# Difficult puzzle

Intelligence - the most important of what distinguishes humans from other members of the animal world. The man used the mind to reach unprecedented heights in science and technology, but sometimes the mind games were not only purely practical and utilitarian in nature: so in the light of a host of different puzzles to solve which is necessary to thoroughly "poraskinut brains." Ten of them can be found in this collection.

### : 1. the world's hardest sudoku

One of the most popular varieties in the world is a crossword puzzle Sudoku - Japanese puzzle with numbers. Its principle is simple, so many fans are trying to create their own versions. In 2012, the Finnish mathematician Arto Incal said that developed "the most difficult sudoku in the world."

According to the British newspaper "The Telegraph", if the most simple of the most common variants of Sudoku on a scale of complexity designated as "1", and the most complex of the popular evaluate to "5", the proposed mathematician version draws on "11".

### 2. The most difficult logic puzzle

There are three gods, A, B, and the C, one of which the God of truth, another god of lies, and the third case of the god, with unclear who is who. God of truth, always speaks the truth, the god of lies cheating, as the case may God say something, and the other in random order. It is necessary to determine who is the one of the gods, by asking three questions that can be answered "yes" or "no", and each question is given only one god. The gods understand the question, but answer in his own language, in which there is the word "da" and "ja", but do not know what the word means "yes" and a "no." This logic problem authored by the American philosopher and logician George Boulos was first published in the Italian newspaper "la Repubblica" in 1992. In comments to the puzzle Boulos makes an important point: more than one question, you can ask God to each, but you can not ask more than three.

### 3. The most difficult in the world to the sum-ku

One of the most popular varieties of sudoku is a sum-up-a-boo, it is also called "killer sudoku". The only difference is that the sum-up-a-boo set additional number - the sum of the values in the groups of cells, with the numbers contained in the group, should not be repeated. The popular Calcudoku.org puzzles service can be tracked ranking published by the complexity of problems, one of them was the sum-up-ku, which is shown here.

### 4. The most difficult "problem recognition" Bongard

This type of puzzle invented outstanding Russian cybernetics, founder of the theory of pattern recognition Moiseevich Michael Bongard: in 1967, he first published one of them in his book, "The problem of recognition." The widespread popularity of "Bongard problems" found when the famous American physicist and computer scientist Douglas Hofstadter mentioned them in his work "Godel, Escher, Bach: this endless garland."

Two of the most sophisticated examples of such problems are taken from Foundalis.com, to address them you will have to find a rule that matches the six images on the left page, but that does not fit under the six images on the right side.

### 5. The most difficult puzzle Calculator dock

This type sudoku similar to the sum-to-ku, but, firstly, to calculate the cell using any arithmetic operation, not only addition, secondly, the field may be the square of any size (the number of cells is not limited to) and thirdly, unlike Sudoku, there need not be present tips from 1 to 9 in each square 3 × 3. Such problems developed Japanese math teacher Tetsuya Miyamoto.

Here you can try to deal with the most difficult-tracing the dock, which was published on April 2, 2013 Calcudoku.org-year. Only 9, 6% of the patrons of the resource managed to solve it.

### 6. The biggest challenge of the "IBM"

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

1. The eight 4-bit audio discs are combined 32-bit system, in which any function of 24 to 32 bits can be calculated is not more than five mathematical operations from the set {+, -, *, /,%, &, |, ~}.

2. After the failure of any two drives of eight, you can restore these 24 bits of information.

there is a regular column on the site "IBM" company "Think about it!", in which the curious logic puzzles published since 1998 year. task listed here - one of the toughest.

### 7. The hardest puzzle Kakuro

Puzzle Kakuro combines the elements of Sudoku, logic, crossword puzzles and basic mathematical operations. The aim is to fill the cells with numbers from one to nine, with the sum of numbers in each horizontal and vertical block must fit in the designated number, and the numbers within the same block must be unique. For horizontal blocks required amount is written immediately to the left, and for the vertical blocks - top.

This example is one of the biggest challenges Kakuro is taken from the popular resource devoted to puzzles Conceptispuzzles.com.

### 8. One of the aims of Martin Gardner

American mathematician Martin Gardner - author of a number of different tasks and puzzles. One of the most interesting of his works - the calculation of the number for which you will need the least amount of steps to reduce it to a single digit by multiplying the digits of that number. For example, for the number 77 will require four such steps: 77 - 49 - 36 - 18 - 8. The number of steps Gardner calls "number of resistance".

The smallest of the numbers to the number of resistance equal to one, - 10, for the number 2, this resistance is 25, the smallest number of stability with 3 - 39, if the number of resistance is 4, the smallest number for him to 77. Is the smallest number to the number of resistance 5 ?

### 9. The most interesting challenge of the game of

Go was invented in China more than 2, 5 thousand years ago, so this is one of the oldest games in the world. Despite the rather simple rules, it still attracts thousands of people to solve interesting strategic objectives. The goal - to enclose the stones of his color more territory than the opponent. The situation depicted above - one of the most difficult in the history of the first: the decision on its most experienced players have spent more than one thousand hours of game time. How this party can win black?

### 10. The difficult of puzzles Fill-A-Pix

Fill-A-Pix invented English mathematician Trevor Truran. This game is similar to the well-known "Minesweeper": the player must, guided solely by the logic to determine which cells need to be painted, and which will remain empty until the image is not formed. Since one cell to affect several key values, it takes some time to produce the final image.

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