Toshe and the baby together were 15 years old. Now Toshe is 13 years old. Through how old will the baby be 9 years old?
(A) 1 (b) 2 (c) 3 (g) 4 (e) 5
18. What is a million times lighter than tons?
(A) 1 c (b) 1 kg (c) 100 g (g) 1 g (d) 1 mg
19. The same digits are encrypted with the same letters in the AAA-BB rebv + C \u003d 260, and different are different. Then the sum A + B + C is equal
(A) 20 (b) 14 (c) 12 (g) 10 (e) 7
20. Instead of stars, Vasya entered such numbers that the sums of numbers in both
The lines were the same. What is the difference in the inscribed numbers?
| 1 | 23 | 47 | 72 | 43 | 7 | * |
| 11 | 33 | 37 | 62 | 53 | 17 | * |
(A) 10 (b) 20 (c) 30 (g) 40 (e) they are equal
Tasks measured in 5 points
21. From the sheet of checkered paper, Masha cut a piece consisting of entire cells. It cuts on the sides of the cells, with four segments marked in the figure, were on the border of the carved piece. What the smallest number of cells could this piece consist of?
(A) 13 (b) 11 (c) 9 (g) 8 (e) 7
22. Katya wrote all the numbers from 1 to 1000 "Snake" in a table with five columns (see Figure). Her brother erased some numbers. How can two neighboring lines from the resulting table look like?
23. Mom allows you to play computer games only on Mondays, Fridays and odd numbers. What is the largest number of days in a row Peter can play?
(A) 7 (b) 6 (c) 4 (g) 3 (e) 2
24. How many triangles are shown in the picture?
(A) 26 (b) 42 (c) 50 (g) 52 (e) 54
25. The teacher said that in the school library approximately 2,000 books, and suggested the guys to guess the exact number of books. Anya called the number 1995, Boria - 1998, Vika - 2009, Gene - 2010, and Dima - 2015. Then the teacher said that no one had guess, but the mistakes were such: 12, 8, 7, 6 and 5 (perhaps in in a different order). Which of the guys turned out to be closest to the right answer?
(A) Anya (b) Boria (c) Vika (D) gene (D) Dima
26. Zinka, Dunno, Victor and Shpunter ate a cake. They ate in turn, and each of them ate so much time as it would take three other consumers to, "working" together, eat half the cake. While how many times they would eat the cake, if it were not in turn, but all together?
(A) 2 (b) 3 (c) 4 (g) 5 (e) 6
_____________________________________________________________________________
Time allotted to solve problems - 75 minutes!
Solving tasks
Solutions of too simple tasks are not shown. The answer blank can be found in the article "On the Kangaroo Olympics".
So, first the correct options for answers:
2. It is clear that that one has the longest step, made the least steps.
3. The figure is 0.1,2,3,4, ... 9.
There are only 10 pieces, so you can choose if no logic is searched. And the logic is as follows:
What figure multiplying on 4 can be obtained 12 (or what figure is 2 times you can get 12). Of course 3. I mean the desired figure greater than 3, since the left side of the equality is worth +12 more than 12. So we try 4. And we get exactly 10-ku. We obtain the equality 4 + 12 \u003d 4 + 4 + 4 + 4. From here it is clear that the child immediately did not see what figures to start searching the solution would lose a bunch of time to select the value. And the child who began the selection with the number 4 Niskolatko will not lose its precious time.
5. 16 * 2 \u003d 32 legs shoes yesterday, buying 16 pairs of shoes. 100-32-14 \u003d 54 legs were shoves before purchase.
7. 11h45min + 20 mim \u003d 11h45min + 15min + 5min \u003d 12ch5min
8. In November 30 days, it means 30 * 24h \u003d 720h in November. 720-13 \u003d 707ch was cloudy. The complexity is only in the correct definition of the number of days in the month. There is a very good method of defining a fist (light and fast). He successfully remembers even a child class 2.
9. The numbers are as follows: 750, 651,552, 453, 354, 255, 156. As seen by their 7 pieces. In such tasks, the child is important to teach the numbers in order.
11. 2 * 6 + 3 * 8 \u003d 36. Then (36-10 * 2) / 4 (since all the animals listed 4 legs) \u003d 16/4 \u003d 4.
12. From the first half of the 3rd sentence, you can come to the conclusion: Katya and Lena learn together. From the second half of this sentence, we learn that: Olya and Anya learn together, and Ira studies with Katya and Lena. It turns out Anya and Olya learn in 3a.
13. First you need to find out how much one half of the scales weighs:
Now learn how much weighing this half of the scales:
It will be 64/2 \u003d 32 g.
Next section:
It will be 32/2 \u003d 16.
Last plot:
14. Half of the 12 floors will be 6 floors, that is, Karl passing 6 floors was on the 8th floor. From here it is seen that Karl lives on the 2nd floor (8-6 \u003d 2), and Clara lives 2 + 12 \u003d 14th floor.
15. We will analyze right to left. 7 This is the number of days in the same week, 24 is the number of hours in one day, 60 Number of minutes in one hour, 60 Number of seconds in one minute. So this is the number of seconds in the same week.
17. Two years ago: (13-2) + kid \u003d 15 years. Kid \u003d 15-11 \u003d 4 years. Now kid 4 + 2 \u003d 6. After 3 years, it will be 9 (9-6 \u003d 3).
19. Since the answer is a three-digit number close to 300, it will be logical to suggest that it means 333 - BB + C \u003d 260. 260 +40 will be 300, and if adding 30 will be added 30. We received a number close to 333. You need to check the result: 40 + 30 \u003d 70, suppose that B \u003d 7, BB \u003d 77. 333-77 \u003d 256. So A \u003d 3, B \u003d 7, C \u003d 4. Their sum: 3 + 7 + 4 \u003d 14
20. It is easy to notice that the numbers in each column differ by 10 units. Here children who will start to calculate the amount will most likely lose time. And the children saw that: 1 and 2 column of the first line are less than 10 than 1 and 2 column of the second line, and 3 and 4 column are the first greater than 10 than 3 and 4 the second will benefit. It means to compare (again not to summarize) only 5 and 6 column: In 5 column, the first line is less than 10, in 6 columns, again, the first line is less than 10. This is the first line less than the second on 20. Vasya means inscribed in the first row 20, and in the second 0. Answer: 20-0 \u003d 20
21. This figure with the smallest number of cells can be drawing in different ways, here are some of them:
22. In this task, it is necessary to understand in which direction a number goes (from left to right or right to left), depending on the numbers in the discharge of units.
If in the category of units cost numbers from 1 to 5, then the row goes left to right if the digits from 6 to 0 then - right to left.
Now the analysis analyze the options for answers. An option (a) 742 seems to be in its place, that is, in the table all the numbers ending with 2 must stand in the second column. But 747 is not there, in his place was 749 should be standing. The child should look at the table and compare the discharge of units and location. That's all the trick. And if the child starts counting 742, 743, 744, etc., most likely, confused in all these versions, or will lose its precious time. The option (b) is not suitable, there is 542 more than 537 - there is no increasing. Although the discharges of units are in their places. Option (B) and (d) - no number fell into its cell. Option (e) - numbers are in their cells.
23. Between Thursday and Friday 2 days: Saturday and Sunday. Two days in a row no other can not be, but it may be odd if it is 31 numbers and the first number of next month. If on Saturday 31 number, then on Thursday there will be 29 numbers. We will start with him. He can play on Thursday (if it is the 29th), then plays on Friday, then on Saturday (this is the 31 number), then on Sunday (it will be the 1 number), then on Monday (it will be 2 numbers), then the 3rd Numbers on Tuesday. It turns out 6 days in a row can play if the 29th number falls on Thursday.
24. There are 26 small triangles. Since the symmetric pattern can be considered half (13) and multiply by 2. Now the triangles consisting of 4 small triangles are 16. Now the triangles are from the 9-small, there are 8 pieces. Now triangles of 16 small - their 2 pieces. Total turns out 52 triangles.
25. Here you need to start with the ends. Which one should give the greatest difference 12. So 1995 + 12 \u003d 2007. It can be seen that it does not fit. The difference between 2007 and 2009 is just 2 years. We try the second end of 2015-12 \u003d 2003. Perhaps books at school 2003. So check. 2003-1995 \u003d 8 years (there is such an option). 2003-1998 \u003d 5 years (also there), 2009-2003 \u003d 6 years, 2010-2003 \u003d 7 years. That's right. The closer to 2003 was the answer of 1998, which said Boria.
26. It is important here to understand that 3 people eat half the cake. So half the cake should be divided into three pieces. The next half, also need to be divided into 3 pieces. It turns out the cake is divided into 6 parts.
If you eat "all together," they eat 4 pieces at once. During this time, in the case of "alternate" one will have time to eat 1 piece. In the second approach, "everyone together" remained 2 pieces, and their four. Cake pieces are clearly not enough. So you need to divide not by 6 parts, and by 12.
The first approach: While the four-fold of 8 pieces of cake (two pieces), 1 there are 2 pieces.
The second approach: the remaining 4 pieces (one piece), 1 has time to eat only 1 piece.
This means: so far all 12 pieces have eaten all 12 pieces, only 3 pieces have time. 12/3 \u003d 4. I coped 4 times faster.
How to quickly determine the number of pieces?
The number of cake pieces should be divided into 4.
4 are divided: 4,8,12, ..
4 and 8 will not suit, because half of the cake should be divided into 3 parts. Half 12 is 6, just divided by 3. So the cake must be divided into 12 parts.
Millions of the guys in many countries of the world have long been no longer needed to explain what "Kangaroo"- This is a massive international mathematical competition-game under the motto - " Mathematics for everyone! ".
The main goal of the competition is to attract as many guys as possible to solving mathematical tasks, show every student that thinking about the task can be a living, fascinating, and even cheerful. This goal is achieved quite successfully: for example, in 2009, more than 5.5 million guys 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, massive mathematical competitions are held in many countries no longer one decade, and Europe in which a new competition originated is so far from Australia! The fact is that in the early 80s of the twentieth century, the well-known Australian mathematician and teacher Peter Holloran (1931 - 1994) came up with two very significant innovations, which significantly changed the traditional school Olympiads. He divided all the tasks of the Olympics into three categories of complexity, and simple tasks should have been available literally to each schoolchild. And besides, the tasks were offered in the form of a test with a choice of responses focused on computer processing of results. The presence of simple, but entertaining issues ensured a wide interest in the competition, and the computer check allowed to promptly process a large number of works.
A new form of competition was so successful that in the mid-1980s, about 500 thousand Australian schoolchildren participated in it. In 1991, a group of French mathematicians, relying on Australian experience, held a similar competition in France. In honor of the Australian colleagues, the competition received the name "Kangaroo". To emphasize the enraged tasks, they began to call it a competition-game. And one more difference - participation in the competition became paid. The fee is very small, but as a result, the competition ceased to depend on the sponsors, and a significant part of the participants began to receive prizes.
In the first year, about 120 thousand French schoolchildren took part in this game, and soon the number of participants increased to 600 thousand. This began the rapid dissemination of the competition for countries and continents. Now it participates about 40 countries in Europe, Asia and America, and in Europe it is much easier to list countries that do not participate in the competition than those where he is held for many years.
In Russia, the Kangaroo competition was first conducted in 1994 and since then the number of its participants is growing rapidly. The competition is included in the program "Productive Game Contests" of the Institute of Productive Training under the leadership of Academician RAO M.I. Bashmakov and is held with the support of the Russian Academy of Education, St. Petersburg Mathematical Society and the Russian State Pedagogical University. A.I. Herzen. Direct organizational work took on the center of testing technology "Kangaroo Plus".
In our country, there has been a clear structure of mathematical Olympiads, covering all regions and accessible to every student who is interested in mathematics. However, these Olympics, starting with the district and ending the All-Russian, are aimed at that from students already passionate about mathematics, allocate the most capable and gifted. The role of such olympics in the formation of the scientific elite of our country is enormous, but the vast majority of schoolchildren remain aside from them. After all, the tasks that are offered there are usually designed for those who are already interested in mathematics and are familiar with mathematical ideas and methods that go beyond the school program. Therefore, the Kangaroo contest, facing the most ordinary schoolchildren, quickly won the sympathy and guys, and teachers.
The tasks of the competition are compiled so that every student, even the one who dislikes mathematics, or even the one who is afraid of her, found interesting and affordable questions. After all, the main goal of this competition is to interest the guys, to instine confidence in their capabilities, and his motto is "mathematics for everyone."
Experience has shown that the guys are happy to solve the tasks of the competition, which successfully fill the vacuum between standard and often boring examples from a school textbook and difficult, requiring special knowledge and training, objectives of urban and district mathematical Olympiads.