What is the hardest puzzle in the world? The hardest logic puzzle in the world Top 10 hardest puzzles

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 the games of the mind were not only purely practical and utilitarian in nature: this is how many different puzzles appeared, 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 deceives, 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 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 Recognition Problem. 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, in order 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, and 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 durability number of one is 10, for a durability number of 2 it will be 25, the smallest number with a durability of 3 is 39, if the durability number is 4, the smallest number for it will be 77. What is the smallest number with a durability 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 enough 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/

Yeah, these puzzles are definitely not for the average mind .. Let's try to decipher some of the most difficult puzzles that I have ever seen in my life.

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?

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”.

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.

Bongard's most difficult "Recognition Problem"

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 Recognition Problem. 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 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, and 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.

The 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.

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

The Hardest of the Fill-A-Pix Puzzles

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.

Man used the mind to reach unprecedented heights in science and technology, but sometimes the games of the mind were not only purely practical and utilitarian in nature: this is how many different puzzles appeared, for the solution of which you have to thoroughly “brain out”.

Ten of them you will find in the selection Faktruma.

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”.

The most difficult logic puzzle

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 deceives, 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 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.

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.

Bongard's most difficult "Recognition Problem"

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 Recognition Problem. 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.

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, and 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.

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

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?

The Hardest of the Fill-A-Pix Puzzles

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.

Above is the Fill-A-Pix puzzle by Conceptispuzzles.com, which has many variations of this game and other fun puzzles.

Today we want to show you the most famous and most difficult puzzles, for the solutions of which you will need a lot of patience.

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?

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”.

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 bag-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.

Bongard's most difficult "Recognition Problem"

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 Recognition Problem. 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 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, and 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.

The 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, it is written at the top.

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, the number 77 will require four such steps: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "the number of resistance." 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 ?

The Hardest of the Fill-A-Pix Puzzles

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.

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.