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The hardest logic puzzle in the world. Incredibly difficult puzzles (9 photos) The most interesting puzzle in the world

Intelligence is the most important thing that distinguishes people from other representatives of the animal world. Man used the mind to reach unprecedented heights in science and technology, but sometimes mind games were not only of a purely practical and utilitarian nature: this is how many different puzzles were born, for the solution of which you have to thoroughly “brain out”. Ten of them you will find in this collection.

1. The hardest sudoku in the world

One of the most popular crossword puzzles in the world is Sudoku, a Japanese number puzzle. Its principle is simple, so many amateurs are trying to create their own options. In 2012, Finnish mathematician Arto Inkala claimed to have developed "the hardest sudoku in the world."

According to the British newspaper The Telegraph, if the simplest of the most common Sudoku variants are marked as “1” on the difficulty scale, and the most difficult of the popular ones are rated at “5”, then the option proposed by the mathematician pulls at “11”.

There are three gods, A, B, and C, one of which is the god of truth, the other is the god of lies, and the third is the god of chance, and it is not clear which is which. The god of truth always tells the truth, the god of lies always lies, and the god of chance can say both at random. It is necessary to determine who each of the gods is by asking three questions that can be answered "yes" or "no", with each question being asked to only one god. The gods understand the questions, but answer in their own language, which has the words "da" and "ja", but it is not known which word means "yes" and which "no".

This logical problem by the American philosopher and logician George Boolos was first published in the Italian newspaper "la Repubblica" in 1992. In the comments to the riddle, Bulos makes an important remark: each god can be asked more than one question, but more than three cannot be asked.

3. The hardest sum-do-ku in the world

One of the popular varieties of Sudoku is sum-do-ku, it is also called the “sudoku killer”. The whole difference is that additional numbers are set in the sum-to-ku - the sums of values ​​in groups of cells, while the numbers contained in the group should not be repeated. In the popular puzzle service Calcudoku.org, you can track the difficulty rating of published problems, one of them was sum-do-ku, which is shown here.

4. The most difficult "Problem of recognition" Bongard

This type of puzzle was invented by the outstanding Russian cybernetician, the founder of the theory of pattern recognition, Mikhail Moiseevich Bongard: in 1967, he first published one of them in his book The Problem of Recognition. The “Bongard problems” gained wide popularity when the famous American physicist and computer scientist Douglas Hofstadter mentioned them in his work “Gödel, Escher, Bach: this endless garland”.

The two most difficult examples of such problems are taken from Foundalis.com, to solve them you have to find a rule that matches the six images on the left side, but which does not match the six pictures on the right side.

5. The most difficult tracing paper puzzle

This type of Sudoku is similar to sum-do-ku, but, firstly, any arithmetic operations are used to calculate the value of the cells, and not just addition, secondly, the field can be a square of any size (the number of cells is not limited), and in Thirdly, unlike Sudoku, clues from 1 to 9 do not have to be present in each 3x3 square. Such tasks were developed by the Japanese math teacher Tetsuya Miyamoto.

Here you can try to figure out the most difficult calcudoku, which was published on Calcudoku.org on April 2, 2013. Only 9.6% of regular visitors to the resource managed to solve it.

It is necessary to develop an information storage system that encodes 24 bits of information on eight disks of four bits each, provided that:

Eight 4-bit disks are united by one 32-bit system, in which any function from 24 to 32 bits can be calculated by no more than five mathematical operations from the set (+, -, *, /, %, &, |,~).

After the failure of any two of the eight disks, these 24 bits of information can be restored.

On the IBM website there is a regular column "Think about it!", In which, since 1998, curious logical problems have been published. The task given here is one of the most difficult.

7. Hardest kakuro puzzle

Kakuro puzzles combine elements of sudoku, logic, crossword puzzles 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 must converge with the specified number, and the numbers within the same block must not be repeated. For horizontal blocks, the required amount is written directly to the left, and for vertical blocks - from above.

This example of one of the hardest kakuro puzzles is taken from the popular puzzle resource Conceptispuzzles.com.

8. One of Martin Gardner's tasks

American mathematician Martin Gardner is the author of many different problems and puzzles. One of his most interesting works is the calculation of the number that will take the least number of steps to reduce it to one digit by multiplying the digits of this number. For example, for the number 77, four such steps are required: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls the "fortitude number."

The smallest number with a tenacity number of one is 10, for a tenacity number of 2 it will be 25, the smallest number with a tenacity of 3 is 39, if the tenacity number is 4, the smallest number for it will be 77. What is the smallest number with a tenacity number of 5 ?

9. The most interesting problem from the game of go

Go was invented in China more than 2.5 thousand years ago, so it is one of the most ancient games on Earth. Despite fairly simple rules, it still attracts thousands of people with the opportunity to solve interesting strategic problems. The goal of the game is to enclose a larger area with stones of your color than the opponent. The situation depicted above is one of the most difficult in the history of Go: the most experienced players spent more than 1 thousand hours of playing time to solve it. How can black win in this game?

10. Hardest Fill-A-Pix Puzzle

Fill-A-Pix was invented by English mathematician Trevor Truran. This game is similar to the well-known Minesweeper: the player must, guided solely by logic, determine which cells should be colored and which will remain empty until the image is formed. Since several key values ​​affect one cell at once, it will take some time to get the final image.

: https://p-i-f.livejournal.com/

A riddle is a metaphorical expression in which one object is expressed by means of another, which has some, even remote, similarity with it; on the basis of the latter, a person must guess the intended object.

In ancient times, a riddle was a means of testing wisdom, now it is a popular pastime. Riddles are found among all peoples, no matter what stage of development they are at. A proverb and a riddle differ in that the riddle must be guessed, and the proverb is a lesson. Material from Wikipedia. We bring to your attention the 15 most difficult riddles in the world. Along with this, we also give answers to immediately determine whether you are able to solve them.

The answer is hidden and located on a separate page of the site by.

• Two people approach the river. Near the shore is a boat that can only support one. Both men crossed to the opposite bank. How did they do it?

  They were on different sides.

• Vasily, Peter, Semyon and their wives Natalya, Irina, Anna have been together for 151 years. Every husband is 5 years older than his wife. Vasily is 1 year older than Irina. Natalya and Vasily together are 48 years old, Semyon and Natalya are together 52 years old. Who is married to whom, and how old is who?

  Vasily (26) - Anna (21); Peter (27) - Natalia (22); Semyon (30) - Irina (25).

• 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?

  5000? Wrong. The correct answer is 4100. Try to recalculate on a calculator.

• Jackdaws flew, sat on sticks. They sit down one by one - the jackdaw is superfluous, they sit two by two - the stick is superfluous. How many sticks were there and how many jackdaws were there?

  Three sticks and four jackdaws.

• Mr. Mark was found murdered in his office. The cause was a bullet wound to the head. Detective Robin, inspecting the scene of the murder, found a cassette recorder on the table. And when he turned it on, he heard the voice of Mr. Mark. He said, “This is Mark. Jones just called me and said that in ten minutes he would be here to shoot me. It's useless to run. I know this tape will help the police arrest Jones. I hear his footsteps on the stairs. Here the door opens... The assistant detective offered to arrest Jones on suspicion of murder. But the detective did not follow his assistant's advice. As it turned out, he was right. Jones wasn't the killer, as was said on the tape. Question: why did the detective have suspicions?

  The cassette in the voice recorder was being revised at the start. Moreover, Jones would have taken the cassette.

• Third-graders Alyosha and Misha go from school and talk:
  “When the day after tomorrow becomes yesterday,” one of them said, “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 speak?

  On Sunday.

• A hare and a cat together weigh 10 kg. Dog with a hare - 20 kg. Dog with a cat - 24 kg. How much in this case will weigh all the animals together: a hare, a cat and a dog?

  27 kg. (solution .)

• There was a stone on the seashore. A word of 8 letters was written on the stone. When the rich read this word, they wept, the poor rejoiced, and the lovers parted. What was that word?

  Temporarily.

• There is a prison, next to the hospital. Around them are rails, and on the rails a train moves around at high speed. One boy needs to go to his grandfather in prison, and one girl to her grandmother in the hospital. How can they do it if the train doesn't stop?

  The boy needs to throw the girl under the train, then he will go to jail, and the girl to the hospital.

• What Russian word can be written from right to left, turned upside down, mirrored, and it will still remain unchanged and not lose its meaning?

  It.

• From which bird do you need to pluck feathers to get morning, afternoon, evening, night at once?

  Day.

• Teresa's daughter is my daughter's mother. Who am I to Teresa?

  1. Grandmother.
  2. Mother.
  3. Daughter.
  4. Granddaughter.
  5. I am Teresa.

  Write your choice in the comments.

Solving puzzles is fun for people: it's great to know that you've just found the answer to one of the hardest logic puzzles in the world. However, this is not the only reason why you need to solve puzzles at least once in a while. Read about other reasons, about the most difficult logical tasks, the benefits of solving them in the article.

The most difficult logic puzzle

The most difficult task is named just like that. The people call it the "Battle of people 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 Boolos. The whole world learned about this puzzle after its publication in the newspaper "Republic", which is published in Italy. This happened in 1992.

Condition

The most difficult one looks intimidating from the very beginning. How is her condition written? Suppose 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 any order.

The god of lies always speaks only a lie, the god of truth, on the contrary, speaks only Finally, the god of chance can speak both the truth and a lie, while 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 just three questions. The most difficult logical task implies that all these questions can be addressed both to one god and to each, but in turn. It all depends on the answers received. Questions should only require an affirmative (“Yes”) or 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 can either hear the word Ja or Da. It is not known 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 all.
• Only after the answer is received, you can ask the next question.
• The god of chance decides what answer to give with the help of a coin in his head.
• There is such a thing as a paradox question. An example would be: "Are you going to answer 'Ja'?" So, you can't ask questions like that.

Solution

Boulos, the logician and philosopher who created the problem, suggested the course of the solution in his article. The first thing to do is to calculate the god of truth or the god of lies. To do this, create a question with complex logical relationships. It should sound something like this: "Let's assume that 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 approximation. With the help of this question, one of the gods can be identified. Then it all depends on how to ask two more questions.

Sudoku "Escargot"

Many people are familiar with sudoku number-swapping games. Solving a puzzle like this is a great way to do a 5-minute brain workout. You may be 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 appeared lately, but this one is considered the most difficult. It's called Escargot. Along with the main challenge, 19 other difficult Sudokus can be found that were also created by the bot.

To find the solution to the world's most difficult logical puzzle, sudoku, you need to allocate enough time for this. The British edition of The Telegraph reported that Escargot Sudoku is rated at 11 points on a difficulty scale, while the usual puzzles of increased complexity “pull” at 5.

The problem of recognition

Mikhail Moiseevich Bongard, a Russian cyberneticist, first published in his book an example of a logic puzzle called "The Recognition Problem" in 1967. However, Bongard's very difficult logical problems gained popularity later. This happened after the American scientist Douglas Hofstadter wrote about them in his book.

To find a solution to the "Problem of Recognition", it is necessary to identify a certain pattern, or rule. The six images that are on the left page match this rule. Accordingly, the images on the right page do not fit it.

Toughness number

Martin Gardner is an American mathematician who is the author of a large number of different puzzles and problems. The most famous of these is the search for the "hardness number". The point is to reduce a certain number to one digit in the least number of steps. To do this, it is necessary to multiply the constituent numbers sequentially.

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 fortitude."

Many kinds of puzzles are published on specialized information resources on the relevant subject, including the most difficult logical tasks - with answers, tips, solution algorithms, etc. They always arouse great interest, so if you want to entertain yourself or your friends on a dank, damp evening , take advantage of this opportunity, or even try to come up with a task yourself. Believe me, finding "strength numbers" is a very exciting activity.

Mystery for geniuses

According to statistics, real geniuses find the solution within ten seconds. According to polls, logical problems - complex, with a catch - do not cause much difficulty for Harvard graduates, it takes them no more than 40 seconds to complete this task. For example, Bill Gates passes this genius test in 20 seconds. 15 percent of the inhabitants of the Earth are gifted people, they find a solution in two minutes. Now look at this picture and guess which figure is superfluous here.

The answer is: figure number one. It has no common features with the rest of the images. Judge for yourself, figure #2 has no white border, and #3 is the only circle. While all other pieces are red, #4 is green, and #5 is obviously smaller than the others. Thus, only the figure at number one does not have striking differences from most of the images, which is its main ... difference.

Islanders

Another interesting riddle is also connected with lies and truth. Suppose two tribes live on the island at once. Liars always lie, and good fellows, 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 doing well, and he was hired as a guide.

During the journey, travelers saw another islander who, judging by the words of the escort, also claimed that he was well done. Attention, question! How to determine whether a conductor was a liar or a good fellow?

The answer sounds like this: on this island everyone says that they are great. Since the guide correctly conveyed the islander's answer to the traveler, it is clear that he is doing well.

Football teams

Above were presented to your attention both medium and very complex logical problems. With the answers written at the end, solving them is, of course, easier. And to strain the 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. On the standings "Torpedo" takes the first place, "Spartak" - the 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 immediately 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 the ability to find page source code for hints or modify image files. Remember that complex logic puzzles are designed to test your intelligence, not to test your knowledge of a computer.

Periodic NSA puzzle

The National Security Agency does not have the best reputation as it has been repeatedly suspected of spying on Internet users and breaching privacy. If you do not take this into account, you can find quite complex logic puzzles with answers on the official site of periodic puzzles. New tasks appear monthly. The answer is posted a few days after the question. The NSA Puzzle periodical only launched last year, which means that a collection of more than 12 puzzles is already available.

blue eyes

It is very interesting to work on solving a difficult puzzle for several days or even weeks. For patient people, the most difficult logic puzzle in the world called Blue Eyes will do. According to XKCD - the best web platform for geeks - it develops logical, mathematical and lateral thinking.

The creator of the puzzle heard it quite by accident and published it on the Internet. He didn't 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 puzzle in the world is very exciting, it takes up all your free time.

Friday's 101 Puzzles, or Richard Wiseman's 101 Puzzles

A professional psychologist named Richard Wiseman became an Internet celebrity thanks to his Youtube channel. He publishes on it various illusions, tricks and so on. On Fridays, the man shares another puzzle or riddle on his blog. To solve them, it is necessary to combine linear, lateral and creative thinking. Famous and other image-based riddles and problems can be found on the psychologist's blog.

"Logic Labyrinths", or puzzles by Robert Abbott

Robert Abbott is a programmer, logician and game developer. Fame came to him after the publication of "Logical Labyrinths", which are available for free. The essence of this puzzle is to go through the maze with the given rules.

The very first game, by the way, the simplest, which is called Easy Maze 1, must be overcome without turning left.

What are puzzles and logic tasks for?

Puzzles and various logic tasks have several positive qualities. Firstly, they train the human brain, secondly, it is very interesting to solve them, and thirdly, they allow you to develop certain character traits in yourself.

How useful can puzzles be for children?

• They develop perseverance in restless guys.
• They practice problem solving skills.
• Persistence 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 show patience.
• Improves hand coordination and fine motor skills when it comes to puzzles like the Rubik's Cube.

Of course, all the most important qualities of character are laid down in children at an early age, and this is greatly facilitated by logical tasks. However, they are also useful for adults who have long since 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 “rejuvenation” for them, namely, to allocate time for solving puzzles.
• Logical tasks stimulate thought processes. Answers to the most difficult questions in life will come much faster if you regularly train your brain.
• There is an increase in serotonin levels. At the same time, the mood improves, but most importantly, the blood vessels that feed the brain begin to renew.
• Improves memory. With age, there are problems with remembering dates, names, cases. Crosswords, puzzles, and logic puzzles are best for developing memory.

As you know, small but tricky puzzles, often referred to as "puzzles", help to "stir up" the brain. Usually these problems are more logical than mathematical in nature. What is the difference?

The fact that when solving a mathematical problem you need to use, as a rule, one or more theorems, remember axioms or formulas. are also mathematical, but let's focus on puzzles that require ingenuity, breadth of thinking and the ability to abstract in order to find the right answer to solve them.

Puzzles are different, but is there one that makes more than one million people work hard to solve it? Of course, the most difficult puzzle in the world exists! Get ready to break your head for more than one evening.

The most difficult puzzle in the world: the battle of people and gods

The puzzle proposed by the American logician and philosopher George Boolos is named. It was first published in the Italian newspaper Respublika in 1992.

It is noteworthy that Bulos did not even let inquisitive minds suffer and attached a solution to the puzzle to the same article. So, the content of the logical puzzle is as follows. There are three gods familiar to each other (Boulos suggests using A, B, and C in no particular order): the god of lies, the god of truth, and the god of chance. The god of truth speaks only the truth, the god of lies only untruth, the god of chance can speak both truth and untruth in any order. We need to determine who is who by asking just three questions, the answer to which is only “yes” or “no”. Each question can only be asked (it is impossible to ask everyone at once). The gods understand human language, but prefer to answer in their own. Their language has two words - "ja" and "da", and we do not know which word is "no" and which is "yes".

The hardest puzzle in the world: some explanation

Boulos also slightly expanded the condition of the problem by adding the following points:

• One god can be asked more than one question. Thus, it may turn out that someone will not get one.
• The next question can be formulated only after receiving an answer to the previous one.
• The god of chance chooses the answer to a question by flipping a coin that is in his head.
• Questions-"paradoxes" are forbidden to ask, for example, "Will you answer "ja" now?

The hardest puzzle in the world: tips for solving

The philosopher and logician Bulos proposed to start by calculating either the god of lies or the god of truth. To do this, you can use complex logical relationships in the question. For example, the following questions might be asked:

• Does it mean that "da" is "yes", moreover, that you are the god of truth, and B is the god of chance?
• Is there an odd number of true statements in this list: "da" means "yes", you are the god of lies, B is the god of chance?

Thus, the most difficult puzzle involves first determining which of the answers means "yes" and which means "no". Further, based on this, you need to move on to the definition of the gods. By the way, you could already identify one of the gods in the first question (if you used one of the approximate options suggested above). We will not reveal all the secrets of the solution, because the most difficult puzzle game can be within your power if you think logically. Remember that you only have two questions left. Formulate difficult questions. You will determine the last god by the method of elimination.