What are interesting facts about Sudoku?

Sudoku is a number game in which missing numbers are to be filled into a 9 by 9 grid of squares which are subdivided into 3 by 3 boxes so that every row, every column, and every box contains the numbers 1 through 9.

Here are some interesting facts about Sudoku:

  1. You don’t need to be an expert to make a Sudoku puzzle. Anyone with basic logical reasoning can make a Sudoku puzzle within minutes.
  2. Yes, there is a minimum number of clues to be given for the Sudoku puzzle has one solution. The least number of clues of a given Sudoku with a unique solution is 17.
  3. There are 6670903752021072936960 Sudoku grids. However, the essentially different Sudoku grids are only 5,472,730,538.  Needlessly to say, you need a handful of lifetimes to solve all of them.
  4. Sudoku is a logic game and involves absolutely no math or language skills.
  5. Actually, Sudoku isn’t a Japanese game it all. It’s American invented. Howard Garns created it as Number Place in 1979 but died in 1989 before Japanese publisher Nikoli got a hold of it. The game didn’t really take off until 2004 though when Wayne Gould convinced The Times in London to publish it.
  6. When Sudoku became a world hit in 2005, it is estimated that it is the biggest phenomenon since the Rubik’s Cube in the 1980s.
  7. There is a worldwide Sudoku Championship every year since Mar 2006. The first World Sudoku Championship was held in LuccaItaly.
  8. Playing Sudoku regularly can have benefits, like boosting your concentration and focus, preventing or easing depression and possibly even preventing dementia and Alzheimer’s disease, according to some studies.
  9. Sudoku is good for anyone and any age and helps develop mental abilities as well as keeps them in good condition.
  10. Sudoku is considered highly addictive, but since there aren’t any harmful side effects (and in fact a list of great side effects), go right ahead and get addicted!

Some of the facts are from this article.

How Do I Measure the Difficulty Level of Sudoku Puzzles

To explain why some Sudoku puzzles are easier to solve while others are more challenging. Let us look at two Sudoku puzzles and judge which one is more difficult at the start of solving it.

For this Sudoku, if you write down their candidate values, and you can immediately solve 12 empty squares.

How Do I Measure Sudoku Difficulty Level - Factor 1: Success Rate
How Do I Measure Sudoku Difficulty Level – Factor 1: Success Rate

Let us take a look at another one. How many empty squares can be inferred immediately? (Answer: 0)

Measure Sudoku Difficulty Level - How Many Empty Squares can be inferred at this time
Measure Sudoku Difficulty Level – How Many Empty Squares can be inferred at this time?

You will have to use an advanced method to solve the second Sudoku, i.e., use advanced methods to refine the candidate numbers of each empty square.

Therefore, at least in the first step, the first Sudoku is easier than the second Sudoku.

Usually, an easy Sudoku can be solved by using OneChoice and Elimination.

  • OneChoice: An empty square has to be a certain number because all other numbers already appear in its row/column/box.
  • Elimination: An untaken number in a row/column/box must be in a certain empty square because all other empty squares can not be this number.

A medium Sudoku puzzle needs to be solved using logical reasoning, such as Interaction, Subset, X-Wing, XY-Wing, XYZ-Wing. These methods, instead of deciding which untaken must goes to an empty square in a row/column/box, or deciding which empty square in a row/column/box has to be a certain number, refines the candidate numbers of each empty square.

A hard Sudoku, you will have to use at least one guess (if a guess of a number in an empty square causes conflict, we can eliminate this number from this empty square’s candidate numbers. This is called ConflictElimination).

An evil Sudoku will generally involve either a significant number of simple guesses or some number of more complicated guesses (Exhaustive Search).

If you made a Sudoku puzzle, an easy way to rate a Sudoku puzzle based on the methods that a Sudoku lover have to use based on the assumption that an advanced method is only used when easier methods do not work. Usually, if an advanced method is used, the average effort for all Sudoku solver would be much higher because some of Sudoku solvers would be stuck because they do not know how to use this advanced method.

The best way is to let Sudoku lovers rate the difficulty level of a Sudoku puzzle. How do you rate this Sudoku puzzle?

Please help judge the difficulty level of this Sudoku
Please help judge the difficulty level of this Sudoku

Solve A Medium Sudoku – Part I

Whether you are traveling or recovering in a hospital, Sudoku is a perfect mental workout for you! It helps develop your logic thinking, patience, concentration to solve problems, and confidence.  In my earlier article “How to Design a Sudoku within minutes,” I talked about the idea of designing a Sudoku in the exact REVERSE WAY of solving a Sudoku. If you want to create a Sudoku, you must be able to solve a Sudoku! In this article, following earlier methods – OneChoice and Elimination, I am going to show you two advanced solving methods – Interaction and Subset that used in solving medium Sudoku puzzles.

Interaction

RowBox-Interaction/ColumnBox-Interaction: If a number in a row/column has to be in one box, this number cannot appear in other empty squares of that box.

BoxRow-Interaction/BoxColulmn-Interaction: If a number in a box has to be in one row/column, this number cannot appear in other empty squares of that row/column.

Interaction Example: In the second column, number 1 only appears in the fourth box so other empty squares in the fourth box cannot be number 1

Using Interaction to solve Sudoku puzzles
Solving Sudoku Method – Interaction

In the second column, number 1 only appears in the fourth box, therefore, either R5C2 or R6C2 will be number 1. If we look at the fourth box, because either R5C2 or R6C2 will be number 1, therefore, all other empty squares in the fourth box will not be number 1. That is, in the fourth box, neither R4C1 nor R5C3 will be number 1. Note: R5C2 is the square at the fifth row and the second column. The fourth box is the intersection of the fourth row to the sixth row and the first column to the third column.

Subset

If the union of candidate values of two/three/four empty squares in a row/column/box are a set of two/three/four different numbers, other empty squares in this row/column/box cannot be any of these two/three/four numbers.

Subset Example: In the third row, the union of candidate values of R3C6 and R3C8 is 3 and 5. Other empty squares in the third row (R3C1, R3C5, R3C7) cannot be 3 or 5.

Subset Example
Subset Example

In the third row, R3C6 and R3C8, their candidate values, combined together, are 3 and 5. Therefore, all other empty squares, including R3C1, R3C5, R3C7 in the third row, cannot be number 3 or 5.

Try today’s medium Sudoku?

Today’s Medium Sudoku 今日数独(难度:中等)

Medium Sudoku
Medium Sudoku on 08/17/2017

 

Solve An Easy Sudoku

Whether you are having a vacation or recovering from the hospital, Sudoku is a perfect number game for you! It develops your logical reasoning ability, patience, your concentration to solve problems, and helps you build confidence.

In my earlier blog “How to Design a Sudoku Within Minutes,” I talked about the idea of designing a Sudoku in the exact REVERSE WAY of solving a Sudoku. If you want to create a Sudoku, you must be able to solve a Sudoku! In this article, I am going to show you two basic methods to solve an easy Sudoku – OneChoice and Elimination.

OneChoice: An empty square can only be filled with a number because all other numbers are taken in its row, column, or box.

Use OneChoice method to infer the number for square R1C9

Using OneChoice to Solve Sudoku puzzle
Using OneChoice to Solve Sudoku puzzle

For the highlighted square, which number must it be? 1 is taken in the ninth column, 2 is taken in the first row, 3 is taken in the third 3×3 box, 4 and 5 are taken in the first row, 6 is taken in the ninth column, 7 and 8 are taken in the first row. Therefore, only number 9 is not taken. The empty square at R1C9 (first row, ninth column) must be filled with number 9.

Elimination: An untaken number in a row/column/box can only be filled in an empty square in that row/column/box because all other empty squares are ruled out.

Where do I put number 6 in the seventh box?  Elimination: In the 7th box, only R8C2 can be filled with number 6.

Solve Sudoku Puzzle Method - Elimination
Using Elimination to Solve Sudoku Puzzle

In the 7th box, number 6 is untaken. Where can we put it? The first column already contains number 6, therefore, R7C1, R8C1, R9C1 can not be filled with number 6. The seventh row already contains number 6, therefore, R7C2, R7C3 can not be filled with number 6. The third column already contains number 6, therefore R9C3 can not be filled with number 6. Therefore, in the seventh 3×3 box, number 6 can only be filled in R8C2.

How about practicing your skills of OneChoice and Elimination and solving today’s Sudoku from createclassicsudoku.com?

 

How Can I Solve a Sudoku Puzzle Fast?

You are given a Sudoku with pre-filled numbers in a nine by nine grid.

Medium Sudoku from https://www.createclassicsudoku.com
Medium Sudoku from https://www.createclassicsudoku.com

Your task is to fill all empty squares in this nine by nine grid so that each row/column/box contains nine numbers 1 through 9.

And you know the methods to solve a Sudoku puzzle, including OneChoice, Elimination, Interaction, Subset, X-Wing, XY-Wing, XYZ-Wing, and guessing. You are able to solve Sudoku puzzles. Now, you wonder, how can I solve a Sudoku puzzle fast? What are good practices solving Sudoku puzzles FAST?

If you are in this phase, congratulations! You are exploring the efficiency of solving Sudokus to be an expert Sudoku solver.

When you solve a Sudoku puzzle, you are constantly checking which number should an empty square be, and where an untaken number in a row/column/box goes to.  If this does not work, you write down all the candidate numbers of each empty square and try to refine them using solving methods. To be efficient, you will need to form a routine of solving Sudoku, a routine that is most suitable for you! This routine includes but not limited to

  • Form a routine how you scan the empty squares. Some people prefer checking the empty squares from the top to the bottom, then from the left to right; while others prefer checking empty square with most clues first. Choose the one you like the best.
  • Form a routine how you examine an untaken number in a row/column/box. Some people prefer checking an untaken number that appears the most in the nine by nine grid; while others prefer checking an untaken number exactly from 1 to 9. Choose the one that works the best for you.
  • Form a routine how you use the solving methods.  First, rank the solving methods. Some may think OneChoice is easier than Elimination. While others think Elimination is easier than OneChoice. You need to rank the solving methods based on your preferences.  After ranking the solving methods, you always use the easier solving methods first. An advanced method is used only when all easier methods do not work.
  • Be careful not making mistake. Double check. Every time you fill a number in an empty square, double check. This way you are less likely making mistake.

If you develop a routine that works the best for you, you will certainly solve Sudoku puzzles faster.  For me, I like using OneChoice and Elimination first because these two methods do not need me to write any candidate numbers for each empty square. Only when these two methods do not work, I will write down candidate values for the empty squares. Using this routine, I solve Sudoku puzzles pretty fast!

How do I solve a Sudoku puzzle?

Sudoku is a number game in which missing numbers are to be filled into a 9 by 9 grid of squares which are subdivided into 3 by 3 boxes so that every row, every column, and every box contains the numbers 1 through 9.

Easy Sudoku puzzle from https://www.createclassicsudoku.com
Easy Sudoku puzzle from https://www.createclassicsudoku.com

You are given a Sudoku puzzle, some of the squares are pre-filled with a number, and your task is to fill the remaining empty squares so that each row/column/box has nine different numbers 1 through 9.

How do I solve a Sudoku puzzle like this? Because this is a logical game, a lot of methods have been summarized to solve Sudoku puzzles, and more to come (you may be the one who will invent new solving methods). The most famous methods are OneChoice, Elimination, Interaction, Subset, X-Wing, XY-wing, XYZ-Wing, and guessing.

  • Here are examples of using OneChoice and Elimination. 
  • Here are examples of using Interaction and Subset. 

One book I like the most is Mensa Guide to Solving Sudoku by Peter Gordon. Almost all methods are summarized and plenty of exercises that will use certain methods are given.

What is a Sudoku puzzle?

Sudoku is a number game in which missing numbers are to be filled into a 9 by 9 grid of squares which are subdivided into 3 by 3 boxes so that every row, every column, and every box contains the numbers 1 through 9.

Sudoku puzzle from https://www.createclassicsudoku.com
Sudoku puzzle from https://www.createclassicsudoku.com

In other words, given a nine by nine grid with some squares are pre-filled with numbers, you need to fill in numbers to all empty squares so that every number 1 through 9 appears once and only once in each row/column/box.

A classic Sudoku has one and ONLY one solution, and two squares that are symmetrical around the center square are either both filled with numbers or both empty.

Sudoku is American invented. Howard Garns created it as Number Place in 1979 but died in 1989 before Japanese publisher Nikoli got a hold of it. Sudoku became mainstream in 1986 by the Japanese puzzle company Nikoli, under the name Sudoku, meaning “single number”. The game didn’t really take-off until 2004 though when Wayne Gould convinced The Times in London to publish it.

There are many online Sudoku websites offering free Sudoku puzzles, such as websudoku.com or New York Times Daily Sudoku.  There is a special online Sudoku website which, besides of billions of Sudoku puzzles, shows you how each of their Sudoku was made, and how each of Sudoku puzzle could be solved.

Reusing Existing Sudoku Puzzles (How Do I Make Millions of Sudoku Puzzles?)

Whether you are having a vacation or recovering from the hospital, Sudoku is a perfect number game for you! It develops your logical reasoning ability, patience, your concentration to solve problems, and helps you build confidence.

In my earlier article “How to Design a Sudoku Within Minutes,” I talked about the idea of designing a Sudoku in the exact REVERSE WAY of solving a Sudoku. After you had finished designing a Sudoku, or you saw a classic Sudoku puzzle in a newspaper or magazine, you can use it to design tens of thousands of new Sudokus. A classic Sudoku is a Sudoku that has one and only one solution, and two symmetrical squares (If you connect two squares, its center lies in the center of the Sudoku, they are symmetrical squares) are either both filled, or both not filled with numbers. For example, today’s medium Sudoku is a classic Sudoku.

Today’s Medium Sudoku 今日数独(难度:中等)

A Medium Sudoku Puzzle from https://www.createclassicsudoku.com
A Medium Sudoku Puzzle from https://www.createclassicsudoku.com

Whether you

  • Exchange the top bottom three rows and the bottom three rows;
  • Exchange the left three columns and the right three columns;
  • Exchange the fourth column and the sixth column;
  • Exchange the fourth row and the sixth row; or
  • Exchange any two numbers;

You will get a new Sudoku. The new Sudoku and the old Sudoku are intrinsically the same because they have the same constraints, and in the new Sudoku, two symmetrical squares (around the center of the Sudoku) are either both filled or not filled with numbers. You can print a new blank Sudoku, such as https://www.createclassicsudoku.com/blankgrid.jsp,  then use the above methods to get new Sudokus. Is the new Sudoku easier, as easy as, or more difficult to solve? You are welcome to discuss this with me. My email address is create.classic.sudoku@gmail.com. Below are several examples of new Sudokus based on today’s Sudoku.

Exchange the top three rows and the bottom three rows (A New Sudoku)

Exchange top 3 rows and bottom 3 rows to get a new Sudoku puzzle
Exchange top 3 rows and bottom 3 rows to get a new Sudoku puzzle

Exchange the fourth column and the sixth column (A New Sudoku)

Exchange the fourth column and the sixth column to get a new Sudoku puzzle
Exchange the fourth column and the sixth column to get a new Sudoku puzzle

Exchange digit 4 and digit 8 (A New Sudoku)

Exchange number 4 and number 8 to get a new Sudoku puzzle
Exchange number 4 and number 8 to get a new Sudoku puzzle

About the author: Yaling is a software programmer, Book author of Create Classic Sudoku (Available on Amazon.com), and founder of www.createclassicsudoku.com.

Design A Classic Sudoku Puzzle (How Can I Design A Sudoku Puzzle Within Minutes?)

Whether you are recovering in the hospital or you are traveling, designing a number puzzle game – Sudoku – would be a perfect brain workout for you! Grab a piece of paper, draw a nine by nine grid, and design a Sudoku puzzle in minutes!

But wait… How can I design a Sudoku puzzle in minutes, i.e., design a Sudoku puzzle with some squares that are pre-filled in a given nine by nine grid, and this Sudoku has one and exactly one solution?

All I can think of is a straightforward method as follows:

  • Start with a blank nine by nine grid.
  • Choose some squares that will be filled with numbers.
  • Fill numbers into the chosen squares carefully to make sure there is no violation of constraints. (You may need to try many times if you did not succeed at the first temptation).
  • Check this designed Sudoku to see whether it has one and at least one solution. If it is, then we made it; otherwise go back to Step 3 or Step 2.

Shortcoming:  The possibility that you made a Sudoku using this straightforward method is low (as low as the probability of winning a lottery). Even step 3 may include many tries. After you tried for ten times, you may want to give up.

To avoid the shortcoming, we can design a Sudoku in the exact REVERSE WAY of solving a Sudoku.

First, we get a nine by nine grid with every row, column, or 3×3 mini-box pre-filled with numbers 1-9.

Second, we remove digits from a pair of symmetrical squares (around the center square) if it is a safe removal. If there exists a path to infer these removed digits, we call it a safe removal. Repeat the second step no more digits can be safely removed from a pair of symmetrical squares.

For the first step, we may recycle a solved Sudoku (i.e., a fully filled Sudoku), or we can use a shortcut, which is extensively explained in the Create Classic Sudoku book available on Amazon.com. The shortcut uses group filling plus circular shift methods. For the second step, it is a gradual step by safely removing digits from the grid and guaranteeing it has one and exactly one solution.

A very easy Sudoku can be created using this innovative method in minutes.

Here is today’s medium Sudoku created using this method.  More Sudokus are available on www.createclassicsudoku.com.

A Medium Sudoku from https://www.createclassicsudoku.com
A Medium Sudoku from https://www.createclassicsudoku.com