What is Sudoku and why should you play it?
Sudoku is one of the most popular puzzle games in the world. It is a logic-based number-placement puzzle that challenges your brain and makes you think. In this article, you will learn about the history, the benefits, and the tips and tricks of Sudoku. You will also find some examples of Sudoku puzzles that you can try yourself.
The history of Sudoku
Sudoku has a long and fascinating history that spans centuries and continents. Here are some of the key events that shaped the evolution of Sudoku.
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How Sudoku evolved from Latin squares to a global phenomenon
The origin of Sudoku can be traced back to an 18th-century Swiss mathematician named Leonhard Euler. He invented a concept called "Latin squares", which are grids filled with symbols or letters such that each row and column contains each symbol exactly once. For example, here is a 4x4 Latin square:
A B C D B C D A C D A B D A B C
Euler's idea inspired many variations of number puzzles in the following centuries. One of them was published in a French newspaper in 1895, where the goal was to fill a 9x9 grid with numbers from 1 to 9 such that each row, column, and diagonal adds up to the same total. This puzzle was called "carré magique diabolique" or "diabolical magic square".
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Another variation was published in an American magazine called Dell Pencil Puzzles and Word Games in 1979. It was created by Howard Garns, a retired architect and freelance puzzle constructor. He called it "Number Place", and it was very similar to modern Sudoku. The puzzle consisted of a 9x9 grid with some numbers given, and the objective was to fill the empty cells with numbers from 1 to 9 such that each row, column, and 3x3 subgrid contains each number exactly once. Here is an example of a Number Place puzzle:
5 _ _ _ _ _ _ _ _ 6 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 2 8 _ _ _ _ _ 6 _ _ _ _ _ 5 9 1 7 4 6 2 _ _ _ _ _ 8 _ _ _ _ _ 4 5 _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7 _ _ _ _ _ _ _ 4 _
How Sudoku reached the Western world and became popular
The puzzle that Garns created did not gain much attention until it was introduced to Japan in 1984 by a puzzle company called Nikoli. They renamed it "Sudoku", which is short for "sūji wa dokushin ni kagiru" or "the digits are limited to one occurrence". They also made some changes to the rules, such as ensuring that each puzzle has only one solution and that each puzzle has a certain degree of symmetry.
Sudoku became very popular in Japan, where people enjoyed its simplicity and logic. It also suited the Japanese culture, where crossword puzzles are grid have three candidates that are not present in any other cells in that row, column, or subgrid. This means that those three candidates must go in those three cells, and therefore any other candidates in those three cells can be eliminated.
X-wing: This is when two rows (or columns) have two cells each that share the same candidate, and those cells form the corners of a rectangle. This means that the candidate must go in either the top or the bottom pair of cells, and therefore it can be eliminated from any other cells in the same columns (or rows).
Swordfish: This is an extension of the X-wing, where three rows (or columns) have three cells each that share the same candidate, and those cells form the corners of a larger rectangle. The same logic applies as in the X-wing.
Backtracking: This is a last resort technique that involves guessing a candidate for a cell and then checking if it leads to a contradiction or a solution. If it leads to a contradiction, then the candidate can be eliminated. If it leads to a solution, then the puzzle is solved. If neither happens, then another candidate has to be guessed and checked. This technique can be time-consuming and tedious, so it should be used sparingly.
By applying these advanced strategies and heuristics, you can solve even the most difficult Sudoku puzzles.
The examples of Sudoku puzzles
Now that you know the history, the benefits, and the tips and tricks of Sudoku, you may want to try some Sudoku puzzles yourself. Here are some of the ways you can find different levels of Sudoku puzzles online or offline.
How to find different levels of Sudoku puzzles online
One of the easiest ways to find Sudoku puzzles online is to use a search engine like Bing and type in "Sudoku puzzles" or "Sudoku games". You will get many results that offer free Sudoku puzzles that you can play on your browser or your mobile device. Some of the popular websites that offer Sudoku puzzles are:
: This website offers billions of Sudoku puzzles in four levels of difficulty: easy, medium, hard, and evil. You can also print out the puzzles or play them online with hints and timer.
: This website offers thousands of Sudoku puzzles in five levels of difficulty: easy, medium, hard, expert, and giant. You can also play them online with pencil marking, undo, redo, and check features.
: This website offers a new Sudoku puzzle every day in six levels of difficulty: very easy, easy, standard, hard, expert, and extreme. You can also play them online with pencil marking, hints, and timer.
These are just some of the examples of websites that offer Sudoku puzzles online. You can also find many other websites or apps that offer different variations of Sudoku puzzles, such as Killer Sudoku, Jigsaw Sudoku, Samurai Sudoku, and more.
How to print Sudoku puzzles for offline use
If you prefer to play Sudoku puzzles offline, you can print them out from some of the websites mentioned above or from other sources. For example, you can use , which offers hundreds of free printable Sudoku puzzles in PDF format. You can choose from different levels of difficulty and sizes of grids. You can also print out the solutions for each puzzle.
Another option is to use , which offers free printable Sudoku puzzles in various formats. You can choose from different levels of difficulty, sizes of grids, number of puzzles per page, and fonts. You can also print out blank grids or solutions for each puzzle.
These are just some of the examples of websites that offer printable Sudoku puzzles. You can also find many other websites or books that offer printable Sudoku puzzles for offline use.
How to solve some sample Sudoku puzzles step by step
To give you an idea of how to solve Sudoku puzzles using the tips and tricks mentioned above, here are some sample Sudoku puzzles with their solutions explained step by step.
The first sample puzzle is an easy one that can be solved by using only obvious clues and scanning techniques. Here is the puzzle:
_ _ 8 _ _ 6 _ _ _ _ 7 _ 8 _ _ 9 _ _ _ _ 6 7 _ 9 _ 8 _ ------+-------+------ _ 8 _ 6 _ 2 _ _ _ _ _ _ _ 4 _ 8 _ _ _ _ 4 _ 9 _ 1 _ 2 _ ------+-------+------ _ 1 _ 5 _ 7 6 _ _ _ _ 7 _ _ 8 2 _ _ _ _ _ _ _ 4 _ 9 _
Here is the solution with the steps explained:
Start by scanning the grid and looking for obvious clues. For example, in the top left subgrid, you can see that the number 1 can only go in the top right cell, because it is already present in the other rows and columns of that subgrid. Fill in the number 1 in that cell.
Repeat this process for other obvious clues. For example, in the top right subgrid, you can see that the number 4 can only go in the bottom left cell, because it is already present in the other rows and columns of that subgrid. Fill in the number 4 in that cell.
Continue scanning the grid and filling in obvious clues until you cannot find any more. For example, in the bottom right subgrid, you can see that the number 6 can only go in the top left cell, because it is already present in the other rows and columns of that subgrid. Fill in the number 6 in that cell.
Now, use pencil marking to write down the possible candidates for each empty cell. For example, in the top left cell of the top left subgrid, you can see that the possible candidates are 2, 3, or 5, because the other numbers are already present in that row, column, or subgrid. Write down those numbers in small font in that cell.
Repeat this process for other empty cells until you have pencil marked all of them. For example, in the bottom right cell of the bottom right subgrid, you can see that the possible candidates are 1 or 3, because the other numbers are already present in that row, column, or subgrid. Write down those numbers in small font in that cell.
Now, use scanning techniques to eliminate some of the candidates based on their presence in other cells. For example, in the top left subgrid, you can see that the number 2 is present in two cells: one with a pencil marked candidate of 2/3/5 and another with a pencil marked candidate of 2/5/9. This means that the number 2 must go in either of those two cells, and therefore it can be eliminated from any other cells in that subgrid. Remove the number 2 from any other cells in that subgrid.
Repeat this process for other candidates and subgrids until you cannot eliminate any more. For example, in the bottom right subgrid, you can see that the number 3 is present in two cells: one with a pencil marked candidate of 1/3 and another with a pencil marked candidate of 3/8. This means that the number 3 must go in either of those two cells, and therefore it can be eliminated from any other cells in that subgrid. Remove the number 3 from any other cells in that subgrid.
Continue scanning the grid and filling in obvious clues based on your pencil marks until you solve the puzzle. For example, in the top left subgrid, you can see that there is only one cell with a pencil marked candidate of 5: the one with a pencil marked candidate of 5/9. This means that the number 5 must go in that cell, and therefore the number 9 can be eliminated from that cell. Fill in the number 5 in that cell and remove the number 9 from that cell.
Here is the final solution of the puzzle:
2 3 8 4 1 6 5 7 9 5 7 4 8 2 3 9 6 1 1 9 6 7 5 9 4 8 3 ------+-------+------ 7 8 3 6 4 2 1 9 5 6 2 1 4 9 8 7 3 4 9 4 5 3 7 1 8 2 6 ------+-------+------ 3 1 2 5 8 7 6 4 _ 8 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
The second sample puzzle is a hard one that can be solved by using some of the advanced strategies and heuristics mentioned above. Here is the puzzle:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ------+-------+------ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _6 _ ------+-------+------ _ ___7 __8 _ _ __4 __1 _ _ __9 __2 _
Here is the solution with the steps explained:
Start by scanning the grid and looking for obvious clues. However, in this puzzle, there are no obvious clues, so you have to use pencil marking to write down the possible candidates for each empty cell.
Repeat this process for all empty cells until you have pencil marked all of them. For example, in the top left cell of the top left subgrid, you can see that the possible candidates are 1, 2, 3, 4, 5, 6, 7, 8, or 9, because none of the numbers are already present in that row, column, or subgrid. Write down those numbers in small font in that cell.
Now, use scanning techniques to eliminate some of the candidates based on their presence in other cells. For example, in the top left subgrid, you can see that the number 7 is present in two cells: one with a pencil marked candidate of 1/7/8 and another with a pencil marked candidate of 2/7/9. This means that the number 7 must go in either of those two cells, and therefore it can be eliminated from any other cells in that subgrid. Remove the number 7 from any other cells in that subgrid.
Repeat this process for other candidates and subgrids until you cannot eliminate any more. For example, in the bottom right subgrid, you can see that the number 5 is present in two cells: one with a pencil marked candidate of 3/5 and another with a pencil marked candidate of 4/5. This means that the number 5 must go in either of those two cells, and therefore it can be eliminated from any other cells in that subgrid. Remove the number 5 from any other cells in that subgrid.
Now, use some of the advanced strategies and heuristics to eliminate more candidates and find more clues. For example, in the top left subgrid, you can see that there is a hidden pair of 1 and 8 in two cells: one with a pencil marked candidate of 1/2/8 and another with a pencil marked candidate of 1/7/8. This means that those two cells must contain either a 1 or an 8, and therefore any other candidates in those two cells can be eliminated. Remove the numbers 2 and 7 from those two cells.
Repeat this process for other hidden pairs or other advanced strategies until you solve the puzzle. For example, in the bottom right subgrid, you can see that there is an X-wing of 3 in two rows: one with a pencil marked candidate of 3/5 and another with a pencil marked candidate of 3/9. This means that the number 3 must go in either the top or the bottom pair of cells, and therefore it can be eliminated from any other cells in the same columns. Remove the number 3 from any other cells in those columns.
Here is the final solution of the puzzle:
4 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ------+-------+------ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __6 _ ------+-------+------ _ ___7 __8 _ _ __4 __1 _ _ __9 __2 _
Conclusion
Sudoku is a fun and challenging puzzle game that can improve your concentration, logic, memory, and mood. It has a rich history that spans centuries and continents, and it has become a global phenomenon that millions of people enjoy. Sudoku puzzles come in different levels of difficulty and variations, and you can find them online or offline. By using some of the tips and tricks we have shared with you, you can solve Sudoku puzzles faster and easier. We hope you have learned something new about Sudoku and that you will try some Sudoku puzzles yourself.
FAQs
Here are some of the frequently asked questions about Sudoku:
Q: How many Sudoku puzzles are there?
A: There is no definitive answer to this question, as different sources may have different criteria for counting Sudoku puzzles. However, one estimate by mathematician Bertram Felgenhauer and computer scientist Frazer Jarvis is that there are about 6.67 x 10^21 (or 6.67 sextillion) valid Sudoku puzzles.
Q: How do I know if a Sudoku puzzle has only one solution?
A: There is no easy way to tell if a Sudoku puzzle has only one solution without actually solving it or using a computer program to check it. However, most reputable sources of Sudoku puzzles ensure that their puzzles have only one solution by using various methods such as testing, symmetry, or uniqueness.
Q: What is the hardest Sudoku puzzle ever?
A: There is no definitive answer to this question either, as different Sudoku puzzles may have different levels of difficulty depending on the solver's skill and preference. However, one candidate for the hardest Sudoku puzzle ever is called "AI Escargot", which was created by Finnish mathematician Arto Inkala in 2006. It has a rating of 11 stars out of 5, and it requires the use of very complex and obscure strategies to solve it.
Q: What is the world record for solving Sudoku?
A: According to the Guinness World Records, the fastest time to solve a Sudoku puzzle is 1 minute and 23.93 seconds, achieved by Jan Mrozowski from Poland at the World Sudoku Championship 2012 in Beijing, China.
Q: How can I improve my Sudoku skills?
A: The best way to improve your Sudoku skills is to practice regularly and challenge yourself with different levels and variations of Sudoku puzzles. You can also learn from other Sudoku solvers by watching their videos, reading their blogs, or joining their forums. You can also use some of the online tools and apps that can help you with solving Sudoku puzzles, such as solvers, generators, analyzers, and trainers.
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