One young man wanted to go to a club for a private party. To enter, visitors had to respond to the phrase spoken by the security guard with a password word. The young man hid not far from the guards and began to eavesdrop on what the guards were asking and what the visitors were answering. The security guard asked the first visitor the question: “Twenty-two?” The visitor answered “Eleven” and was allowed inside the club. The guard asked the second visitor the question: “Twenty-eight?” The visitor answered “Fourteen” and was allowed inside the club. The hidden young man thought that he had solved the code and approached the guard, who asked the question: “Forty-two?” The young man replied: “Twenty-one.” The security guard did not let him in and said that the party was for invitees only, i.e. The cipher was named incorrectly. What do you think the guard should have answered to this question if answer twenty-one is not correct?
Solving puzzles makes people happy: it's very satisfying to know that you just figured out the answer to one of the most difficult logic problems in the world. However, this is not the only reason why you need to solve puzzles at least sometimes. Read about other reasons, the most complex logical problems, and the benefits of solving them in the article.
The most difficult logic puzzle
The most difficult task is named just that. People call it the “Battle of Men and Gods.” The most difficult logical problem was first proposed by a philosopher and logician from the United States of America. His name is George Boulos. The whole world learned about this puzzle after its publication in the Republic newspaper, which is published in Italy. This happened in 1992.
Condition
The most difficult one looks intimidating from the very beginning. How is its condition written? Let's say there are three gods who know each other. One of them is the god of lies, the other of truth, and the third of chance. It is customary to designate them with the letters A, B and C, using the letters in random order.
The god of lies always speaks only lies, the god of truth, on the contrary, says only And finally, the god of chance can speak both the truth and lies, but it is impossible to predict what he will say now.
The challenge is to figure out who each god is. To do this, you can ask only three questions. The most difficult logical problem implies that all these questions can be addressed either to one god or to each, but in turn. It all depends on the answers received. Questions should only require an affirmative (“Yes”) or a negative (“No”) answer.
It is indicated that the gods understand the language in which questions will be asked, but they answer in their own. You may hear either the word Ja or Da. It is unknown which one means “No” and which one means “Yes”.
- Questions can be asked in different ways: ask something from each of the gods, or not from all of them.
- Only after The answer is received, you can ask the next question.
- The God of Chance decides what answer to give using a coin in his head.
- There is such a thing as a “paradox question”. An example would be the expression: "Are you going to answer 'Ja'?" So, such questions cannot be asked.
Solution
Boulos, the logician and philosopher who created the problem, suggested the solution in his article. The first thing to do is to figure out the god of truth or the god of lies. To do this, you should create a question with complex logical connections. It should sound something like this: “Suppose you are the god of truth, B is the god of chance, will Da mean “yes”?” Of course, this is not an exact wording, it is only an approximate version. Using this question you can identify one of the gods. Then it all depends on how to ask two more questions.
Sudoku "Escargot"
Many people are familiar with games that focus on rearranging numbers in Sudoku. Solving a puzzle like this is a great way to get a 5-minute brain workout. Perhaps you are good at solving Japanese Sudoku. But can you solve the most difficult problem in your group?
AI Sudoku is an algorithm for creating complex Sudoku, built by a mathematician named Arto Incala in 2012. More and more bots have been appearing lately, but this one is considered the most difficult. It's called Escargot. Along with the main task, you can find 19 other difficult Sudokus, which were also created by the bot.
To find a solution to the most difficult logical Sudoku problem in the world, you need to allocate a sufficient amount of time for this. The British publication The Telegraph reported that on the difficulty scale of Sudoku “Escargot” is rated at 11 points, while the usual puzzles of increased complexity “pull” 5.
Recognition problem
Mikhail Moiseevich Bongard, a Russian cyberneticist, first published an example of a logic puzzle in his book in 1967 called "The Recognition Problem". However, Bongard's very complex logic problems gained popularity later. This happened after the American scientist Douglas Hofstadter wrote about them in his book.
To find a solution to the Recognition Problem, it is necessary to identify a certain pattern, or rule. The six images on the left page follow this rule. Accordingly, the images on the right page do not fit it.
Durability number
Martin Gardner is an American mathematician who is the author of a large number of different puzzles and problems. The most famous of them is the search for the “persistence number”. The idea is to reduce a certain number to one digit in the least number of steps. To do this, you need to sequentially multiply the component numbers.
The most common example of a solution is “77”. You can reduce it to one number in a few steps. 7*7=49, 4*9=36, 3*6=18, 1*8=8. The action was performed four times, this is the “number of endurance”.
On specialized information resources on the relevant topics, many different kinds of puzzles are published, including the most complex logical problems - with answers, hints, solution algorithms, etc. They always arouse keen interest, so if you want to keep yourself or your friends busy on a dank damp evening , take advantage of this opportunity or even try to come up with a task yourself. Believe me, finding “persistence numbers” is a very exciting activity.
Riddle for geniuses
According to statistics, real geniuses find a solution within ten seconds. According to surveys, logical problems - complex, with a trick - do not cause any particular difficulties for Harvard graduates; they take no more than 40 seconds to complete this task. For example, Bill Gates passes this genius test in 20 seconds. 15 percent of the world's inhabitants are gifted people; they find a solution in two minutes. Now look at this picture and guess which figure is the odd one out.
The answer is: figure number one. It does not have any common features with other images. Judge for yourself, figure No. 2 does not have a white frame, and No. 3 is the only circle. While all the other pieces are red, No. 4 is green, and No. 5 is obviously smaller than the others. Thus, only the figure number one has no striking differences from most of the images, which is its main... difference.
Islanders
Another interesting riddle is also related to lies and truth. Let's say two tribes live on an island. Liars always lie, but good people, on the contrary, always tell the truth. A traveler who met an islander asked him a question to find out who he was. He said that he was a great guy, and he was hired as a guide.
During the journey, the travelers saw another islander, who, judging by according to the attendant, also claimed that he was great. Attention, question! How to determine whether the conductor was a liar or a good fellow?
The answer is: on this island everyone says they are great. Since the guide correctly conveyed the islander’s answer to the traveler, it is clear that he is a good fellow.
Football teams
Above, both medium and very complex logic problems were presented to your attention. With the answers written at the end, it is, of course, easier to solve them. And to strain your brain even more, you can create additional difficulties for yourself: do not write down the condition and try to find the right solution in your mind. So here's another puzzle.
There are several football teams. In the standings, Torpedo takes first place, Spartak is fifth. Dynamo is in the middle between these two teams. Next, you need to be very careful: if Spartak is ahead of Lokomotiv, and Zenit takes place right after Dynamo, which of the five teams will take second place? You must answer within 30 seconds. It will sound like this: “Locomotive”.
Internet puzzles
The Internet can be called a repository of puzzles. But many tasks require basic technical skills, such as finding the source code of a page for tooltips or modifying image files. Remember that complex logic problems are designed to test your intelligence, not test your computer skills.
NSA Periodic Puzzle
The National Security Agency does not have the best reputation, having been repeatedly suspected of spying on Internet users and violating privacy. If you do not take this into account, you can find quite complex logic problems with answers on the official website of periodic puzzles. New tasks appear monthly. The answer is published a few days after the question. The NSA Puzzle periodical was launched just last year, which means that a collection of more than 12 puzzles is already available.
Blue Eyes
It's fun to work on solving a difficult puzzle over several days or even weeks. For patient people, the most difficult logic puzzle in the world called Blue Eyes will suit you. According to XKCD - the best web platform for child prodigies, it develops logical, mathematical and lateral thinking.
The creator of the puzzle heard it completely by accident and published it on the Internet. At the same time, he did not even use words. To find the key to solving it, you need to read the riddle, retell it and try to mentally find the answer to it. The most difficult logic problem in the world is very exciting, it takes up all your free time.
"101 Friday Puzzles" or Richard Wiseman's 101 Puzzles
A professional psychologist named Richard Wiseman became an Internet celebrity thanks to his YouTube channel. He publishes various illusions, tricks, etc. on it. On Fridays, a man shares another puzzle or riddle on his blog. Solving them requires a combination of linear, lateral and creative thinking. Famous and also other riddles and problems based on images can be found on the psychologist's blog.
"Logic labyrinths", or Robert Abbott's puzzles
Robert Abbott is a programmer, logician and game developer. Fame came to him after the publication of “Logical Labyrinths,” which are freely available. The essence of this puzzle is to go through a maze with given rules.
The very first game, by the way, the simplest one, called Easy Maze 1, must be overcome without turning left.
What are puzzles and logic problems for?
Puzzles and various logic problems have several positive qualities. Firstly, they train the human brain, secondly, solving them is very interesting, and thirdly, they allow you to develop certain character traits.
How useful can puzzles be for children?
- They develop perseverance in restless children.
- They train problem solving skills.
- Perseverance is another quality that puzzles develop in children. After all, as you know, puzzles are difficult to solve the first time, for this you need to be patient.
- Hand coordination and fine motor skills improve when it comes to puzzles like the Rubik's Cube.
Of course, all the most important character qualities are laid in children at an early age, and logical tasks greatly contribute to this. However, they are also useful for adults who have long graduated from school. The brain needs to be trained just like the body.
- In order for brain cells to age more slowly and less, it is necessary to regularly arrange procedures for them to “rejuvenate”, namely, allocate time for solving puzzles.
- Logical tasks stimulate thought processes. Answers to life's most difficult questions will come much faster if you regularly train your brain.
- There is an increase in serotonin levels. At the same time, your mood improves, but most importantly, the blood vessels that feed the brain begin to renew themselves.
- Memory improves. With age, problems arise with remembering dates, names, and things to do. Crosswords, puzzles and logic problems are best for developing memory.
Finally, Krol looked up from the computer and decided to take a walk and get some fresh air. It was only later that Fomuvi found out that the electricity had simply been turned off. But the point is not that, but how the furry friend found excellent children's riddles about football.
It all started with the fact that Krol was simply tired of shooting games and racing on the computer. Online games are also boring. What to play? We need to try games of other genres! On the advice of one of his friends, he decided to download fifa, a football simulator known throughout the world. But at the hottest moment of the football match, when Krol was taking a penalty kick, the electricity was turned off and the screen went dark. I had a fight and a fight, but there was nothing to do. So I decided to go outside. Captivated by the passion of football, he took the ball, dressed like a football player, and walked out the door.
He knew that the guys often kicked the ball around in the yard and that finding a team there was as easy as shelling pears. Making his way through the jungle of cars, Krol went out to the playground. His surprise knew no bounds. All the guys stood in a row, and Uncle Kolya walked back and forth in front of them. Previously, Krol had only seen Nikolai in the park with other old men playing , and . So it was a complete surprise to see him here.
— Football is a team game! There must be not only physical dexterity, but also team spirit. And the team spirit is supported not only by victories. You won’t always be able to win, I’m telling you this – the best player of this yard in the past. Here we need chants and football riddles. So, I ask a riddle - you answer! Is everyone clear?
- Yes, Uncle Kolya!
- And you, Krol, why are you standing on the sidelines? March in a row! Let's begin.
I see that the team spirit is high! You guys are great. You click football riddles like seeds. Now I will teach you how to play together, otherwise you are running around like loners. Krol, you will be the goalkeeper for the first time. Otherwise, I rarely see you here, watch and learn the rules of football. Well, catch the ball, of course!
Trick riddles are riddles with a common question and a non-standard answer. At first glance, the answer may seem strange and incorrect, but if you read the riddle more carefully and think about the answer, it will turn out to be quite logical. Riddles with a trick, as a rule, are not without a sense of humor. Not only do they develop quick wit and out-of-the-box thinking, but they are also fun. Tell tricky riddles to your friends and relatives, have a fun and useful time.
The same person always came to the football match. Before the game started, he guessed the score. How did he do it?
Answer: Before the game starts the score is always 0:0
82805
More than an hour, less than a minute.
Answer: Seconds (hand of some watch models)
Tag. Anna
48492
What language is spoken silently?
Answer: Sign language
138495
Why is the stop valve on trains red and on airplanes blue?
Answer: Many will say: “I don’t know.” Experienced people will answer: “There are no stop valves on airplanes.” In fact, airplanes have a stop valve in the cockpit.
Makarova Valentina, Moscow
32397
The boy paid 11 rubles for a bottle with a cork. A bottle costs 10 rubles more than a cork. How much does a cork cost?
Answer: 50 kopecks
Orlov Maxim, Moscow
40963
One French writer really disliked the Eiffel Tower, but always dined there (on the first level of the tower). How did he explain this?
Answer: This is the only place in all of vast Paris from where it is not visible
Borovitsky Vyacheslav, Kaliningrad
38373
In which city is a man's name and cardinal direction hidden?
Answer: Vladivostok
Mezhuleva Yulia
44366
Seven sisters are at the dacha, where each is busy with some kind of business. The first sister reads a book, the second cooks food, the third plays chess, the fourth solves Sudoku, the fifth does laundry, the sixth takes care of plants. What does the seventh sister do?
Answer: Plays chess
Gobozov Alexey, Sochi
44176
Why do they often walk, but rarely drive?
Answer: By stairs
177161
It goes uphill, then downhill, but stays in place.
Answer: Road
137838
Which word has 5 "e"s and no other vowels?
Answer: Migrant
Radaev Evgeniy, Petrozavodsk
40594
Two people approach the river. There is a boat at the shore that can only support one. Both people crossed to the opposite bank. How?
Answer: They were on different banks
25 25, Vladivostok
30484
Vasily, Peter, Semyon and their wives Natalya, Irina, Anna are 151 years old together. Each husband is 5 years older than his wife. Vasily is 1 year older than Irina. Natalya and Vasily are 48 years old together, Semyon and Natalya are 52 years old together. Who is married to whom, and how old is someone? (Age must be expressed in whole numbers).
Answer: Vasily (26) - Anna (21); Peter (27) - Natalya (22); Semyon (30) - Irina (25).
Chelyadinskaya Victoria, Minsk
18729
Jackdaws flew and sat on sticks. If they sit down one at a time, there’s an extra jackdaw; if they sit down in twos, there’s an extra stick. How many sticks were there and how many jackdaws were there?
Answer: Three sticks and four jackdaws
Baranovsky Sergey, Polotsk
25515
Where does it happen that a horse jumps over a horse?
Answer: In chess
)))))))) Renesmee, L.A.
35698
What table has no legs?
Answer: Dietary
Boyko Sasha, Volchikha
30155
Do not write anything or use a calculator. Take 1000. Add 40. Add another thousand. Add 30. Another 1000. Plus 20. Plus 1000. And plus 10. What happened?
Answer: 5000? Wrong. The correct answer is 4100. Try using a calculator.
Ivanova Daria, Daria
33398
How can a person not sleep for 8 days?
Answer: Sleep at night
Sone4ka0071, Sosnogorsk
33987
What animal do people walk on and cars drive over?
Answer: Zebra
Tanya Kostryukova, Saransk
26484
Which word uses “no” 100 times?
Answer: Moans
Muslimova Sabina, Dagestan (Derbent)
31609
What's an elephant without a nose?
Answer: Chess
Ksenia Prokopieva, Moscow
27415
Mr. Mark was found murdered in his office. The cause turned out to be a bullet wound to the head. Detective Robin, examining the murder scene, found a cassette recorder on the table. And when he turned it on, he heard Mr. Mark's voice. He said: “This is Mark speaking. Jones just called me and said that in ten minutes he would be here to shoot me. There is no use in running. I know this footage will help the police arrest Jones. I hear his footsteps on the stairs. The door opens..." The assistant detective suggested that Jones be arrested on suspicion of murder. But the detective did not follow his assistant's advice. As it turns out, he was right. Jones was not the killer, as was stated on the tape. Question: why did the detective become suspicious?
Answer: The tape in the recorder was reviewed at the beginning. Moreover, Jones would have taken the tape.
Katarina, Moscow
10937
Sherlock Holmes was walking down the street. And suddenly he saw a dead woman lying on the ground. He walked over, opened her bag and took out her phone. Tel. in the book he found her husband's number. He called. Speaks:
- Come here urgently. Your wife has died. And after a while the husband arrives. He looks at his wife and says:
- Oh, honey, what happened to you???
And then the police arrive. Sherlock points his finger at the woman's husband and says:
- Arrest this man. He was the one who killed her. Question: Why did Sherlock think that?
Answer: Because Sherlock didn't tell her husband the address
Tusupova Aruzhan
19064
Two fifth-graders Petya and Alyonka are walking home from school and talking.
“When the day after tomorrow becomes yesterday,” said one of them, “then today will be as far from Sunday as the day that was today, when the day before yesterday was tomorrow.” What day of the week did they talk?
Answer: On Sunday
Khrushka, Ololoshkino
14151
There is a rich house and a poor one. They are burning. Which house will the police extinguish?
Answer: Police don't put out fires, fires are put out by firefighters
79404
What route has no one ever walked or ridden before?
Answer: Milky Way
Tikhonova Inessa, Aktyubinsk
23390
How many years are there in a year?
Answer: one (summer)
Maksim, Penza
28654
What kind of stopper can't stop any bottle?
Answer: Road
Volchenkova Nastya, Moscow
23890
In what word is the drink and natural phenomenon “hidden”?
Answer: Grapes
Anufrienko Dasha, Khabarovsk
23369
What sign must be placed between 6 and 7 so that the result is less than 7 and greater than 6?
Answer: Comma
Mironova Violetta, Saratov
20603
Without what can nothing ever happen?
Answer: Untitled
Anyutka, Omsk
24143
Union, number then preposition -
That's the whole charade.
And so that you can find the answer,
We need to remember about rivers.
Answer: i-sto-k
Nazgulichka, Ufa
16722
What muscle is the strongest in the human body?
Answer: The common belief is language. In fact, it is the calf and masseter muscles.
Anonymous
18371
You can tie it, but you can’t untie it.
Answer: Conversation
Dasha, Chelyabinsk
22371
To what mere mortal does even the president take off his hat?
Answer: Hairdresser
Nastya Slesarchuk, Moscow
21070
How to put 2 liters of milk in a liter jar?
Answer: Turn it into cottage cheese
Anonymous
18391
Once upon a time there lived an orphan girl in a thicket; she had only two kittens, two puppies, three parrots, a turtle and a hamster with a hamster who was supposed to give birth to 7 hamsters. The girl went to get food. She goes through the forest, field, forest, field, field, forest, forest, field. She came to the store, but there was no food there. It goes further, through the forest, forest, field, field, forest, field, forest, field, forest, field, field, forest. And the girl fell into the hole. If she gets out, dad will die. If she stays there, mom will die. You can't dig a tunnel. What should she do?
Answer: She is an orphan
I'm Yulechka, Omsk
14332
They are metallic and liquid. What are we talking about?
Answer: Nails
Babicheva Alena, Moscow
15195
How to write "duck" in 2 cells?
Answer: In the 1st - the letter “y”, in the 2nd - a dot.
Sigunova 10 years old Valeria, Zheleznogorsk
20885
Name a word in which one letter is a prefix, the second is a root, the third is a suffix, and the fourth is an ending.
Answer: Gone: u (prefix), sh (root), l (suffix), a (ending).
Little Daniel
14699
Guess the riddle: who has the heel behind the nose?
Answer: Shoes
Lina, Donetsk
17793
There were 20 people on the bus. At the first stop 2 people got off and 3 people got on, at the next - 1 got off and 4 got on, at the next - 5 got off and 2 got on, at the next - 2 got off and 1 got on, at the next - 9 got off and no one got on, at the next - 2 more came out. Question: how many stops were there?
Answer: The answer to the riddle is not that important. This is a riddle with an unexpected question. While you are telling the riddle, the guesser begins to mentally count the number of people on the bus, and at the end of the riddle, with a question about the number of stops, you will puzzle him.
40291
There lived a husband and wife. The husband had his own room in the house, which he forbade his wife to enter. The key to the room was in the bedroom chest of drawers. They lived like this for 10 years. And so the husband went on a business trip, and the wife decided to come into this room. She took the key, opened the room, and turned on the light. The wife walked around the room, then saw a book on the table. She opened it and heard someone opening the door. She closed the book, turned off the light and locked the room, putting the key in the chest of drawers. It's my husband who came. He took the key, opened the room, did something in it and asked his wife: “Why did you go there?”
How did the husband guess?
Answer: My husband touched the light bulb, it was hot.
SLEPTSOVA VIKUSIA, OMSK
12145
A husband and wife, a brother and sister, and a husband and brother-in-law were walking. How many people are there in total?
Answer: 3 people
Arkharov Mikhail, Orekhovo-Zuevo
15068
This name in full sounds like Danuta. What is it abbreviated as?
Answer: Dana
Hanukova Danuta, Bryansk
13116
A river that “fits” in your mouth?
Answer: Gum
Bezusova Anastasia, Overyata village