The most difficult logic problem in the world. What is the most difficult puzzle in the world

21.09.2019

In this article we will look at the most interesting puzzles intended for children, but not every adult can master them. They managed to stupefy more than one Internet user and gained enormous popularity on the Internet, as did comic tests with answers - but how quickly can you cope with them? The correct answers are waiting for you at the end of the article!

Where does the bus go?

If we talk about the most popular children's tasks on the Internet, this is one of them. Here is a picture of a bus. Which way is he heading?

How many points are there?

More attentiveness tasks for the most eagle-eyed users: how many black dots do you see at the intersections of lines?

Which circle is bigger?

Now let's solve interesting graphic puzzles. Can you answer which of the yellow circles shown in the picture is larger?

Moving the matches

The following children's puzzles are also often given to first-graders to solve: they require you to move matches in a certain way to get a given figure.

Find the panda!

The Internet was also blown up by the following graphic puzzles by artists who placed an image of a panda in complex pictures and invited other users to find it. They hid the panda among a crowd of Star Wars stormtroopers, a metalhead gathering, and even tried to hide it among a myriad of massage tables. Check your attentiveness!

Japanese IQ test

But what kind of IQ test did the Japanese come up with? On the shore there is a man with two sons, a mother with two daughters and a policeman with a criminal. In front of them is a raft on which they need to get to the other side. Try to think about how they can be transported there, taking into account such interesting conditions:

Only two people can fit on the raft at a time, and it cannot float without people at all.
Children can only travel on the raft with an adult. But sons cannot remain alone with the girls’ mother, and daughters cannot remain alone with the boys’ father.
And the criminal cannot be left alone with others without the supervision of a police officer.

Found the answer? If not, watch this interesting test in the video:

Right answers

There can be two correct answers to this puzzle. The first is that the bus goes to the left, since on the other side, invisible to the viewer, there are doors through which passengers get inside. This answer is valid for our roads with right-hand traffic. But for countries where traffic is on the left, the correct answer is to the right.

The picture shows parking spaces, and a car occupies one of them. If you turn the picture over, you will realize that you originally saw the numbers upside down. Therefore, the number under the car is 87. No matter how much you try to calculate some clever polynomial here, such interesting puzzles are not designed for algebraic logic, but rather for ingenuity.

Missing value = 2. To solve such children's puzzles, you need to put yourself in the shoes of the children. Do kids know how to solve complex equations and count arithmetic progressions? But they notice that the values in the columns depend on the number of circles in each set of numbers. Let's take, for example, the row 6855: in the number 6 there is one circle, and in the number 8 there are two, so the output is 1+2 =3, that is, 6855=3. And in row 2581 only the number 8 has two circles, so the solution is 2.

There are 12 points in total in the figure. But our brain is designed in such a way that it does not allow us to see them all at the same time, so at a time we can only notice three or four black dots.

The mugs are exactly the same! Such simple puzzles are built on visual illusion. The blue circles on the left side of the picture are large and some distance from the yellow one. The circles on the right side are small and stand close to the yellow circle, which is why it seems to us that it is larger than the first one.

Here's how to solve interesting children's puzzles with matches:

Unmasking the panda:

There is a rich house and a poor one. They are burning. Which house will the police extinguish?

Police don't put out fires, firefighters put out fires

How can a person not sleep for 8 days?

Sleep at night

You enter a dark kitchen. It contains a candle, a kerosene lamp and a gas stove. What will you light first?

A girl is sitting, and you cannot sit in her place, even if she gets up and leaves. Where is she sitting?

She sits on your lap

You are standing in front of three switches. Behind an opaque wall are three light bulbs that are turned off. You need to manipulate the switches, go into the room and determine which light bulb each switch belongs to.

First you need to turn on two switches. After some time, turn off one of them. Enter the room. One light bulb will be hot from the switch on, the second will be warm from the switch off, the third will be cold from the untouched switch.

It is known that among the nine coins there is one counterfeit one, which weighs less than the rest of the coins. How can you identify a counterfeit coin in two weighings using a cup scale?

1st weighing: 3 and 3 coins. The counterfeit coin is in the pile that weighs less. If they are equal, then the fake is in the third pile. 2nd weighing: Any 2 coins from the pile with the lowest weight are compared. If they are equal, then the remaining coin is fake

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?

They were on different banks

Two fathers, two sons found three oranges and divided them. Everyone got a whole orange. How can this be?

The dog was tied to a ten-meter rope and walked 300 meters. How did she do it?

The rope was not tied to anything

How can a thrown egg fly three meters without breaking?

You need to throw the egg four meters, then the first three meters it will fly intact

The man was driving a large truck. The lights on the car were not turned on. There was no moon either. The woman began to cross the road in front of the car. How did the driver manage to see her?

It was a bright sunny day

If five cats catch five mice in five minutes, how long does it take one cat to catch one mouse?

Five minutes

Is it possible to light a match underwater?

It is possible if you pour water into some container, for example, into a glass, and hold the match below the glass

The boat rocks on the water. A ladder was thrown from it along the side. Before high tide, the water covered only the bottom step. How long will it take for the water to cover the 3rd step from the bottom if during high tide the water rises at 20 cm per hour and the distance between the steps is 30 cm?

Never, because the boat rises with the water

How to divide five apples between five girls so that each gets an apple and at the same time one of the apples remains in the basket?

Give one girl an apple along with a basket

One and a half pike perch costs one and a half rubles. How much do 13 pike perch cost?

Traders and potters. In one city all the people were traders or potters. Merchants always told lies, but potters always told the truth. When all the people gathered in the square, each of those gathered said to the others: “You are all traders!” How many potters were there in this city?

The potter was alone because:

If there were no potters, then the traders would have to tell the truth that all the other traders are traders, and this contradicts the conditions of the problem.
If there were more than one potter, then each potter would have to lie that the rest were traders.

There are two coins on the table; they add up to 3 rubles. One of them is not 1 ruble. What coins are these?

1 and 2 rubles

The satellite makes one revolution around the Earth in 1 hour 40 minutes, and the other in 100 minutes. How can it be?

100 minutes is 1 hour 40 minutes

As you know, all Russian female names end with either the letter “a” or the letter “ya”: Anna, Maria, Irina, Natalya, Olga, etc. However, there is only one female name that ends with a different letter. Name it.

What has no length, depth, width, height, but can be measured?

Time, temperature

If it rains at 12 o'clock at night, can we expect sunny weather 72 hours later?

No, because in 72 hours it will be night

Seven brothers have one sister. How many sisters are there in total?

One yacht goes from Nice to Sanremo, the other from Sanremo to Nice. They left the harbors at the same time. For the first hour, the yachts moved at the same speed (60 km/h), but then the first yacht increased its speed to 80 km/h. Which yacht will be closer to Nice when they meet?

At the moment of their meeting they will be at the same distance from Nice

A woman was walking towards Moscow, and three men met her. Everyone has a bag, in each bag there is a cat. How many creatures were heading to Moscow?

Only the woman went to Moscow, the rest went in the other direction

There were 10 birds sitting on a tree. A hunter came and shot one bird. How many birds are left on the tree?

Not a single one - the rest of the birds flew away

The train runs from east to west, and the wind blows from north to south. In which direction does the smoke fly from the chimney?

You are running a marathon and have passed the runner who was running second. What position do you take now?

Second. If you answered that you are now first, then this is incorrect: you overtook the second runner and took his place, so you are now in second position

You are running a marathon and have passed the last runner. What position do you take now?

If you answered that it was the penultimate one, you were wrong again :). Think about how you can overtake the last runner? If you are running after him, then he is not the last. The correct answer is - it is impossible, you cannot overtake the last runner

There were three cucumbers and four apples on the table. The child took one apple from the table. How much fruit is left on the table?

3 fruits, and cucumbers are vegetables

The product first rose in price by 10%, and then fell in price by 10%. What is its value now relative to its original value?

99%: after the price increase, 10% was added to 100% - it turned out to be 110%; 10% of 110% = 11%; then subtract 11% from 110% and get 99%

How many times does the number 4 appear in the integers from 1 to 50?

15 times: 4, 14, 24, 34, 40, 41, 42, 43, 44 - twice, 45, 46. 47, 48, 49

You have driven your car two-thirds of the way. At the beginning of the journey, the car's gas tank was full, but now it is one quarter full. Will there be enough gasoline until the end of the trip (at the same consumption)?

No, because 1/4< 1/3

Mary's father has 5 daughters: Chacha, Cheche, Chichi, Chocho. What is the name of the fifth daughter?

A deaf and mute man went into a stationery store to buy a pencil sharpener. He stuck his finger into his left ear and made a spinning motion with the fist of his other hand near his right ear. The seller immediately understood what was being asked of him. Then a blind man entered the same store. How did he explain to the salesman that he wanted to buy scissors?

I just said, he's blind, but not dumb

A rooster has flown to the border between Russia and China. I sat down exactly on the border, absolutely in the middle. Layed an egg. It fell exactly across: the border divides it in the middle. Which country does the egg belong to?

Roosters don't lay eggs!

One morning, a soldier who had previously been on night guard approached the centurion and said that that night he had seen in a dream how the barbarians would attack the fortress from the north that evening. The centurion did not really believe in this dream, but still took measures. That same evening, the barbarians actually attacked the fortress, but thanks to the measures taken, their attack was repulsed. After the battle, the centurion thanked the soldier for the warning and then ordered him to be taken into custody. Why?

Because he slept on duty

There are ten fingers on the hands. How many fingers are there on ten hands?

A plane with English tourists was flying from Holland to Spain. He crashed in France. Where should the surviving (wounded) tourists be buried?

The survivors do not need to be buried! :)

You were driving a bus with 42 passengers from Boston to Washington. At each of the six stops, 3 people got out of it, and at every second - four. What was the driver's name when the driver arrived in Washington 10 hours later?

How about you, because in the beginning it was said that You drove the bus

What can you find in minutes, seconds and days, but not in years, decades and centuries?

How many times can you subtract 3 from 25?

Once, because after the first subtraction the number "25" will change to "22"

Mrs. Taylor's entire bungalow is decorated in pink, with pink light fixtures, pink walls, pink carpets, and a pink ceiling. What color are the stairs in this bungalow?

There are no stairs in the bungalow

In the ancient castle where the prison was located, there were 4 round towers in which prisoners were imprisoned. One of the prisoners decided to escape. And then one fine day he hid in a corner, and when a guard came in, he stunned him with a blow to the head, and he ran away, changing into different clothes. Could this happen?

No, since the towers were round and there were no corners

The 12-story building has an elevator. Only 2 people live on the ground floor; from floor to floor the number of residents doubles. Which button in the elevator of this building is pressed most often?

Regardless of the distribution of residents by floor - button “1”

A pair of horses ran 20 kilometers. Question: How many kilometers did each horse run individually?

20 kilometers

What can stand and walk, hang and stand, walk and lie at the same time?

Is it possible to predict the score of a football match before it starts, and if so, how?

The score of any match before it starts is always 0:0

What can a person increase in diameter by 7 times in a few seconds?

Pupil. When transitioning from bright light to darkness, the diameter can change from 1.1 to 8 mm; everything else either hardly increases or increases in diameter by no more than 2-3 times

A seller at the market sells a hat that costs 10 rubles. A buyer comes up and wants to buy it, but he only has 25 rubles. The seller sends the boy away with these 25 rubles. change it to a neighbor. The boy comes running and gives 10 + 10 +5 rubles. The seller gives the hat and change 15 rubles, and 10 rubles. keeps it for himself. After some time, a neighbor comes and says that 25 rubles. fake, demands to give her money. The seller returns her money. How much money was the seller defrauded of?

The seller was deceived for a counterfeit 25 rubles.

How many animals did Moses take on his ark?

It was not Moses who took the animals into the ark, but Noah.

2 people entered the entrance at the same time. One has an apartment on the 3rd floor, the other on the 9th. How many times will the first person get there faster than the second? Note: They simultaneously pressed buttons on 2 elevators moving at the same speed.

The usual answer is 3 times. Correct answer: 4 times. Elevators usually go from the 1st floor. The first one will travel 3-1=2 floors, and the second 9-1=8 floors, i.e. 4 times more

This riddle is often offered to children. But sometimes adults can rack their brains for a long time to figure out how to solve such a problem, so you can organize a competition: invite everyone to try to solve the problem. Whoever guesses it, regardless of age, deserves a prize. Here's the task:

6589 = 4; 5893 = 3; 1236 = 1; 1234 = 0; 0000 = 4; 5794 = 1; 1111 = 0; 4444 = 0; 7268 = 3; 1679 = 2; 3697 = 2

2793 = 1; 4895 = 3

The main thing is to look at the problem like a child, then you will understand that the answer is 3 (three circles in the writing of numbers)

Two horsemen competed to see whose horse would reach the finish line last. However, things did not go well, both stood still. Then they turned to the sage for advice, and after that they both rode at full speed.

The sage advised the horsemen to exchange horses

One student tells another: “Yesterday our college basketball team won the basketball game with a score of 76:40. At the same time, not a single basketball player scored a single goal in this match.”

Women's teams played

A man walks into a store, buys sausage and asks to cut it, not across, but lengthwise. The saleswoman asks: “Are you a fireman?” - "Yes". How did she guess?

The man was in uniform

The lady did not have a driver's license with her. She did not stop at the railroad crossing, although the barrier was down, then, not paying attention to the “brick,” she moved along a one-way street against the traffic and stopped only after passing three blocks. All this happened in front of a traffic police officer, who for some reason did not consider it necessary to intervene.

The lady was walking

On one Odessa street there were three tailoring workshops. The first tailor advertised himself as follows: “The best workshop in Odessa!” The second is “The best workshop in the world!” The third “outdid” them both.

“The best workshop on this street!”

Two brothers were drinking at a bar. Suddenly, one of them began to argue with the bartender, and then pulled out a knife and, not paying attention to his brother’s attempts to stop him, hit the bartender. At his trial he was found guilty of murder. At the end of the trial, the judge said: “You have been found guilty of murder, but I have no choice but to let you go.” Why did the judge have to do this?

The culprit was one of the conjoined twins. The judge could not send a guilty person to prison without putting an innocent person there as well.

We were traveling in the same compartment: Baba Yaga, Zmey Gorynych, a stupid ensign and a smart ensign. There was a bottle of beer on the table. The train entered the tunnel and it became dark. When the train came out of the tunnel, the bottle was empty. Who drank the beer?

The stupid ensign drank the beer, since the other creatures are unreal and do not occur in life!)

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

The most interesting problem from the game Go

Go was invented in China more than 2.5 thousand years ago, making it one of the most ancient games on Earth. Despite the fairly simple rules, it still attracts thousands of people with the opportunity to solve interesting strategic problems. The goal of the game is to fence off a larger area than the enemy with stones of your own color. 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 game time solving it. How can black win in this game?

The most difficult sudoku in the world

One of the most popular types of 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 Incala claimed to have developed “the world’s hardest Sudoku.”

As the British newspaper “The Telegraph” reports, if the simplest of the common variants of Sudoku on the difficulty scale are designated as “1”, and the most complex of the popular ones are rated as “5”, then the version 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, also called “killer Sudoku”. The only difference is that sum-do-ku contains additional numbers - 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 "Problem of Recognition"

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 problem” gained wide popularity when the famous American physicist and computer scientist Douglas Hofstadter mentioned them in his work “Gödel, Escher, Bach: This Infinite 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, not just addition, secondly, the field can be a square of any size (the number of cells is not limited), and -third, unlike Sudoku, there does not have to be clues from 1 to 9 in each 3x3 square. Such problems were developed by Japanese mathematics teacher Tetsuya Miyamoto.

Kakuro's hardest 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 within the same 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 many different problems and puzzles. One of his most interesting works is calculating the number that will require the fewest steps to reduce it to a single digit by multiplying the digits of that number. For example, the number 77 will require four such steps: 77 - 49 - 36 - 18 - 8. Gardner calls the number of steps the “persistence number.” The smallest number with a toughness number of one is 10, for a toughness number of 2 it would be 25, the smallest number with a toughness number of 3 is 39, if the toughness number is 4 the smallest number for it would be 77. What is the smallest number with a toughness number of 5 ?

The Hardest Fill-A-Pix Puzzle

Let's now get acquainted with more serious puzzles that older children will be able to do and will delight any adult with their complexity.

Full list of puzzles you will learn about:

Part 1: Puzzles for children 3-7 years old and their parents (Duet puzzle, Day and Night, Camelot, Smart Car, New Construction of Olya and Kolya, Shy Rabbit, Trucks, Color Code, Mother Hens, Masha and the Bear: Playing Hide and Seek , ANGRY BIRDS at the top, Crossing for kids, Pathfinder Kolobok, Pirates Hide and Seek, Safari Hide and Seek, North Pole: Camouflage, Little Mermaids, Penguins on ice floes)
Part 2: Puzzles for children 5-10 years old and adults (Fidget Frogs, Anaconda, Monsters, Antivirus, Rush Hour, Safari in Africa, Bricks, Corners, Hide your tracks, Cube puzzle, Chocolate set, Operation Interception, Labyrinth for the smart adventurer, Balls: Flexible shapes, Super Office, Uncle's farm, Vikings, ANGRY BIRDS under the structure, Ant path)
Part 3. Complex puzzles for children 8-16 years old and adults - You are currently reading this review (Airport, Troy, Subway, Dangerous Crossing, Chess for One, Sliding Chips, Spy, Titanic, Turnstile, Cheese Mice, Crossroads, Cheese Mice, Interlock, Megapolis, Save the Hedgehogs)
Part 4: Compact puzzles for the road (Labyrinth, Tangos: Items, Tangos: Animals, Tangos: People, Underwater World, Business Bugs, Magic Forest, Noah's Ark, Cheese Loopholes, Masha and the Bear: Business Masha, IQ-Enigma, IQ- Twist, IQ-Rings, Super Cells, Gas Station, Orbo)
Part 5: Puzzles from Professor Puzzle (Da Vinci, Newton, Master of Dooms, Give It a Heat, Headscratcher, Headspinner, Stupor, Eggheads, Bamboozlers, Revolver)

Airport Puzzle

A plastic organizer houses the puzzle components, and the task booklet contains 30 patterns that players must assemble. Unfortunately, there is no storage bag, although it is not particularly needed - the puzzle needs a smooth surface, so you will most likely only play at home.

17 squares, 6 arcs and one intersection - on each element there are halves of cars of four colors.

Each car consists of a front and a rear part, and these parts are different. The photo shows that 4 types of cars hit the roads: sedan (yellow), coupe (red), SUV (blue) and pickup truck (green). The halves can only be connected using the above method.

The tasks include a diagram and the initial section of the route. Please note that all modules are numbered. This is done for the convenience of presenting solutions to the puzzle and for initial placement.

The player's goal is to complete the route drawn in the booklet. In this case, the parts of all the cars must match (where you saw the halves of the cars driving around). The solution to the first task is in front of you - judging by the movement of cars, we are definitely not in old England...

Subsequent tasks will not be so easy to solve - the difficulty lies in the fact that there are a lot of squares, but not every one of them will fit. Therefore, having collected almost the entire route, you can... return to the starting point, since you placed the segment you need incorrectly in another place. An interesting and challenging puzzle.

Interlock Puzzle

Inside the box there are: a playing field, 5 badger faces, a mother hedgehog, a monolithic "U" shaped figure of 10 balls, a bag for storing components and a booklet with tasks. I note that the puzzle is very beautifully designed for young children.

The mother hedgehog figurine is intended solely to decorate the playing field and create an atmosphere. The first puzzle in which one of the elements serves as a beautiful accessory and does not participate in the game.

The field consists of spherical holes with square holes into which badger head pins are inserted. Everything in the game is thought out - the square holes do not allow the badgers to turn around their own axis, and everything on the field looks beautiful and symmetrical.

The task requires you to place badgers in the holes and place a block with hedgehogs in a certain place on the field. The player's task is to roll over the hedgehogs, approach the exit, bypassing the ill-mannered badgers, and jump over the fence.

The balls in the block perfectly match the recesses, so the hedgehogs can be fixed in a vertical position without any problems. Remember that you only need to move a piece by rolling it across the field - you can’t lift hedgehogs, they are afraid of heights!

There is only one way to move a block out of the field - by falling over the side. This requirement complicates the task: it is not enough to reach the saving slot, you need to “roll up” to it with the necessary side.

The task is completed - the entire family of hedgehogs goes home, and the ill-mannered badgers are left on the field with nothing. The first task is introductory, solved in 3 steps and teaches the child the principles of moving a block across the field.

The further you go, the more difficult it will be to get the hedgehogs out of the maze, but nothing is impossible for the young rescuer! You can easily estimate the difficulty level of the puzzle from the above photo of the 50th task. Decided? In this case, you can entrust the rescue of a prickly family to a child from six years old - in a difficult situation you will always come to the rescue. If not, then wait a year and sit down to decide together - the rescue operation will give you many pleasant moments.

I hope I managed to interest you in the magical and interesting world of puzzles. Because if you are still not familiar with him, then it’s time to correct this annoying mistake - do not deprive your children and yourself of pleasure and development opportunities.

I invite you to read Part 4 of the Great Review of Puzzles - Compact puzzles for the road »

Intelligence is the most important thing that distinguishes people from other representatives of the animal world. Man used his mind to achieve unprecedented heights in science and technology, but sometimes the games of the mind were not only of a purely practical and utilitarian nature: this is how many various puzzles, for the solution of which you have to thoroughly “think about it.” You will find ten of them in this collection.

1. The most difficult Sudoku in the world

2. The most difficult logic puzzle

There are three gods, A, B, and C, one of which is the god of truth, another the god of lies, and the third 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 in any order. It is necessary to determine who each of the gods is by asking three yes or no questions, each question being asked of only one god. The gods understand the questions, but 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 his comments to the riddle, Boulos makes an important point: 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

4. Bongard's most difficult "Problem of Recognition"

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

5. The most difficult tracing paper puzzle

Here you can try to figure out the most difficult calcu-doku, 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 most difficult task 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 with no more than five mathematical operations from the set (+, -, *, /, %, &, |, ~).
After the failure of any two disks out of eight, these 24 bits of information can be restored.

On the IBM website there is a regular column “Think About This!”, in which interesting logical problems have been published since 1998. The task given here is one of the most difficult.

7. Kakuro's hardest puzzle

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

8. One of Martin Gardner's problems

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

9. The most interesting problem from the game Go

10. 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 “Mineweeper”: 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 obtain the final image.

Above you can see the Fill-A-Pix puzzle, prepared by the staff of Conceptispuzzles.com, where you can find many variations of this game and other interesting problems.