Today we want to show you the most famous and most difficult puzzles, to solve which you will need a lot of patience.
Go was invented in China over 2,500 years ago, making it one of the oldest games on Earth. Despite the fairly simple rules, it still attracts thousands of people with the ability to solve interesting strategic problems. The goal of the game is to fence off a larger territory with stones of your own color than the enemy. The situation pictured above is one of the most difficult in the history of go: the most experienced players spent more than 1,000 hours of playing time on its solution. How can black win this game?
World's Hardest Sudoku
One of the most popular crossword puzzles in the world is Sudoku, a Japanese number puzzle. Its principle is simple, so many amateurs try to create their own versions. In 2012, the Finnish mathematician Arto Inkala stated that he had developed "The world's hardest Sudoku".
According to the British newspaper "The Telegraph", if the simplest of the common variants of Sudoku on the scale of difficulty is designated as "1", and the most difficult of the popular ones are rated at "5", then the variant proposed by the mathematician is "11".
The most difficult sum-do-ku in the world
One of the popular varieties of Sudoku is sum-do-ku, it is also called "killer sudoku". The only difference is that additional numbers are set in the sum-do-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 the published problems, one of which is the sum-do-ku, which is shown here.
Bongard's Hardest "Recognition Problem"
This type of puzzle was invented by the outstanding Russian cyberneticist, 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 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 only addition, and secondly, the field can be a square of any size (the number of cells is not limited), and in - thirdly, unlike Sudoku, hints from 1 to 9 in each 3 × 3 square do not have to be present here. Such problems were developed by the Japanese mathematics teacher Tetsuya Miyamoto.
The hardest puzzle kakuro
Kakuro puzzles combine elements of Sudoku, logic, crosswords and basic math. 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 inside one block must not be repeated. For horizontal blocks, the required amount is written directly to the left, and for vertical blocks, at the top.
American mathematician Martin Gardner is the author of a wide variety of problems and puzzles. One of his most interesting works is calculating a number that takes the least number of steps to bring it down to one digit by multiplying the digits of that number. For example, for the number 77, four such steps are required: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "the number of fortitude." The smallest number with a toughness number of one is 10, for a toughness number of 2 it will be 25, the smallest number with a toughness number 3 is 39, if the toughness number is 4, the smallest number for it will be 77. What is the smallest number with a toughness number 5 ?
Hardest Fill-A-Pix Puzzle
Fill-A-Pix was invented by the 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 ones 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.
Yes, such puzzles are definitely not for the average mind .. Let's try to decipher some of the most difficult puzzles I've ever seen in my life.
The most interesting problem from the game of go
Go was invented in China over 2,500 years ago, making it one of the oldest games on Earth. Despite the fairly simple rules, it still attracts thousands of people with the ability to solve interesting strategic problems. The goal of the game is to fence off a larger territory with stones of your own color than the enemy. The situation pictured above is one of the most difficult in the history of go: the most experienced players spent more than 1,000 hours of playing time on its solution. How can black win this game?
World's Hardest Sudoku
One of the most popular crossword puzzles in the world is Sudoku, a Japanese number puzzle. Its principle is simple, so many amateurs try to create their own versions. In 2012, Finnish mathematician Arto Inkala announced that he had developed "the world's hardest Sudoku."
According to the British newspaper "The Telegraph", if the simplest of the common variants of Sudoku on the scale of difficulty is designated as "1", and the most difficult of the popular ones are rated at "5", then the variant proposed by the mathematician is "11".
The most difficult sum-do-ku in the world
One of the popular varieties of Sudoku is sum-do-ku, it is also called "killer sudoku". The only difference is that additional numbers are set in the sum-do-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 the published problems, one of which is the sum-do-ku, which is shown here.
Bongard's Hardest "Recognition Problem"
This type of puzzle was invented by the outstanding Russian cyberneticist, 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 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 only addition, and secondly, the field can be a square of any size (the number of cells is not limited), and in - thirdly, unlike Sudoku, hints from 1 to 9 in each 3 × 3 square do not have to be present here. Such problems were developed by the Japanese mathematics teacher Tetsuya Miyamoto.
The hardest puzzle kakuro
Kakuro puzzles combine elements of Sudoku, logic, crosswords and basic math. 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 inside one block must not be repeated. For horizontal blocks, the required amount is written directly to the left, and for vertical blocks, at the top.
One of Martin Gardner's tasks
American mathematician Martin Gardner is the author of a wide variety of problems and puzzles. One of his most interesting works is calculating a number that takes the least number of steps to bring it down to one digit by multiplying the digits of that number. For example, for the number 77, four such steps are required: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "the number of fortitude." The smallest number with a toughness number of one is 10, for a toughness number of 2 it will be 25, the smallest number with a toughness number 3 is 39, if the toughness number is 4, the smallest number for it will be 77. What is the smallest number with a toughness number 5 ?
Hardest Fill-A-Pix Puzzle
Fill-A-Pix was invented by the 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 ones 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.
Intelligence is the most important thing that distinguishes people from other representatives of the animal world. Man used his mind to reach unprecedented heights in science and technology, but sometimes the mind games were not only purely practical and utilitarian in nature: this is how many different puzzles were born, for the solution of which one has to thoroughly "brainwash". You will find ten of them in this collection.
1. World's Hardest Sudoku
One of the most popular crossword puzzles in the world is Sudoku, a Japanese number puzzle. Its principle is simple, so many amateurs try to create their own versions. In 2012, Finnish mathematician Arto Inkala announced that he had developed "the world's hardest Sudoku."
According to the British newspaper "The Telegraph", if the simplest of the common variants of Sudoku on the scale of difficulty is designated as "1", and the most difficult of the popular ones are rated at "5", then the variant proposed by the mathematician is "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 of them is which. The god of truth always speaks the truth, the god of lies deceives, and the god of chance can say both in no particular order. 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 to one god. The gods understand the questions, but they answer in their own language, which contains the words "da" and "ja", but it is not known which word means "yes" and which "no".
This logical problem, authored by the American philosopher and logician George Boulos, 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 most difficult sum-do-ku in the world
One of the popular varieties of Sudoku is sum-do-ku, it is also called "killer sudoku". The only difference is that additional numbers are set in the sum-do-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 the published problems, one of which is the sum-do-ku, which is shown here.
4. The most difficult "Recognition problem" of Bongard
This type of puzzle was invented by the outstanding Russian cyberneticist, 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."
Two of the most difficult examples of such problems are taken from Foundalis.com, to solve them you have to find a rule that matches six images on the left page, but six images on the right do not match.
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 only addition, and secondly, the field can be a square of any size (the number of cells is not limited), and in - thirdly, unlike Sudoku, hints from 1 to 9 in each 3 × 3 square do not have to be present here. Such problems were developed by the Japanese mathematics teacher Tetsuya Miyamoto.
Here you can try to figure out the most difficult tracing document, 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 would encode 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 failure of any two disks out of eight, you can recover these 24 bits of information.
On the IBM website there is a regular column “Think about it!”, In which interesting logical problems have been published since 1998. The task presented here is one of the most difficult.
7. Hardest Kakuro puzzle
Kakuro puzzles combine elements of Sudoku, logic, crosswords and basic math. 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 inside one block must not be repeated. For horizontal blocks, the required amount is written directly to the left, and for vertical blocks, at the top.
This example of one of the hardest kakuro puzzles is taken from the popular puzzle resource Conceptispuzzles.com.
8. One of the tasks of Martin Gardner
American mathematician Martin Gardner is the author of a wide variety of problems and puzzles. One of his most interesting works is calculating a number that takes the least number of steps to bring it down to one digit by multiplying the digits of that number. For example, for the number 77, four such steps are required: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "the number of fortitude."
The smallest number with a toughness number of one is 10, for a toughness number of 2 it will be 25, the smallest number with a toughness number 3 is 39, if the toughness number is 4, the smallest number for it will be 77. What is the smallest number with a toughness number 5 ?
9. The most interesting problem from the game of go
Go was invented in China over 2,500 years ago, making it one of the oldest games on Earth. Despite the fairly simple rules, it still attracts thousands of people with the ability to solve interesting strategic problems. The goal of the game is to fence off a larger territory with stones of your own color than the enemy. The situation pictured above is one of the most difficult in the history of go: the most experienced players spent more than 1,000 hours of playing time on its solution. How can black win this game?
10. Hardest Puzzle Fill-A-Pix
Fill-A-Pix was invented by the 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 ones 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.
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Intelligence is the most important thing that distinguishes people from other representatives of the animal world. Man used his mind to reach unprecedented heights in science and technology, but sometimes the mind games were not only purely practical and utilitarian in nature: this is how many different puzzles were born, for the solution of which one has to thoroughly "brainwash". You will find ten of them in this collection.One of the most popular crossword puzzles in the world is Sudoku, a Japanese number puzzle. Its principle is simple, so many amateurs try to create their own versions. In 2012, Finnish mathematician Arto Inkala announced that he had developed "the world's hardest Sudoku."
According to the British newspaper "The Telegraph", if the simplest of the common variants of Sudoku on the scale of difficulty is designated as "1", and the most difficult of the popular ones are rated at "5", then the variant proposed by the mathematician is "11".
2. The hardest 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 of them is which. The god of truth always speaks the truth, the god of lies deceives, and the god of chance can say both in no particular order. 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 to one god. The gods understand the questions, but they answer in their own language, which contains the words "da" and "ja", but it is not known which word means "yes" and which "no".
This logical problem, authored by the American philosopher and logician George Boulos, 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 most difficult sum-do-ku in the world 
One of the popular varieties of Sudoku is sum-do-ku, it is also called "killer sudoku". The only difference is that additional numbers are set in the sum-do-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 the published problems, one of which is the sum-do-ku, which is shown here.
4. The most difficult "Recognition problem" of Bongard 
This type of puzzle was invented by the outstanding Russian cyberneticist, 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."
Two of the most difficult examples of such problems are taken from Foundalis.com, to solve them you have to find a rule that matches six images on the left page, but six images on the right do not match.
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 only addition, and secondly, the field can be a square of any size (the number of cells is not limited), and in - thirdly, unlike Sudoku, hints from 1 to 9 in each 3 × 3 square do not have to be present here. Such problems were developed by the Japanese mathematics teacher Tetsuya Miyamoto.
Here you can try to figure out the most difficult tracing document, which was published on Calcudoku.org on April 2, 2013. Only 9.6% of regular visitors to the resource managed to solve it.
6. The hardest challenge from IBM
It is necessary to develop an information storage system that would encode 24 bits of information on eight disks of four bits each, provided that:
1. 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 (+, -, *, /,%, &, |, ~).
2. After failure of any two disks out of eight, you can recover these 24 bits of information.
On the IBM website there is a regular column “Think about it!”, In which interesting logical problems have been published since 1998. The task presented here is one of the most difficult.
7. Hardest Kakuro puzzle 
Kakuro puzzles combine elements of Sudoku, logic, crosswords and basic math. 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 inside one block must not be repeated. For horizontal blocks, the required amount is written directly to the left, and for vertical blocks, at the top.
This example of one of the hardest kakuro puzzles is taken from the popular puzzle resource Conceptispuzzles.com.
8. One of the tasks of Martin Gardner 
American mathematician Martin Gardner is the author of a wide variety of problems and puzzles. One of his most interesting works is calculating a number that takes the least number of steps to bring it down to one digit by multiplying the digits of that number. For example, for the number 77, four such steps are required: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "the number of fortitude."
The smallest number with a toughness number of one is 10, for a toughness number of 2 it will be 25, the smallest number with a toughness number 3 is 39, if the toughness number is 4, the smallest number for it will be 77. What is the smallest number with a toughness number 5 ?
9. The most interesting problem from the game of go 
Go was invented in China over 2,500 years ago, making it one of the oldest games on Earth. Despite the fairly simple rules, it still attracts thousands of people with the ability to solve interesting strategic problems. The goal of the game is to fence off a larger territory with stones of your own color than the enemy. The situation pictured above is one of the most difficult in the history of go: the most experienced players spent more than 1,000 hours of playing time on its solution. How can black win in this game?
10. Hardest Puzzle Fill-A-Pix 
Fill-A-Pix was invented by the 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 ones 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 you can see the Fill-A-Pix puzzle, prepared by the staff of the Conceptispuzzles.com resource, where you can find many variations of this game and other interesting tasks.
Intelligence is the most important thing that distinguishes people from other representatives of the animal world. Man used his mind to reach unprecedented heights in science and technology, but sometimes mind games were not only purely practical and utilitarian in nature: this is how many different puzzles, for the solution of which you have to thoroughly "brainwash". You will find ten of them in this collection.
1. World's Hardest Sudoku
One of the most popular crossword puzzles in the world is Sudoku, a Japanese number puzzle. Its principle is simple, so many amateurs try to create their own versions. In 2012, Finnish mathematician Arto Inkala announced that he had developed "the world's hardest Sudoku."
According to the British newspaper "The Telegraph", if the simplest of the common variants of Sudoku on the scale of difficulty is designated as "1", and the most difficult of the popular ones are rated at "5", then the variant proposed by the mathematician is "11".
2. The hardest 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 of them is which. The god of truth always speaks the truth, the god of lies deceives, and the god of chance can say both in no particular order. 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 to one god. The gods understand the questions, but they answer in their own language, which contains the words "da" and "ja", but it is not known which word means "yes" and which "no".
This logical problem, authored by the American philosopher and logician George Boulos, 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 most difficult sum-do-ku in the world
One of the popular varieties of Sudoku is sum-do-ku, it is also called "killer sudoku". The only difference is that additional numbers are set in the sum-do-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 the published problems, one of which is the sum-do-ku, which is shown here.
4. The most difficult "Recognition problem" of Bongard
This type of puzzle was invented by the outstanding Russian cyberneticist, 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."
Two of the most difficult examples of such problems are taken from Foundalis.com, to solve them you have to find a rule that matches six images on the left page, but six images on the right do not match.
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 only addition, and secondly, the field can be a square of any size (the number of cells is not limited), and in - thirdly, unlike Sudoku, hints from 1 to 9 in each 3 × 3 square do not have to be present here. Such problems were developed by the Japanese mathematics teacher Tetsuya Miyamoto.
Here you can try to figure out the most difficult tracing document, which was published on Calcudoku.org on April 2, 2013. Only 9.6% of regular visitors to the resource managed to solve it.
6. The hardest challenge from IBM
It is necessary to develop an information storage system that would encode 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 failure of any two disks out of eight, you can recover these 24 bits of information.
On the IBM website there is a regular column “Think about it!”, In which interesting logical problems have been published since 1998. The task presented here is one of the most difficult.
7. Hardest Kakuro puzzle
Kakuro puzzles combine elements of Sudoku, logic, crosswords and basic math. 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 inside one block must not be repeated. For horizontal blocks, the required amount is written directly to the left, and for vertical blocks, at the top.
This example of one of the hardest kakuro puzzles is taken from the popular puzzle resource Conceptispuzzles.com.
8. One of the tasks of Martin Gardner
American mathematician Martin Gardner is the author of a wide variety of problems and puzzles. One of his most interesting works is calculating a number that takes the least number of steps to bring it down to one digit by multiplying the digits of that number. For example, for the number 77, four such steps are required: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "the number of fortitude."
The smallest number with a toughness number of one is 10, for a toughness number of 2 it will be 25, the smallest number with a toughness number 3 is 39, if the toughness number is 4, the smallest number for it will be 77. What is the smallest number with a toughness number 5 ?
9. The most interesting problem from the game of go
Go was invented in China over 2,500 years ago, making it one of the oldest games on Earth. Despite the fairly simple rules, it still attracts thousands of people with the ability to solve interesting strategic problems. The goal of the game is to fence off a larger territory with stones of your own color than the enemy. The situation pictured above is one of the most difficult in the history of go: the most experienced players spent more than 1,000 hours of playing time on its solution. How can black win this game?
10. Hardest Puzzle Fill-A-Pix
Fill-A-Pix was invented by the 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 ones 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 you can see the Fill-A-Pix puzzle, prepared by the staff of the Conceptispuzzles.com resource, where you can find many variations of this game and other interesting tasks.
