Difficulty

 

 The calculation of the difficulty index, to determine Whether solved in first fixed procedure.

 If you can not be solved even using the procedures, put the number that can be placed in the empty squares, and repeat as to whether or not solvable in a fixed procedure again.

 Once empty trout filled all, all of the used procedure, was time to aggregate to the indexation it took to solve depending on the type of the procedure.

 

The number of problems using the analysis is 1,012 questions.

The breakdown is as follows.

Newspaper of the problem: 61 questions (1 commercial newspaper)

Commercially available this problem: 750 questions (commercially available book of 11)

Self-made problem: 201 questions

 

In all of the answer scene, we were counting how technique is what could be used.

The number of answer scene 246,772.

 

Answer time of the average of every answer scene is as follows for each technique.

Number of techniques, put in order answer the number is large.

(A: row direction, B: column direction, C: box direction)

      01A:    138

      01B:    191

      02 :    102

      03A:    533

      03B:    577

      03C:    556

      04A:  3,606

      04B:  3,712

      04C:  3,842

      05A:  3,724

      05B:  3,826

      06A:  6,373

      06B:  6,536

      07A:  4,015

      07B:  4,084

      07C:  4,368

      08 : 19,158

      09A:  2,621

      09B:  2,802

      09C:  2,697

      10A:  5,085

      10B:  5,310

      11A: 72,545

      11B: 71,345

      12A:  1,596

      12B:  1,626

      13A:  3,679

      13B:  3,866

      14A:  5,675

      14B:  6,061

      15A:  2,482

      15B:  2,684

      16A:  3,308

      16B:  3,441

      17A:  3,409

      17B:  3,627

      18A:  4,810

      18B:  5,374

      19 :  2,947

      20A:  6,591

      20B:  6,811

      21A:  5,632

      21B:  5,799

      21C:  6,545

      22A:     71

      22B:    148

      23 :  3,759

      24A: 77,341

      24B: 78,206

      25A:  8,435

      25B:  8,618

      26A:  5,469

      26B:  5,659

      26C:  5,371

      27A:  4,037

      27B:  4,097

      28 :  8,663

      29A:  3,663

      29B:  4,462

      30 :  4,379

 

The degree of difficulty of each problem, it was calculated as follows.

 1) every answer scene of the problem, I am looking for an answer was obtained technique

 2) I will add the answer time of the answer was obtained technique

 3) adding to Determine the value of total

 4) it will divide the sum of the values in 1000

 5) And the difficulty the results obtained

 

 However, in the process of solution, it was used a contradiction if not solved in the prepared techniques.

 Answer time when using the reductio ad absurdum was for the sake of convenience 1,000,000,000.

 Such difficulty of 900,309 problem is the problem of the scene that can not be solved in the prepared techniques occurs nine times.

 

Level of difficulty of each problem are as follows.

  Easy: difficulty 1-100

  Normal: difficulty 101-160

  Difficult: difficulty  161-1000

  Very difficult: the difficulty is 1001 or more

 

 Shows an example of the difficulty index.

 

   1) There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration

        Gary McGuire, Bastian Tugemann, Gilles Civario  August 31, 2013 

      http://www.math.ie/McGuire_V2.pdf 

          Figure 1: A 17-clue sudoku puzzle   difficulty:198

 

   2) WATANABE Hiroshi

      http://apollon.issp.u-tokyo.ac.jp/~watanabe/sample/sudoku/index.html

          Notice (Mar. 13):             difficulty:200,086

          Notice (Mar. 13) 9 PM:  difficulty:400,073

          Notice (Mar. 22):             difficulty:700,097

          Abstract:                            difficulty:           97

          Background (a):               difficulty:700,072

          Background (b):               difficulty:900,309

 

   3) The New Sudoku Players' Forum

      http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539.html

          The hardest sudokus (new thread)

          q1 Top 5         

          Rating:99529  difficulty:600,113

          Rating:99495  difficulty:402,416

          Rating:99486  difficulty:700,218

          Rating:99432  difficulty:800,102

          Rating:99420  difficulty:900,068