Logic puzzle on the smell. Mathematical puzzles
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In connection with the beginning school year We decided to check how smart and inventive subscribers. And you can solve all submitted by us, tasks?
"Skate-ka"
Let's check if you can count?
Solve without the help of the calculator here is this example: to 1000 you need to add 40, then another 1000. Then add 30. Is there? Now again 1000. Add 20. Once again 1000. And finally 10.
How much did it work out?
Now check all times with your phone. Coincided?
"What is cheerful in the morning?"
And now the problem is on logic.
The woman dropped into a glass, full of coffee, his ring. How could he stay dry?
What do you think, what's the secret here?
"Match for children is not a toy"
How many matches in the picture?
"Green Man"
This is the mystery that you decide with the help of children's naivety. We are confident, it can be guessing the first time! Answer the question: what should be done when you see a green man?
"Mugs"
The teacher draws several circles on a piece of paper and asks one student: "How many circles here?". "Seven" - the student answers. "Right. So how many circles here? " - Ask again a teacher of another student. "Five" - \u200b\u200banswers the one. "Right" - teacher says again. So how many circles did he paint on a piece?
Do you think everything is so easy? And now try to solve the tasks that are considered the most complex in the world!
"Super Sudoku"
The first one that we suggest you break your head is the most complex Sudoku in the world.
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Sudoku is a Japanese puzzle with numbers. The principle is not intimidated at all. But the one that we offered to you, not everyone can solve!
"Gods of logical tasks"
There are three God, a, b, and c, one of which is the God of Truth, another god lies and the third God God, and it is unclear who of them who are. God of truth always tells the truth, the God of Lie deceives, and the God of Case can say that, and more in any order. It is necessary to determine who each of the gods is, asking three questions, which can be answered "yes" or "no", while every question is asked only to one God. The gods understand the questions, but they answer in their own language, in which there are words "DA" and "JA", but it is not known what word is "yes", and what "no".
This logical task for the authorship of the American philosopher and the logic of George Blos was first published in the Italian newspaper La Repubblica in 1992. Also in the riddle there are comments of the creators:
- You can ask one God for more than one question (therefore, no question may not be specified by other gods).
- What will be the next question and who will be set, may depend on the response to the previous question.
"The God of Case corresponds to randomly, depending on the threads of the coin, hidden in his head: If Avers falls, it responds truthfully if the reverse is still lying.
- The God of Case answers "DA" or "JA" to any question to which you can answer "yes" or "no".
Answers to all tasks can be viewed by
Brick weighs 1 kilogram plus half of its own weight.
How many brick weigh?
Fly
Two trains at a distance of 200 km move towards each other at a speed of 50 km / h each. The fly takes the start from one of the trains and flies towards another at a speed of 75 km / h. Avenue to another train, fly unfolds and flies back to the first. So it flies there and back, while two trains are faced, and the insect dies.
What distance did fly fly?
There are two ways to solve this task, one is simple, the other is hard.
A severe way to solve the problem: calculate every segment of the path. It is much easier to solve the problem, if it is elementary to calculate the distance that flies fly in 2 hours (it was after two hours of the train) at a constant speed of 75km / h.
It will fly 150km.
Trains
From Boston in New York, a commodity train comes out, moving at a speed of 60 km / h. 30 minutes later, a passenger train comes from New York to Boston, moving at a speed of 80 km / h.
Which of the trains will be closer to New York at the time of the meeting? (Ask the help of schoolchildren - they will surely cope with a task faster.)
When the trains are willing, they both will be approximately at the same distance from New York.
The train left from New York will be closer to New York about the distance equal to the length of one train, because the trains move in the counter direction. Well, this is if under the word "will meet" you mean it is "will meet", and not "will cross at the very moment when one of the trains are taught by all its cars with the second-trains wagons."
average speed
Half the way to the city, located at a distance of 60 km, I drove at an average rate of 30 km / h.
How fast should I go to the rest of the path so that the total average speed of the whole trip would be 60 km / h?
Wire over the equator
Earth circle is approximately 40,000 km. If you stretch the wire above the equator around the earth so that the wire length is only 10 meters (0.01 km) longer than the circumference of the Earth, can it crawl under this wire? Mouse? Human?
Let's compare the initial perimeter with a wire length. The initial perimeter is 2πr (two radius multiplied by the number PI), while the wire length is 2π (new R) (two new radius, multiplied by the number PI). The difference between them is approximately 1.6m.
A low person will easily pass under such a wire in full heightBut people will have to get bend to the Gusk.
Diofant
Little is known about the life of one Greek mathematics from Alexandria, whose name is called the algebra. It is assumed that he lived in the 3rd century of our era. According to the stories, the following epitaph was carved on his tombstone:
"Diophant's childhood of 1/6 of life occupied; 1/12 of the life Diofant Beard rustled; Another 1/7 of the life of Diophanta passed before he married. 5 years after the wedding, Diophanta was born a son who lived only half of the years that his father lived. And 4 years after the death of the son died Diofant. "
How old did Diofant live?
Papyrus Akhmesa
In 1858, the Scottish collector Henry Rindd acquired ancient Egyptian papyrus signed by the name "Ahmes". This scroll of a papyrus, 33 cm wide and a length of 5.25 meters, is a copy of an even more ancient mathematical manual relating to the time of Pharaoh Amenchet III. Here is one task of this ancient of mathematical collections:
One hundred grain measures should be divided between five employees so that the second get so bigger than the first, how much is more than the second, and as much as the fourth more than the third, and as much as the fifth more than the fourth. How many grain measures should everyone get if the first and second workers get grains together seven times less than the other three employees?
To solve the problem, we will make two equalities. 5W + 10D \u003d 100; 7 * (2w + d) \u003d 3W + 9D, where W is the amount of grain for the first employee, D is the difference in the amount of grain between the two (next in order) employees. Answer: The first employee of 10/6 grain measures, the second employee of 65/6 grain measures, the third employee 120/6 (20) grain measures, the fourth employee of 175/6 grain measures, the fifth anniversary of 230/6 grain measures.
How much left until midnight?
Two hours before midnight, it will remain two times less than it would be possible in an hour.
What time is it now?
Clock hands
At noon, the hour, minute and second hour clock arrow coincide at one point of the dial. A little more than an hour and five minutes, the hour and minute arrows coincide again. Find up to the millisecond time when they coincide.
What angle with them will be at this time to make a second arrow?
This task can be solved in several ways, but I like the next most simple. This situation (when the hour and minute arrows coincide) is repeated 11 times every 12 hours. It is easy to guess that the 1/11 mark of the dial circle is on time 1: 05: 27,273, that is, the second arrow will stand at a mark of 27,273 seconds.
The angle between the hour and second arrow in this case will be 131 degrees.
Pool
Four pipes are suitable for the pool for which through the cranes you can control the speed of filling the pool. Opening the first crane, you can fill in the pool for 2 days, the second - for 3 days, the third - for 4 days and the fourth - in 6 hours.
How much time will you need to fill the pool by opening all four cranes at the same time?
Since in the days of 24 hours, the first crane for an hour will fill 1/48 basin, the second crane - 1/72, the third crane is 1/96, and the fourth fill the pool to 1/6. From here we get: (6 + 4 + 3 + 48) / 288 \u003d 61/288. The pool will be filled after 288/61 hours, that is, after 4 h, 43min and approximately 17ps.
Moving through the desert
Military car with an important message should cross the desert. However, the full gas tank is only enough for half of the way. At the disposal of the military base there are several such cars, and gasoline can be pumped from one tank to another. They cannot use any canters and cables.
How to deliver a message without throwing a single car in the desert? (Try for clarity to lose the situation with toy machines.)
Magic believer
The magic belt that performs the desires of the owner is reduced twice in length and 3 times wide after each desire. After the completion of three desires, the front area was 4 cm2.
What was the initial length of the belt if its initial width was 9 cm?
Boldvili.
All residents of Boldville miscellaneous number Hair on the head. There is not a single resident who would have exactly 518 hair on the head. The population of the city exceeds the number of hair on the head of any of the inhabitants Boldville.
What is the maximum possible population of Boldville?
Invalid wives
Anthropologist who studied the tribe in the remote corner of the Amazon jungle, discovered strange custom. When her husband learned that his wife would change, he had to publicly execute her at midnight of the same day. About any woman changing husband, always knew all residents of the tribe, except her husband. But no one ever talked her husband about the treasures of his wife, because it contradicted the Code of honor. The same code of honor did not allow hangers to inform the wife, whose husband was wrong with her. Otherwise, she would shoot her husband in the same evening. On the day of his departure, an anthropologist convened all representatives of the tribe and announced: "I know that there are wrong wives in this tribe." And on the ninth day, all wrong husbands were executed.
How many wrong husbands?
If you take the number of wrong husbands in the number "n", the number of wrong husbands, known for each wife of the wrong husband, is "n-1" (because everyone is exactly known about everything - only about the loyalty of his own husband has to guess). Now we construct the next logical chain.
Suppose that the number of incorrect husbands is equal to one. Then everyone, except for one, it is known that among the inhabitants there are one wrong husband, while the wife of this wrong husband is sure that all husbands are faithful to her wives. As soon as she hears that among the inhabitants there are at least one wrong husband, she will immediately realize that only her husband can be, so in the same evening she would shoot him down.
Now imagine that among the inhabitants there are two wrong husband. Each wife of such incorrect husbands is sure that among the inhabitants there are only one wrong husband, so waiting for some of the wives to shoot her husband. But this evening no one shot no one, and it can only mean one thing: her Own husband She is also wrong and is the second wrong husband in the tribe. The first wife of the first incorrect husband comes to exactly the same conclusions (she also waited for someone from the wives would shoot her husband). Thus, both insulted wives at the first evening understand that their husbands change them, and the next evening (second day) target both husbands.
Following this logic, it is not difficult to guess that the number of incorrect husbands "N" will be targeted in "n" in the evening.
1 = 2
Find a mistake in mathematical calculations:
X \u003d 2.
x (x - 1) \u003d 2 (x-1)
x2 -x \u003d 2x-2
x2 -2x \u003d x-2
x (x-2) \u003d x-2
x \u003d 1.
Connect 9 points to four straight lines without taking out the hands and does not rub the lines.
Motto
In my youth, I discovered that thumb Legs sooner or later makes a hole in the sock. Therefore, I stopped to wear socks.Albert Einstein
Intellect is the most important thing from what distinguishes people from other representatives of the animal world. Man used the mind to achieve unprecedented heights In science and technology, but sometimes the minds of the mind were not only purely practical and utilitarian: so many different puzzles appeared on the light, for the solution of which it is necessary to thoroughly "figure out the brains." Ten of them you will find in this selection.
1. The most difficult sudoku
One of the most popular crossword varieties in the world is Sudoku - a Japanese puzzle with numbers. Its principle is nested, so many lovers try to create their own options. In 2012, the Finnish mathematician Arto Inkala said that he developed the "Sudoku's most difficult in the world."
According to the British newspaper "The Telegraph", if the simplest of the common sudoku variants on the difficulty scale designate, as "1", and the most complex from popular to evaluate to "5", then the option proposed by mathematician pulls on "11".
2. The most complex logical puzzle
There are three God, a, b, and c, one of which is the God of Truth, another god lies and the third God God, and it is unclear who of them who are. God of truth always tells the truth, the God of Lie deceives, and the God of Case can say that, and more in any order. It is necessary to determine who each of the gods is, asking three questions, which can be answered "yes" or "no", while every question is asked only to one God. The gods understand the questions, but they answer in their own language, in which there are words "DA" and "JA", but it is not known what word is "yes", and what "no".
This logical task for the authorship of the American philosopher and the logic of George Blos was first published in the Italian newspaper La Repubblica in 1992. In the comments to the riddle of Bulo makes important note: Every God you can ask more than one question, but it is impossible to ask more than three.
3. The most difficult in the world Sum-up-ku
One of the popular varieties of Sudoku is Sum-up-ku, it is also called the "Sudoku killer". The entire difference is that additional numbers are given in sum-up-to-ku - the amounts of values \u200b\u200bin cell groups, while the numbers contained in the group should not be repeated. In the popular Calcudoku.org puzzle service, you can track the complexity rating of published tasks, one of them became sum-to-ku, which is depicted here.
4. The most difficult "troubleshooting problem" Bongard
This type of puzzle invented an outstanding Russian cybernetic, the founder of the theory of recognition of images Mikhail Moiseevich Bongard: In 1967, he first published one of them in his book "The problem of recognition". The widespread popularity of the "Bongard Problems" found when the famous American physicist and informatik Douglas Hofstadter mentioned them in his work "Gödel, Escher, Bach: This infinite garland."
Two very complex example These tasks are taken from foundalis.com, to solve them, you must find a rule that corresponds to six images on the left page, but under which six pictures are not suitable on the right side.
5. The most difficult puzzle of the trading dock
This kind of sudoku is similar to Sum-up-ku, but, firstly, any arithmetic operations are used to calculate the cell values, and not just addition, secondly, the field can be a square of any size (the number of cells is not limited), and - Third, unlike Sudoku, it is not necessary to present tips from the 1st to 9 in each square 3 × 3. Such tasks have developed a Japanese teacher of mathematics Tetsuya Miyamoto.
You can try to deal with the most difficult trading dock, which was published on Calcudoku.org on April 2, 2013. Only 9.6% of permanent resource visitors managed to solve it.
6. The most difficult task of "IBM"
It is necessary to develop a storage system that would encode 24 bits of information on eight discs four bits each provided that:
- Eight 4-bit disks are combined with one 32-bit system in which any function from 24 to 32 bits can be calculated no more than five mathematical operations from the set (+, -, *, /,%, &, |, ~).
- After the failure of any two eight discs, these 24 bits of information can be restored.
On the website of the IBM website there is a regular heading "Think about it!", In which curious has been published since 1998 logic tasks. The given task is one of the most difficult.
7. The most difficult puzzle of Kakuro
Kakuro puzzles combine elements of Sudoku, logic, crosswords and basic mathematical operations. The goal is to fill the cells with numbers from one to nine, and the sum of the numbers in each horizontal and vertical block should come together with the specified number, and the numbers inside one block should not be repeated. For horizontal blocks, the desired amount is written directly to the left, and for vertical blocks - top.
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Do you know how to check the logic at the scouts? And with the help of which kind of riddles the degree of development logical thinking Schoolchildren in B. soviet times? Not? Then we advise you to visit this site. On it, you will not only find the answers to these questions, but also be able to test yourself for attentiveness, and also determine if you have analytics and talent of the strategist. In any case, you will not regret what you visited this site, because you will spend time and with benefit.
http://fit4brain.com/shelf/puzzles.
If you want to develop your intelligence, to enjoy an interesting and erudite interlocutor, with whom it is not boring at either a party or on the road, then you should visit the puzzle site. Looking here one day, you will probably become a regular visitor, because there are logical tasks for every taste. Supporters of the exact sciences - tasks in mathematics and physics, fans of elegant literature - charades, anagram and pseudo-native nonsense, and those who just love to have fun - frivolous challenges.
http://www.smekalka.pp.ru/Money tasks and jokes, words and labyrinth games, mathematical tricks and rebuses, charaks and encryptions - all of this you will find on the site, the creators of which took care of your stay on it fascinating and informative. The puzzles catalog stores tasks for attention and spatial thinking, logic and erudition. Everyone will find a riddle in the soul, and if you want to play friends, throw them a puzzle, who does not have a relapse, "there are also there.
http: //puzzle-ru.blogspot.com/search/Label/Golovole ...Love break your head over logical tasks and find non-standard solutions? Think yourself with an erudite and think that there is no question to which you would not know the answer? Do you adore trick tasks? Then you hit the address. On the site offered to your attention, presented logical tasks for every taste. Users allocated three often puzzles. Want to know what? Click on the site address, come on main page And dare.
http://mozgun.ru/
Do you think that you teeth have any brandry task? Are you considered an erudite and click the most complex logical tasks like nuts? Then welcome to the world of logic and non-standard solutions! The site that we advise to visit, keeps not one puzzle, about which teeth of intellectual analytics broke, more than once proving the presence of logical thinking and abilities possible options. Easy forces with the best, and let the strongest will win the strongest!
http: //www.potehechas.ru/golovolomki/golovolomki.s ...
The presence of logic, the ability to act in extreme situations and quickly make decisions are often determining on the issue of building a successful career. The author of this site offers to check how flexible is your thinking and are you able to see the exit where it seemed to be not. The puzzles collected here will allow you to evaluate your own opportunities and decide what kind of activity you better do. Simple tasks, answers to which can not find any adult.
http://www.profguide.ru/myshlenie/logic/
This site deserves your attention, because such a diverse collection of puzzles you will not find anywhere else. Questions for erudition will be forced to revive the knowledge gained in the memory of school yearsParadoxes will teach to look for non-standard solutions, card tasks will improve attention and memory, and sophisms will prove: even in analogous statements there is logic. By subscribing to the newsletter, you will receive new puzzles on the mail. On the site you can also lay out your own puzzles.
http://gadaika.ru/slova.
