Solving logical problems in a tabular way. Solving logical problems in a tabular way Yura and Grisha are engaged in a theater studio
Topic: "Logic". Lesson: "Solving logical problems in a tabular way."
Description of work: Logic is one of the traditional topics that is present in any version of the computer science course. This material will be useful for computer science teachers who want to make their lessons more interesting, motivate students to further study the topic. The successful solution of a difficult problem that required considerable mental effort brings a sense of satisfaction, regardless of whether they are distinguished by special talent or not, but in addition, these activities contribute to the improvement of the ability to solve the problems that life puts before us. The development of problem-solving skills certainly contributes to an increase in the level of intelligence. The age of students is 7 - 9 grade. The presented tasks can be used both in the process of conducting a lesson on the subject, and for extracurricular activities, or included in test work. Some problems are given with solutions.
Lesson objectives:
- Familiarity with logical tasks. Acquaintance with the tabular method of solving problems.
- development logical thinking, increasing the level of intelligence.
- Improving your ability to solve the problems that life puts before you.
During the classes:
1. Explanation of the topic, joint problem solving
2. Independent work
3. Homework
1. Explanation of the topic, joint problem solving.
The main thing in the proposed tasks is the method of solution - the construction of a table, the rows of which correspond to the elements of one of the sets considered in the condition of the problem, the columns - to the elements of another, the intersection of a row and a column - a combination of two elements of different sets. With the help of such a table, the conditions of the problem are analyzed, conclusions are drawn, redundancy, completeness and correctness of the conclusions are checked.
Task 1. After the competition, the runners on the scoreboard appeared the inscription:
Rustam was not second.
Eduard lagged behind Rustam by two places.
Jacob was not the first.
Galina was neither the first nor the last.
Karina finished right behind Yakov.
Who won these competitions? What was the distribution of runners at the finish line?
Decision:
We draw a table where the columns are the names of the children, and the rows are the numbers of places. We read the task, analyze the condition step by step and put in the table "+" if the match is established and "-" if there is no exact match.
Since Rustam was not second and Eduard was two places behind Rustam, Eduard cannot be either first, second, or fourth.
Yakov was not the first and Galina was neither the first nor the last, and since Karina finished right behind Yakov, she could not be either the first or the second.
This shows that Rustam was the first, while Edward (according to condition 2) was the third.
Since Karina finished right behind Yakov, it is obvious that Yakov was fourth, and Karina was the last, and then Galina was second.
So, one can single out
Five simple steps towards finding solutions to logical problems.
1. Make a table, since the table manages to take into account all possible options.
2. Read each statement carefully, as each contains something that will allow you to exclude at least one of the options.
3. Try to find the key statement, it will help to untie the whole tangle.
4. After you have compared all the statements and excluded from them those whose improbability was on the surface, compare the statements with each other, establish connections and contradictions.
5. The solution can be found by a simple method of successive eliminations.
The more you practice, the better you will get at it. And now to business.
Task 2.
On Saturday evening, Semyon, Kolya and Vitya decided to have fun. They had a choice: a movie, a rock concert or dancing.
Semyon loves cinema, but he is less intolerant of dancing than rock music.
Kolya loves to dance, but is ready to go to the cinema rather than to a rock concert.
Vitya loves rock music less than dancing, but the cinema is still not as unpleasant for him as dancing or a concert.
Since the issue will be decided by a majority vote, where do you think these guys went?
Task 3.
Three boys Kostya, Foma and Marat were friends with three girls - Zhenya, Sveta and Marina. But soon the company split into pairs, because it turned out:
Sveta hates skiing.
Kostya, Zhenya's brother often goes skiing with his girlfriend
And Foma is now running on a date with Kostya's sister.
Who does Marat spend time with?
Task 4.
Six friends, waiting for the train, dropped into the buffet.
Egor had the same breakfast as Anya, but he preferred potato chips to a sandwich with a cutlet.
Sasha ate the same as Mila, but instead of a milkshake he drank lemonade.
What did each friend's breakfast consist of?
Solution: Because
Masha took the same as Yegor, and in addition a sandwich with cheese;
Anya bought the same as Sasha, but did not buy chocolate cookies;
Kirill ate the same as Mila, but without onion chips;
Egor had the same breakfast as Anya, but he preferred potato chips to a sandwich with a cutlet;
Sasha ate the same as Mila, but instead of a milkshake he drank lemonade, then:
The second time we analyze the conditions.
Masha took the same as Yegor, and in addition, a sandwich with cheese.
Anya bought the same as Sasha, but did not buy chocolate cookies.
Kirill ate the same as Mila, but without onion chips.
Egor had the same breakfast as Anya, but preferred potato chips to a sandwich with a cutlet, and Masha took the same as Egor, and in addition, a sandwich with cheese.
Let's analyze the conditions for the third time.
Anya bought the same as Sasha, but did not buy chocolate cookies.
Sasha ate the same as Mila, but instead of a milkshake he drank lemonade, then Kirill ate the same as Mila, but without onion chips.
Anya bought the same as Sasha, but did not buy chocolate cookies
Masha took the same as Yegor, and in addition, a sandwich with cheese
Task 5.
In one small cafe, 5 people worked simultaneously in a shift: an administrator, a cook, a confectioner, a cashier, a janitor. Miss Galbraith, Miss Sherman, Mr. Williams, Mr. Wortman and Mr. Blake went to work at the same time. At the same time, it is known that:
1. The cook is a bachelor.
2. The cashier and the receptionist lived in the same room when they were in college.
3. Mr. Blake and Ms. Sherman only meet at work.
4. Mrs. Williams was upset when her husband told her that the administrator had denied him time off.
5. Wortman is going to be the best man at the wedding of the cashier and pastry chef.
Who is in what position in this cafe?
Decision:
Naturally, in the lesson I do not use all the proposed tasks, but select them individually for each class, depending on their preparedness and abilities.
2. Tasks for independent solution.
You can divide students into groups and give each group an individual task or select tasks for each student.
Task 1.
Kolya, Borya, Vova and Yura took the first four places in the sports competition. When asked what places they took, they answered:
1) "Kolya did not take either first or fourth place."
2) "Borya took second place."
3) "Vova was not the last."
What place did each boy take?
Task 2.
Three classmates - Vlad, Timur and Yura met 10 years after graduation. It turned out that one of them became a doctor, another - a physicist, and the third - a lawyer. One became interested in tourism, the other - in running, the third - in rugby.
1. Yura said that he does not have enough time for tourism, although his sister is the only doctor in the family, an avid tourist.
2. The doctor said that he shares the passion of a colleague.
3. It's funny, but two of my friends do not have a single letter of their names in the names of their professions and hobbies.
Who likes to do what in their free time and who has what profession?
Task 3.
Three friends - Ivan, Dmitry, Stepan teach various items(chemistry, literature, physics) in schools in Moscow, Kaliningrad and Perm. Known:
1) Ivan does not work in Moscow, and Dmitry does not work in Kaliningrad;
2) a Muscovite does not teach physics;
3) someone who works in Kaliningrad teaches chemistry;
4) Dmitry does not teach literature.
What subject and in what city does each of the comrades teach?
Task 4.
Four girls Masha, Tanya, Sofia and Polina took juice from a cafe. Each of them bought only one juice, and two of them bought apple juice, one grape juice, and one pear juice. It is known that Masha and Tanya have different tastes. Different juices were taken by Masha with Sofia, Polina with Sofia, Polina with Masha and Tanya with Sofia. In addition, it is known that Masha did not buy pear juice. Determine what juice each of them drank.
Task 6.(One of the variants of "Einstein's Problem")
Five houses line the road, one after the other.
1. Associate Professor lives in a red house.
2. Undertaker keeps dogs.
3. The plumber drinks tea.
4. The green house is to the left of the white one.
5. The owner of the green house drinks coffee.
6. Prima lover is holding a bird.
7. The owner of the yellow house smokes Belomor Canal.
8. In central house love milk.
9. The receiver of glass containers lives in the first house.
10. Smoking "Java" neighbor of the owner of cats.
11. The owner of the horses is a neighbor of the smoking "Belomor".
12. Beer lover smokes "Cuban" cigars.
13. The night watchman prefers "Friend" cigarettes.
14. The receiver of glass containers lives next to the blue house.
15. Smoking "Java" neighbor drinking water.
Who is keeping the fish? (house number, color profession, drinks)
Decision:
3. Homework.
Make up your own logic puzzle.
Good luck to you!
Problems created by my students.
Ivanova Svetlana, 7"B" class.
4 girls went to the disco: Masha, Olya, Rita. Sergey, Roma, Sasha, Pasha invited them to a slow dance. Who danced with whom if:
1) Olya did not dance with Pasha;
2) Tanya did not dance with Pasha and Roman;
3) Rita danced with Roma;
4) Olya liked Sergey, but she did not dance with him.
Mayakova Oksana, 9"A" class.
Businessmen Borya Vova Grisha and Gena earn crazy money, their names are classified, but they managed to find out, though it is not clear which one belongs to whom. Their names are: Ivanov, Enin, Sidorov, Petrov. Our spies also found out:
1) Borya and Petrov do not have private planes.
2) Grisha and Ivanov have nothing personal at all, except for accounts in a Swiss bank.
3) Gena is now more important than Enin, although Enin has a private plane.
4) Petrov is more important than Enin.
Who has a last name?
Koneva Ksenia, 9"A" class.
Four girlfriends: Dasha, Masha, Olga and Tanya went to the store to buy gifts. And every gift is different. Notepad, album, keychain, and book. When asked who bought what gifts, they answered as follows:
1) Dasha and Olya did not know who bought the notebook;
2) Olya said that Dasha and Masha visited a store with her where they sell key chains.
3) Dasha did not buy the album.
Who bought what present?
DEPARTMENT OF EDUCATION OF THE EXECUTIVE COMMITTEE
CITIES OF NABEREZHNY CHELNY
MUNICIPAL INSTITUTION
"INFORMATION - METHODOLOGICAL CENTER"
MUNICIPAL EDUCATIONAL INSTITUTION
"SEVERAGE SCHOOL №55"
X CITY COMPETITION OF PROFESSIONAL SKILLS
"TEACHER OF THE YEAR OF THE CITY OF NABEREZHNY CHELNY"
Russian language lesson in grade 3
Karimullina Liliya Rafaelevna
Teacher primary school
I qualification category
2010 -
Subject: main members of the proposal. The subject expressed by animate and inanimate nouns.
Goals:
Didactic:
- Learn to recognize the main members in the sentence.
- Learn how to express the subject with animate and inanimate nouns.
- Contribute to the formation of spelling skills of unchecked unstressed vowels at the root.
Educational:
- Raise interest in the Russian language, in the Russian word.
- To educate the need to use Russian language dictionaries, encyclopedias, reference books.
Developing:
- To promote the development of spelling vigilance, speech of students, mindfulness.
- Help enrich students' vocabulary.
Equipment: interactive presentation, cards with letters A and O, explanatory dictionary, ed. Ozhegov, school etymological dictionary.
Lesson type: learning new material.
During the classes:
- Organization of the class for the lesson.
We can do this!
II. Calligraphic letter.
aoa oao
Aah oooh
What letters are written?
Determine the pattern and write it down in your notebook.
III. Knowledge update.
Vocabulary work. (slide 2)
B_GAZH P_MIDOR
G_ROKH K_ROVA
S_LOMA K_NVERT
G_ZETA GV_ZDIKA
L_PATA UR_ZHAI
Z_VOD V_GON
Students raise cards with the letters A or O, write the words in a notebook.
Can you check the spelling of the words? Why?
What do all words have in common? Spelling at the root;
The words - nouns;
Dictionary words.
Find the extra word. Cow - animate noun.
(slide 3)
What about the rest of the words? Inanimate.
How do you understand phraseology?Like a cow licked with her tongue?
(slide 3)
Quickly and without a trace disappeared.
What part of the sentence will the word be cow ?
Subject.
- Guys, what topic are we going to work on today?
The subject expressed by animate and inanimate nouns. (slide 4)
IV. Learning new material.
- Analysis of proposals. Dictation recording.
A dawn lit up in the sky.(dawn - bright illumination of the horizon
before sunrise or sunset)
Dawn is grazing in the meadow.(Dawn is a cow)
Find the subject.
What question does it answer?
What part of speech is it?
How are the words different? (by spelling)
How are the words similar? (by sound)
Lights up in the sky dawn. (n., inanimate, common noun)
What?
Dawn is grazing in the meadow. (n., soul., own)
Who?
Conclusion: the subject can be expressed by animate and inanimate nouns.
Let's single out the predicates. How to find a predicate in a sentence?
(from the subject expressed by the name
Noun, we ask the question what does it do?)
- Reading the rule in the textbook on page 11
From the subject, expressed by an inanimate noun, to the predicate, you can also ask questions what does it do? what will he do? Actions seem to be attributed to inanimate objects.
- Fizkultminutka.
- The game "Claps": animate - inanimate.
Book, whale, candy, potato, kitten, cow, kangaroo, pencil, cabbage, crucian carp, crocodile, class, skates, bed, cat, mosquito, cuckoo, saucepan, flat.
What do these words have in common? Nouns starting with the letter K.
2. A game of mindfulness.
VI. Work on the topic of the lesson.
1. Working with text. Task: write sentences with the corresponding letter. Select subject. (slide 5)
Seryozha (Oh, oh) rlov I saw in the sky (Oh, oh) eagles.
Here is (Sh, sh) arik caught an air (sh, sh) arik
Petya (S, s) kvortsovmade a house for (C, c) quartzes.
What part of speech is the subject? noun
Animated or inanimate?
2. Work on the textbook. Ex. 3, p. 11 (oral).
Read the sentences. What is each one about?
What nouns - animate or inanimate - are the subjects expressed? Name them.
Can these sentences be combined into a text? Read.
2, 1, 3.
Willow grows near the house. In the spring, fluffy earrings appear on it. Willow pleases passers-by with its unusual outfit.
3. Exercise 6, p. 12. Task: write down the sentences, underline the subjects.
What did you learn about the subject?
VII. Development educational project"Encyclopedia of one word".
Guys, remember what word we talked about at the beginning of the lesson?
I propose to carry out the project "Encyclopedia of one word", and dedicate it to the word"cow".
(an assistant at the blackboard enters students' answers into the encyclopedia)
Watching the cartoon "How a man sold a cow."
VIII. Summary of the lesson. Student assessment.
Today in class we learned...
It was interesting to me…
It caused trouble...
Homework: p. 12 exercise. 7
Develop a project "Encyclopedia of one word" with any word from the dictionary.
We have succeeded!
Preview:
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Slides captions:
main members of the proposal. The subject expressed by animate and inanimate nouns. Russian language, grade 3 Karimullina L.R. Primary school teacher MOU "Secondary School No. 55" Naberezhnye Chelny 2010
Fill in the missing letters: b _ garage p _ midor g _ rokh k _ rova s _ scrap k _ nvert g _ zeta gv _ zdika l _ pata ur _ zhai z _ water v _ gona o o o a o a o o o about a
to about ditch Like a cow licked her tongue.
The subject expressed by animate and inanimate nouns.
Seryozha (Oh, o) rlov saw in the sky (Oh, o) rlov. Here (Sh, sh) arik caught the air (Sh, sh) arik. Petya (S, s) kvortsov made a house for (S, s) kvortsov. Seryozha Orlov saw eagles in the sky. Here Sharik caught a balloon. Petya Skvortsov made a house for starlings. Put in the correct letter:
Yura and Grisha are engaged in a theater studio. Sveta and her mother often walk in the nearby park. In the corner of the room, two puppies were playing on a mat.
Ladybug
Today at the lesson we learned ... Caused difficulty ... I was wondering ... Homework: P. 12 exercise. 7
Literature: 1. Volina V.V. Russian language. We learn by playing. - Ekaterinburg: "ARGO", 1996. 2. Dal V.I. Dictionary Russian language. - M., 2002.
Tasks on the topic "Logic"
Task 1.
Bad story. A window was broken in one of the classrooms. Only one of the four students could break the glass: Lenya, Dima, Tolya and Misha. When questioning students, each of them gave three testimonies.
Lenya. 1. I'm not to blame. 2. I didn't even go to the window. 3. Misha knows who did.
Dima. 1. I didn't break the glass. 2. I did not know Misha before entering school.
3. Tolya did it.
Tolya. 1. I didn't break the glass. 2. Misha did it. 3. Dima tells a lie, claiming that I broke the glass.
Misha. 1. I'm not to blame. 2. Lenya broke the glass. 3. Dima can vouch for me, because knows me since the day I was born.
Upon further questioning, each student stated that he had made two correct statements and one false statement. Try using mathematical logic to find the culprit.
Task 2.
One of the four boys messed up the switch. When asked who did it, the following answers were received:
Either Misha or Kolya did it.
Either Vitya or Kolya did it.
Neither Tolya nor Misha could do this.
Either Vitya or Misha did it.
Task 3.
At the marathon run, two forecasts were made about the places that the athletes Vasilenko, Levchenko and Simchenko will take, who really claim prizes:
"Simchenko will be the first, Vasilenko - the second, and Levchenko - the third";
"Vasilenko will win, Levchenko will come second, and Simchenko will be third."
Task 4.
coming sport competitions between four ninth grades of the same school. In the teacher's room, possible results are vividly discussed, forecasts are made.
The first place will be taken by 9A, and the second - by 9 B, - said the math teacher.
Yes you! the geography teacher said. - I recently went hiking with them and I know their capabilities. 9A will take second place, and 9G - only third.
And I think that 9B will be in second place, - said the head teacher of the school, and 9G will be in last place.
Task 5.
Six athletes - Adamov, Belov, Vetrov, Glebov, Dronov and Ershov - took the first six places in the competition, and not a single place was divided between them. About who took what place, the following statements were received:
It seems that Adamov was the first, and Dronov the second.
No, Ershov was in the first place, and Glebov was in the second.
That's the fans! After all, Glebov was in third place, and Belov was in fourth place.
And it was not like that at all: Belov was the fifth, and Adamov was the second.
You mixed everything up: the fifth was Dronov, and in front of him was Vetrov.
Task 6.
The attention of Andrei, Denis and Marat was attracted by a car rushing past.
This is an English car of the Ferrari brand, - Andrey said.
No, the car is Italian Pontiac, Denis objected.
It's a Saab and it's not made in England, Marat said.
What brand is this car and in what country is it made.
Task 7.
Anton, Boris, Petr, Viktor and Oleg came to the service dog breeding club for the next training session with their dogs. Wanting to play a trick on the new instructor, to his question “Who is the owner of each of the dogs?”, Each young man gave one correct and one incorrect answer.
Anton said: "My dog is Rex, and Peter's dog is Laima."
Boris said, "Rex is my dog and Victor's dog is Jack."
Peter said: "Victor's dog is Zeus, and mine is Rex."
Victor said: "My dog is Jack, and Oleg's dog is Bicho."
Oleg said: "Yes, my dog is Bicho, and Boris's dog is Zeus."
Who is actually the owner of each of the dogs?
Task 8.
Three friends, fans of Formula 1 motor racing, were arguing about the results of the upcoming stage of the race.
You'll see, Schumacher won't come first," John said. Hill will be first.
No, the winner will be, as always, Schumacher! Nick exclaimed. - And there is nothing to say about Alesi, he will not be the first.
Hill will never see the first place, but Alesi pilots the most powerful car.
Task 9.
The symphony orchestra hired three musicians - Brown, Smith and Wesson, who can play the violin, flute, viola, clarinet, oboe and trumpet. It is known that:
Smith is the tallest;
The violin player is smaller than the flute player;
Violin and flute players and Brown love pizza;
When a quarrel arises between the violist and the trumpeter, Smith reconciles them;
Brown can't play either the trumpet or the oboe.
Task 10.
Three classmates - Vlad, Timur and Yura met 10 years after graduation. It turned out that one of them became a doctor, the other - a physicist, the third - a lawyer. One was fond of tourism, the other - running, the passion of the third - rugby. Yura said that he does not have enough time for tourism, although his sister is the only doctor in the family, an avid tourist. The doctor said that he shared his colleague's passion. It's funny, but two of the friends do not have a single letter of their names in the names of their professions and hobbies.
Who likes to do what in their free time and who has what profession?
Task 11.
The three daughters of the writer Doris Kay - Judy, Iris and Linda are also very talented. They gained fame in various art forms - singing, ballet and cinema. They all live in different cities, so Doris often calls them in Paris, Rome and Chicago. It is known that:
Judy doesn't live in Paris, and Linda doesn't live in Rome;
the Parisian does not act in films;
one who lives in Rome, a singer;
Linda is indifferent to ballet.
Task 12.
Vadim, Sergey and Mikhail are studying various foreign languages: Chinese, Japanese and Arabic. When asked what language each of them studied, one answered: “Vadim is studying Chinese, Sergey is not studying Chinese, and Mikhail is not studying Arabic.” Subsequently, it turned out that in this answer only one statement is true, and the other two are false. What language is each of the young people learning?
Task 13.
On the trip, five friends - Anton, Boris, Vadim, Dima and Grisha got acquainted with a fellow traveler. They asked her to guess their names, and each of them made one true and one false statement.
Dima said: "My surname is Mishin, and Boris's surname is Khokhlov."
Anton said: "Mishin is my last name, and Vadim's last name is Belkin."
Boris said: "Vadim's last name is Tikhonov, and my last name is Mishin."
Vadim said: "My surname is Belkin, and Grisha's surname is Chekhov."
Grisha said: "Yes, my last name is Chekhov, and Anton's last name is Tikhonov."
What is the last name of each friend?
Task 14.
Returning home, Maigret called the Orfevre embankment.
Megre says. Any news?
Yes, chief. There were messages from the inspectors. Torrance established that if François was drunk, then either Etienne was the murderer or François was lying. Jussier believes that either Etienne was the murderer or François was not drunk and the murder took place after midnight. Inspector Lucas asked me to tell you that if the murder happened after midnight, then either Etienne is the killer or François is lying. Then called...
All. Thank you. It's enough. The commissioner hung up. He knew that François never lies. Now he knew everything. What did Commissioner Maigret find out?
Task 15.
four students Pedagogical Institute go in for sports and participate in amateur performances. Which of them does what, if known:
Boxer loves apples, and Peter prefers pears.
A choreography student is friends with volleyball players.
Gennady, - a great original.
A student studying in a theater studio believes that if a chess player were strong, like Timofey, and dexterous, like Peter, then he would enjoy tremendous success with the girls.
The boxer considers it below his dignity to engage in choreography.
Timofey does not think so, but he does not do choreography
Volleyball player Timofey does not know and does not want to know.
Boxer loves Marina, Marina loves Arkady, and Arkady loves to sing.
Only one of the students: Peter, Gennady or Arkady is a football player.
Task 16.
In one temple there were three statues of gods: the God of Lies, the God of Truth, the God of Diplomacy. All of them were similar to each other, but the questions they were asked were answered in different ways.
The God of Lies always lied, the God of Truth always told the truth, the God of Diplomacy sometimes lied and sometimes was truthful.
Nobody could identify them. But then one day a man did it. Entering the temple, he asked the first God on the left: “Who is standing next to you?”
The God of Truth, was the answer.
The man asked God in the center "Who are you?"
God of Diplomacy, he replied.
The last question was asked to the God on the right: "Who is standing next to you?"
The God of Lies, the statue replied.
Now everything is clear to me, - said the man.
Problem 17.
The bottle, glass, jug and jar contain milk, lemonade, kvass and water. It is known that water and milk are not in a bottle, a vessel with lemonade stands between a jug and a vessel with kvass, there is neither lemonade nor water in a jar; a glass stands between a jar and a vessel with milk. Which vessel contains each of the liquids?
Task 18.
Alla, Galya, Sima and Dasha participate in gymnastics competitions. Fans speculated about the possible winners:
Sima will be the first, Galya the second;
Sima will be the second, Dasha - the third;
Alla will be the second, Dasha - the fourth.
Task 19. "At the Congress"
Four scientists met at the congress: a physicist, a biologist, a historian and a mathematician. Each scientist spoke two of the four languages (Russian, English, French and Italian), but there was no such language that all four could speak. There is only one language in which three people could speak at once. None of the scientists speaks both French and Russian. Although the physicist does not speak English, he can serve as an interpreter if the historian and biologist wish to chat. The historian speaks Russian and can speak with a mathematician, although he does not know a single Russian word. Physicist, biologist and mathematician cannot speak the same language.
What two languages does each scientist speak?
Problem 20. "Four witnesses"
There are two suspects in the murder case: A and B. Four witnesses were questioned.Testimony of the first witness: "But not guilty."
Testimony of the second witness: "B is not guilty."
Testimony of the third witness: "Of the two testimonies, at least one is true."
Testimony of the fourth witness: "The testimony of the third witness is false."
The fourth witness was right. Who committed the murder
Task 21. "Young archaeologists"
Alyosha, Borya and Grisha found an old vessel in the ground. Considering the amazing find, each made two assumptions:Alyosha: "This vessel is Greek and made in the 5th century."
Borya: "This vessel is Phoenician and was made in the 3rd century."
Grisha: "This vessel is not Greek and was made in the 4th century"
The history teacher told the children that each of them was correct in only one of two assumptions.
Where and in what century was the vessel made?
Problem 22. "Mathematical Olympiad"
Victor, Roman, Leonid, and Sergey won four first places at the Mathematical Olympiad. When asked about the distribution of seats, they gave three such answers:
Sergey is the first, Roman is the second;
Sergey - the second, Victor - the third;
Leonid is the second, Victor is the fourth.
How were the places distributed?
Task 23. "Kidnapper"
Brown, Jones and Smith are charged with being an accessory to a bank robbery. The thieves fled in a waiting car. At the inquest, Brown testified that the perpetrators fled in a blue Buick, Jones said it was a black Chrysler, and Smith claims it was a Ford Mustang and by no means blue. It became known that, wanting to confuse the investigation, each of them correctly indicated either only the make of the car or its color.What color and what brand was the car?
Problem 24.
Square, circle, rhombus and triangle are cut out of white, blue, red and green paper. It is known that the circle is neither white nor green, the blue figure lies between the rhombus and the red figure, the triangle is neither blue nor green, the square lies between the triangle and the white figure. What figure is cut out of green paper?
A) circle.
B) Rhombus.
B) square.
D) a triangle.
D) Circle or rhombus.
Problem 25.
The bank robbery suspects testified as follows:
Petrov: "I didn't do it."
Ivanov: "Sidorov did it."
Sidorov: "I didn't do it."
Alekseev Ivanov did it.
The witness claims that only one of them told the truth. Who committed the crime?
A) Alekseev.
B) Petrov.
