Sudoku and Solver         

                                                                                                                                            date:2020.10.24 ver:1d


Advanced Sudoku and Solver


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Introduction

 This website is for the elderly and young men and women of all types, from beginners to advanced class, to enjoy  Sudoku  using Sudoku Solver which was developed by author of this website and can solve "The World's Hardest Sudoku".  It is a  gentle commentary, so anyone can understand the essence of the Sudoku.  The rules of the Sudoku are easy, but  there is a deep puzzle with fans all over the world.  Come on, let's all enjoy the brain training workout!
 
                       LET'S  ENJOY SUDOKU !          

 According to Dr. Arto Inkala, Finland, who developed The World's Hardest Sudoku, “To solve Sudoku, there is no need to  be able to add.  Logical thinking, attention, and perseverance are needed”. The World's Hardest Sudoku sample and  solution  are as follows.
                                 
                     

1. What is the Sudoku?
 It is a puzzle that arranges the numbers from 1 to 9 on the board of 9X9.  The rules are quite simple, only that the  numbers do not overlap in the vertical, horizontal or 3X3 area.

☆ Rule 1: Each column must have the numbers 1-9
☆ Rule 2: Each row must have the numbers 1-9
☆ Rule 3: Each 3X3 block must have the numbers 1-9
 
Howard Garns of the United States in 1979 made this puzzle a "Number Place", but did not hit too much.  The name  Sudoku was born in 1984 from Nikoli's "The numbers are limited to single".  New Zealander Wayne Gould has developed a  program to create  Sudoku, which has been well received by The Times in the UK in 2004.  After that, it became popular  under the name of "Sudoku" or "Number Place" in the wave of internationalization.  Sudoku is a puzzle for brain training,  which anyone can enjoy regardless of language.
Note: The name "Sudoku" is a registered trademark of NIKOLI co.,ltd in Japan.  Outside of the company, the name "Number Place" is used.

2. Display method and coordinates
 In this website, for convenience, vertical rows (rows), horizontal columns (columns), 3X3 cells are called areas (also  called  blocks), and squares are called cells.
                        ← Area
                 ↑ cell
The coordinates are displayed in the area (row, column), so the coordinates of the cell★ become H (5i).

Moreover, in this website, each technique is displayed as follows for convenience.
B           technique 1    (Fill in the sideways)
↑                ↑                ↑
Class     Technique #    (Technique Name)

3. How to solve the Sudoku
 There are two ways to solve a human being and a computer(Sudoku Solver) in the same  way.
□ Human being
A: Logical / Rationale
 It is the main stream of how to solve Sudoku, a royal road.  We will fill in the cells one by one in Logical.  In this website,  three classes are defined as follows,
  *Beginner: required simple Sudoku rules
  *Intermediate: required a close scrutiny of numbers
  *Advanced: required advanced techniques for difficult questions and super challenges

B: Hypothesis  method
 If it can not be solved logically, We will solve it assuming a certain number of cells (IF ...).  If a contradiction occurs, the  assumption is incorrect and we will solve it with other possible numbers.  If you use the hypothesis method, it will take  time, but you can always solve the sample.  This work is "manual labor" and not "brain labor".  As a rule, this method is  not always used as a treasurer of the House when solving super puzzles in the last and last part of the "forbidden hand".

□ Sudoku Solver
A: Logical / Rationale
 Sudoku Solver is poor at intermediate class and higher techniques.  Even with techniques that humans can understand  relatively easily, it is very difficult to translate the algorithm into software.  
B: Hypothesis  method
 The computer is good at the hypothetical method.  In this Sudoku Solver, trial and error are implemented by temporarily  placing it in three steps.
  *Step1: Logical calculation by adding one possible two-digit number, if it is not possible
  *Step2: In addition to step1, logical calculation by adding 2 possible 2 numbers, if  not  
  *Step3: In addition to step 2, perform logical calculations by adding one possible two-digit  number.
In the final step3, 1 + 2 + 1 = 4 numbers are added to perform logical calculations.
Now the world's hardest Sudoku can finally be analyzed.  

The Sudoku samples can be analyzed in 4 levels by Sudoku Solver in this web site, which are beginner, intermediate,  advanced and super.

4. Sudoku and newspaper / monthly magazine in Japan
   Sudoku is a puzzle loved by everyone, so it is also published in the leading daily  newspaper in Japan.  
 The A newspaper is published Sudoku column every Saturday.  The difficulty level is indicated by the number of ★, and  the basic class of this website in ★★★, the intermediate class in ★★★★, and the advanced class in ★★★★★.  
 The N newspaper is also published every Saturday, and the skill of the reader is displayed here in the required time.  It is  possible to answer 100% by the technique of this intermediate class to solve this website.  
 In the B-monthly magazine, a beginner class problem has been published with the name Sudoku as "Essential and  Thinking Puzzle".  10,000 yen will be sent to 10 people by lottery for the correct person.  It is a simple matter, so the  probability of winning will be similar to a lottery.

5. Sudoku common sense quiz
  Then, please try to the Sudoku common sense quiz.
If the following question is correct, put ○ in ( ), and if incorrect, put X in ( ) and correct it.  You don't have to be so  serious because it's a play.

( ) Q1: This puzzle has a Japanese name for Sudoku and an English name for Number  place.

( ) Q2: Sudoku is not a puzzle except for numbers.

( ) Q3: It is better to have a mathematical background to solve Sudoku.

( ) Q4: The simpler Sudoku, the larger the number of given cells and the fewer empty cells.

( ) Q5: There are never more than one solution in Sudoku.

( ) Q6: A minimum of 15 given cells are required for Sudoku to become a sample.

( ) Q7: The most difficult sample that cannot be answered using the hypothesis method (temporary placement).

( ) Q8: A minimum of one day is required to solve the “The World Hardest Sudoku” problem  logically.

( ) Q9: The famous technique called XY wing can be applied even if the number is 3 digits and the condition is satisfied.

( ) Q10: Not all samples can be analyzed even with excellent Sudoku solver.
                                           

Please see here for the answer ↓.
                     Sudoku common sense quiz(answer)

*Introduction to the author
When author was 70 years old, he started  Sudoku as part of his brain training, and he is still practicing "Sudoku Studies".  he learned VBA(Visual Basic for Applications) to develop the Sudoku analysis software, and completed  "Sudoku Solver"  which is used in this website.

* Note *
This website is published as comments of a personal hobby.  As it does not guarantee the accuracy, feasibility, uniqueness etc. of the contents,  please refer to each person's responsibility.  This website has no responsibility for the result.  In addition, the contents of this publication and the  modification and unauthorized conversion etc. of the program are strictly prohibited.

"Sudoku" is the registered trademark of NIKOLI co.,ltd.
"VBA","OFFICE/Excel" are the registered trademark  or trademark of Microsoft Corporation(US).

                                 ****** All contents may be subject to change without  notice *******