How old is Hottabych if the first and last. Interesting problems for extracurricular activities in mathematics (Three fishermen and one boat
1. Three fishermen and one boat. Three fishermen share a boat, but each of them has his own lock and key. How to attach a boat to a post on the shore so that any of the fishermen can unhook it using only their key?
2. Big family. Gathered at the dinner table: 1 grandfather, 1 grandmother, 2 fathers, 2 mothers, 4 children, 3 grandchildren, 1 brother, 2 sisters, 2 sons, 1 father-in-law, 1 mother-in-law and 1 daughter-in-law. How many people should the table be set for?
3. The age of old man Hottabych is written as a number consisting of various digits. If you cross out the first and last digits of this number, you get a 2-digit number, which, with the sum of the digits equal to 13, is the largest. The first digit of a number is 4 times greater than the last. How old is old man Hottabych?
4. Will. Someone, dying, left his wife in anticipation of a child and made the following remark before his death: in the event of the birth of a son, give him 2/3 of the property, and 1/3 to the mother; : in the event of the birth of a daughter, give her 1/3 of the property, and the mother - 2/3 of the property. The testator's widow gave birth to twins - a boy and a girl. How to divide property according to a will?
5. The bottle and glass hold the same amount of liquid as the jug. The bottle holds the same amount as a glass and a beer mug. Three beer mugs hold the same amount as two jugs. How many glasses of liquid can one beer mug hold?
6. Book. One schoolchild was given a book. How many pages are in this book if it took 2775 digits to number its pages?
7. Darts. While playing darts, Zhenya threw three darts at the target three times. If a dart hits a certain target circle, it is scored with the corresponding number of points. The first time Zhenya received a total of 29 points, the second time – 43 points (see figure). How many points did Zhenya receive the third time?
Let's remember geometry.
1. What is the maximum possible number of internal angles equal to 90° that can be in a hexagon (not necessarily convex)?
2. There are 6 segments, the lengths of which are 1 cm, 2 cm, 3 cm, 2001 cm, 2002 cm and 2003 cm. You need to select 3 of these segments so that you can form a triangle from them. How many different triangles can you get?
3. In rectangle ABCD, points P, Q, R and S are the midpoints of the sides AB, BC, CD and AD, respectively, and T is the midpoint of the segment RS. What fraction of the area of rectangle ABCD is the area of triangle TQP?
3. Misha assembled a rectangular parallelepiped from 42 identical cubes with an edge of 1 cm. The perimeter of the base of the parallelepiped turned out to be 18 cm. What is the height of the constructed parallelepiped?
4. On the edges of a square piece of paper divided into 25 squares, points A, B, C, D, E, M and N are marked, as shown in the figure. Find the sum of the angles MAN, MBN, MCN, MDN and MEN.
2.Two squares of the same size cover a circle of radius 3 cm, as shown in the figure. Find the area of the colored part of the circle.
Fun challenges.
1. A stone is thrown at a window from the sidewalk at a speed of 5 m/s. Estimate how fast it will fly back from there.
2. 20 words per minute will fly into one ear of a schoolchild, and 10 words per minute will fly out of the other. Find the time it takes for the student to become wiser.
3. At what speed should you use a fork in order to use it to eat a full portion of porridge in two minutes?
1. From what height should a skydiver fall without a parachute so that there is no wet spot left behind?
Preview:
Fairytale tasks
A mathematician who is not partly a poet will never achieve perfection in mathematics.
K. Weierstrass.
1. Gold of King Dadon.
Six robbers robbed King Dadon. The loot turned out to be rich - less than a hundred identical bars. The robbers began to divide the loot equally, but one ingot turned out to be too much. The robbers got into a fight and one of them was killed in the fight. Those who remained again began to divide the gold and again one piece turned out to be extra. And again one of the robbers died in the fight. And so on: each time one ingot was too many and one of the robbers died in the fight. In the end, only one robber remained, who died from his wounds. How many bars were there?
Solution: if initially there would have been one less ingot, then the division would have taken place. A number that is less than 100 and divisible by 2, 3, 4, 5, 6 is 60. That means there are 60+1=61 bars in total.
Answer: 61 bars.
2. The little mook and the royal walker.
The little mook and the royal walker competed in a race along a 30 km long track that went around a large meadow. According to the conditions, the winner will be the one who overtakes the other by running one more lap. Skorokhod makes a circle in 10 minutes, and Muk in 6 minutes. Both run evenly. In how many minutes will Muk overtake the walker?
Solution:
- 30:10=3 (km/min) speed of the walker
- 30: 6=5 (km/min) speed Flour
- 5 – 3 =2 (km/min) faster than Muk
- 30:2 = 15 (min)
Answer: in 15 minutes little Mook will win.
3. Old Man Hottabych.
Old Man Hottabych's age is written as a number with different digits. The following is known about this number: 1) if you cross out the first and last digits, you get two-digit number, which is the largest when the sum of the digits is 13; 2) the first digit is 4 times greater than the last. How old is Old Man Hottabych?
Solution: 13= 7+6=8+5=9+4, which means 94 is the largest two-digit number, the sum of its digits is 13. If the last digit is 1, then the first is 4, but according to the condition, all digits are different. Then the last one is 2, the first one is 8, there are no other options. Hottabych's age is 8942 years.
Answer: 8942 years.
4. The Eighth Voyage of Sinbad.
Sinbad the Sailor ended up on an island. It is inhabited by truth-tellers and liars. Sinbad was accompanied by a resident of the island. Soon they met another resident of the island. Sinbad sent a guide to find out who this resident was - a truth-teller or a liar. The conductor returned and said that he said he was a liar. Who was the guide - a truth-teller or a liar?
Solution:
Resident: truth-teller - answer truth-teller
Liar - answer truth teller
expected answer: a truth-teller, but the guide said he’s a liar, which means the guide lied, he’s a liar.
Answer: the conductor is a liar.
5. About the Serpent Gorynych
“The Serpent Gorynych is defeated!” - such rumor reached Mikula Selyanovich. He knew that one of the heroes could have done this: either Ilya Muromets, or Alyosha Popovich, or Dobrynya Nikitich. Soon Mikula was informed: 1. It was not Ilya Muromets who defeated the Snake Gorynych; 2) Zmey Gorynych defeated Adesha Popovich. After some time it turned out that one message was false. Who defeated the Serpent.
Solution:
- Ilya Muromets - winner
1 – false
2 – false
2) Alyosha Popovich – winner
1 – true
2 – true
3) Dobrynya Nikitich – winner
1 – true
2 – false
Answer: Snake Gorynych defeated Dobrynya Nikitich
Problems for independent solution.
- Nils and the geese
Nils flew in the flock on the back of Martin the goose. He noticed that the formation of the flock resembles a triangle: the leader is in front, then two geese and so on. The flock stopped for the night on an ice floe. Nils saw that the arrangement of the geese this time resembled a square, consisting of rows and in each row the same number of geese, and the number of geese in each row was equal to the number of rows. There are less than 50 geese in the flock. How many geese are there in the flock? (36 = 1+2+3+4+5+6+7+8, 36=6*6)
- Prostokvashino
In the village of Prostokvashino, Uncle Fyodor, the cat Matroskin, the dog Sharik and Pechkin are sitting on a bench in front of the house. If Sharik, sitting on the far left, sits between Matroskin and Fedor, then Fedor will be on the far left. Who sits where? (SH F M P)
- Sages
A certain ruler, wanting to test the sages, told them: in front of you are three caps - a black one and two white ones. These caps will be put on you. Which one of you will be the first to guess what color the cap is on? The sages were taken into a dark room and put on a white cap, then they were brought back. They looked at each other for a long time. Finally one of them exclaimed: “I’m wearing a white cap.” How did he reason? (“If I were wearing a black cap, others would immediately guess, but they are silent”)
- Gardener
The king ordered the gardener to install a pipe in the garden to water the roses. A square-shaped garden plot (side length 40 m) consists of 6 identical square beds. It is necessary to lay a pipe 100 m long and divide the area into two equal parts. Show me how to lay the pipe.
- Little Red Riding Hood
Little Red Riding Hood goes to her grandmother. She carries 14 pies: with meat, cabbage, and mushrooms. There are the largest number of pies with cabbage, and there are twice as many of them as pies with meat. And there are fewer pies with meat than pies with mushrooms. How many mushroom pies? (5)
- Planet
The aliens informed the inhabitants of the Earth that in the system of their star there are three planets A, B, C. They live on the second planet. Then the transmission began to deteriorate due to interference, but 2 more messages were received, which, as scientists established, were both incorrect: 1) A is not the third planet from the star; 2) B – second planet. On what planet do aliens live?
- Mowgli
Mowgli asked 5 monkeys to bring him nuts. The monkeys picked up an equal amount of nuts and carried Mowgli. On the way they quarreled, and each monkey threw a nut at each other. As a result, they brought in half as much as they collected. How many nuts did Mowgli get?
- Pinocchio
They say that Tortilla gave the Golden Key to Pinocchio for a reason. She brought out three boxes: red, blue and green. On the red one it is written: “Here lies the golden key”, on the blue one it is written: “The green box is empty”, on the green one it is written “There is a snake sitting here”. Tortilla said: “Indeed, in one of the boxes there is a golden key, and in the other there is a snake, and the third is empty, but all the inscriptions are not correct. If you guess where the golden key is, it’s yours.” Where is the golden key?
- Kuma Pumpkin House
Godfather Pumpkin dreamed from childhood that he would someday have his own house. From the age of 15, he bought one brick at a time for future construction. After some time, Master Grape counted these bricks. There were 18 of them. Mr. Grape said that these bricks were not enough. Godfather decided to work more and eat less. Now he managed to buy 4 bricks a year. When all the bricks turned out to be 118, Pumpkin began to build a house. How old is Kumu Pumpkin?
- Ali Baba
To open Ali Baba's cave, you need to solve the puzzle:
Try to describe the reason for the violation as specifically as possible, this way you will help us figure it out much faster. Hottabych is a character in the Soviet fairy tale “Old Man Hottabych.” This book was written by Lazar Lagin. It was written in 1938 and published in the same year in parts, first in “ Pioneer Truth", and then in the magazine "Pioneer".
How old is Old Man Hottabych?
“Old man Hottabych” is a Soviet story-fairy tale by Lazar Lagin. It tells about the adventures of the young pioneer Volka Kostylkov, who discovered a jug with a genie named Hassan Abdurrahman ibn Hottab (aka old Hottabych) who had been sitting in it for three and a half thousand years. Grateful to his savior, Hottabych begins to serve the protagonist, performing all sorts of miracles, and over time, Volka re-educates Hottabych into a Soviet citizen.
Question: How old was old Hottabych?
My age is written as a number in which all the digits are different, and the first digit of this number is 4 times greater than the last. If you cross out the first and last digits of this number, you will get the largest of the two-digit numbers with the sum of the digits equal to 13. How old is Hottabych?
The age of old man Hottabych is written in four digits...
The book "Old Man Hottabych" by the famous Soviet writer Lazar Lagin (1903-1979) was probably read by every representative of the older generation. And if you haven’t read it, you’ve certainly watched the movie of the same name. Even if you didn’t watch it, you heard the name. So if you ask, “Do you know who Hottabych is?”, the answer will be in the affirmative. Some will even remember full name old man: Hassan Abdurrahman ibn Hottab. Someone will tell you the details of the fairy tale.
Hottabych
Every soviet child dreamed that one day a genie would appear to him, fulfilling his cherished wishes with the help of a magic beard. Surely many were jealous of Volka Kostylkov, because this boy managed to ride a magic carpet and eat a free popsicle. Old Man Hottabych has become a cult literary hero, children loved Lazar Lagin’s book no less than the adventures of Pinocchio or the fairy tale about Cheburashka and the crocodile Gena.
The age of old man Hottabych is written as a 4-digit number.
· If you cross out the first and last digits, you get a two-digit number, which, with the sum of the digits equal to 13, is the largest; First, you need to find two digits of one two-digit number; using the method of calculations, the number comes out to be 94. If you add up the two numbers, you get thirteen, which is given in the problem. This means that the answer to the first condition is that the second number is 9, and the third is 4.
The age of old man Hottabych is recorded... — Univer soloBY
The age of old man Hottabych is written as a number with different digits. The following is known about this number: 1. if you cross out the first and last digits, you get a two-digit number, which, with the sum of the digits equal to 13, is the largest:
2. the first digit is 4 times greater than the last.
How old is Hottabych?
Help me solve the problem. The age of old man Hottabych...
Jinn Abdurrahman ibn Hottab lived for the last three and a half thousand years in a jug from which he was freed by Volkoy. As his savior, Hottabych began to serve Volka, performing all kinds of miracles. At first, the genie has lordly, slave-owning habits, which, of course, is reflected in his miracles - but not fatally, since the genie turns out to be a very kind creature. Over time, Volka re-educates Hottabych into a Soviet citizen.
Old Man Hottabych - biography of the genie, interesting facts.
In the hot summer of 1957, the film “Old Man Hottabych” was released on Soviet screens, on which more than one generation of children in our country grew up. On the 60th anniversary of the first screening of the film, I invite you to remember this wonderful story and find out who Old Man Hottabych really is.
Questions»Hottabych’s age|Enroll in a university
Let's try to establish the age of old man Hottabych by logical thinking, so that it satisfies all the conditions of the task: a) The sum of the two digits in the middle of the age date must be equal to 13 and the number must be the largest. It can only be the number 94.
The fairy tale "Old Man Hottabych": summary, history of creation, heroes
All of us, as children, loved to read various adventures and fairy tales. And why all? The answer is simple. Childhood is a time when a child believes in miracles, which means that a work in which this or that magical phenomenon occurs captures the attention of the little viewer.
Scratch - How old is Old Man Hottabych?
Notes and Credits Author; Marushchak Anton, fourth grade student of State Educational Institution " high school No. 12, Orsha", Vitebsk region, Belarus The project was completed for participation in the republican competition "Programming in the Scratch environment". Nomination "Animated task". 2018
The age of old man Hottabych is written as a number with different...
1 short biography Lazar Lagin2 What is the mystery of the fairy tale Old Man Hottabych?3 Why did Lagin encrypt his works?4 What kind of fiction do readers need?5 How do modern “Serebrennikovs” interpret the fairy tale6 Afterword “The Soviets have their own pride,” Vladimir Mayakovsky once wrote. This also applied to fairy tales. There was a Soviet Pinocchio - Pinocchio, a Soviet Dolittle - Aibolit, a Soviet Wizard of Oz - The Wizard Emerald City... Well, the Soviet genie was given to us by a writer named Lazar Iosifovich Lagin.