Analysis of zz-www.sudokuwiki.org-0114-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=114

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=114

position: ..1.3.....4.1.6.9.8.....3..2....5.......9..1...73....2..3.....4.6.7.1.5.....5.8.. initial

Autosolve

position: ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 2,5 => CTR => C3: 6,9
* DIS # E6: 4,8 => CTR => E6: 1,6
* DIS # H6: 6 => CTR => H6: 4,8
* PRF # C8: 4,9 => SOL
* DIS # A9: 4,9 => CTR => A9: 1,7
* DIS # C8: 2,9 => CTR => C8: 4,8
* CNT   6 HDP CHAINS /  25 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # C3: 2,5 => CTR => C3: 6,9
* DIS C3: 6,9 # E6: 4,8 => CTR => E6: 1,6
* DIS C3: 6,9 + E6: 1,6 # H6: 6 => CTR => H6: 4,8
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 # E4: 4,8 => CTR => E4: 1,6,7
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 # D5: 4,8 => CTR => D5: 2,6
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 # F5: 4,8 => CTR => F5: 2,7
* PRF C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # C8: 4,9 => SOL
* STA C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 + C8: 4,9
* CNT   7 HDP CHAINS /  25 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

..1.3.....4.1.6.9.8.....3..2....5.......9..1...73....2..3.....4.6.7.1.5.....5.8.. initial
..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538.. autosolve
721938645345126798896547321219875436438692517657314982583269174964781253172453869 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
C2: 2,5
F6: 4,8
A8: 4,9
G8: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E6: 1.. / E4 = 1  =>  6 pairs (_) / E6 = 1  =>  4 pairs (_)
A9,B9: 1.. / A9 = 1  =>  4 pairs (_) / B9 = 1  =>  7 pairs (_)
B4,E4: 1.. / B4 = 1  =>  4 pairs (_) / E4 = 1  =>  6 pairs (_)
A6,A9: 1.. / A6 = 1  =>  7 pairs (_) / A9 = 1  =>  4 pairs (_)
D5,F5: 2.. / D5 = 2  =>  4 pairs (_) / F5 = 2  =>  9 pairs (_)
E8,D9: 4.. / E8 = 4  =>  0 pairs (X) / D9 = 4  =>  9 pairs (_)
D1,D3: 5.. / D1 = 5  => 10 pairs (_) / D3 = 5  =>  4 pairs (_)
A7,B7: 5.. / A7 = 5  =>  5 pairs (_) / B7 = 5  =>  7 pairs (_)
A1,C3: 6.. / A1 = 6  =>  0 pairs (X) / C3 = 6  =>  4 pairs (_)
C3,H3: 6.. / C3 = 6  =>  4 pairs (_) / H3 = 6  =>  0 pairs (X)
E4,F5: 7.. / E4 = 7  =>  8 pairs (_) / F5 = 7  =>  4 pairs (_)
B7,C8: 8.. / B7 = 8  => 18 pairs (_) / C8 = 8  =>  5 pairs (_)
E2,I2: 8.. / E2 = 8  =>  8 pairs (_) / I2 = 8  =>  6 pairs (_)
C8,E8: 8.. / C8 = 8  =>  5 pairs (_) / E8 = 8  => 18 pairs (_)
H1,H6: 8.. / H1 = 8  => 10 pairs (_) / H6 = 8  =>  5 pairs (_)
G8,I9: 9.. / G8 = 9  => 11 pairs (_) / I9 = 9  => 12 pairs (_)
I4,I9: 9.. / I4 = 9  => 11 pairs (_) / I9 = 9  => 12 pairs (_)
* DURATION: 0:00:19.195270  START: 05:32:51.094453  END: 05:33:10.289723 2017-05-01
* CP COUNT: (17)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C2,F6,G8)
* ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538..
* PAIR C2: 2,5 BLK 1
B1: 2,5,7,9                              # reduction candidate for 2,5
B1: 2,5                                  #  7 pairs
B3: 2,5,7,9                              # reduction candidate for 2,5
B3: 2,5                                  #  7 pairs
C3: 2,5,6,9                              # reduction candidate for 2,5
C3: 2,5 => CTR
* 6.1.3....34.176298872...3612....5.3953..9..1.9.736.5.2753689124468721953129453876
C3: 6,9                                  #  5 pairs
* PAIR C2: 2,5 ROW 2
G2: 2,5,7                                # reduction candidate for 2,5
G2: 7                                    #  7 pairs
G2: 2,5                                  #  7 pairs
* PAIR F6: 4,8 BLK 5
D4: 4,8,6                                # reduction candidate for 4,8
D4: 4,8                                  #  8 pairs
E4: 4,8,1,6,7                            # reduction candidate for 4,8
E4: 4,8                                  #  8 pairs
D5: 4,8,2,6                              # reduction candidate for 4,8
D5: 4,8                                  # 12 pairs
F5: 4,8,2,7                              # reduction candidate for 4,8
F5: 4,8                                  # 14 pairs
E6: 4,8,1,6                              # reduction candidate for 4,8
E6: 4,8 => CTR
* ..1.3468.34.1862978.6.7234128.61573963.297418..7348562..38691.4468721953...4538.6
E6: 1,6                                  #  5 pairs
* PAIR F6: 4,8 ROW 6
H6: 4,8,6                                # reduction candidate for 4,8
H6: 6 => CTR
* ..1.3.68.34.1862978.6...3412....5.3963..9..18..73...62..3...1.4.68721953....538.6
H6: 4,8                                  #  6 pairs
* PAIR F6: 4,8 COL F
F1: 4,8,2,7,9                            # reduction candidate for 4,8
F1: 4,8                                  #  7 pairs
F1: 2,7,9                                #  4 pairs
* PAIR A8: 4,9 BLK 7
C8: 4,9,2,8                              # reduction candidate for 4,9
C8: 4,9 => SOLVED
* 721938645345126798896547321219875436438692517657314982583269174964781253172453869
C8: 2,8                                  #  5 pairs
A9: 4,9,1,7                              # reduction candidate for 4,9
A9: 4,9 => CTR
* ..193..853451862978..57.3.1284615739.36297418197348562..38.9124.68721953912453876
A9: 1,7                                  #  5 pairs
C9: 4,9,2                                # reduction candidate for 4,9
C9: 4,9                                  #  8 pairs
* PAIR A8: 4,9 COL A
A6: 4,9,1,5,6                            # reduction candidate for 4,9
A6: 4,9                                  #  7 pairs
A6: 1,5,6                                #  4 pairs
* PAIR G8: 2,9 ROW 8
C8: 2,9,4,8                              # reduction candidate for 2,9
C8: 2,9 => CTR
* .21.3..4.3451267988.654.3212...75.3663..9..17.573.4.82583...174469781253..2453869
C8: 4,8                                  #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0114-base-pr-000.dot
* REASONING
* DIS # C3: 2,5 => CTR => C3: 6,9
* DIS # E6: 4,8 => CTR => E6: 1,6
* DIS # H6: 6 => CTR => H6: 4,8
* PRF # C8: 4,9 => SOL
* DIS # A9: 4,9 => CTR => A9: 1,7
* DIS # C8: 2,9 => CTR => C8: 4,8
* CNT   6 HDP CHAINS /  25 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C2,F6,G8)
* ..1.3....34.1.6.9.8.....3.12....5.3..3..9..1...73....2..3...1.4.6.7.1.53....538..
* PAIR C2: 2,5 BLK 1
B1: 2,5,7,9                              # reduction candidate for 2,5
B1: 2,5                                  #  7 pairs
B3: 2,5,7,9                              # reduction candidate for 2,5
B3: 2,5                                  #  7 pairs
C3: 2,5,6,9                              # reduction candidate for 2,5
C3: 2,5 => CTR
* 6.1.3....34.176298872...3612....5.3953..9..1.9.736.5.2753689124468721953129453876
* PAIR C2: 2,5 ROW 2
G2: 2,5,7                                # reduction candidate for 2,5
G2: 7                                    #  8 pairs
G2: 2,5                                  #  8 pairs
* PAIR RESTART
* PAIR C2: 2,5 BLK 1
B1: 2,5,7,9                              # reduction candidate for 2,5
B1: 2,5                                  #  7 pairs
B3: 2,5,7,9                              # reduction candidate for 2,5
B3: 2,5                                  #  7 pairs
* PAIR C2: 2,5 ROW 2
G2: 2,5,7                                # reduction candidate for 2,5
G2: 7                                    #  8 pairs
G2: 2,5                                  #  8 pairs
* PAIR F6: 4,8 BLK 5
D4: 4,8,6                                # reduction candidate for 4,8
D4: 4,8                                  #  9 pairs
E4: 4,8,1,6,7                            # reduction candidate for 4,8
E4: 4,8                                  #  9 pairs
D5: 4,8,2,6                              # reduction candidate for 4,8
D5: 4,8                                  # 13 pairs
F5: 4,8,2,7                              # reduction candidate for 4,8
F5: 4,8                                  # 15 pairs
E6: 4,8,1,6                              # reduction candidate for 4,8
E6: 4,8 => CTR
* ..1.3468.34.1862978.6.7234128.61573963.297418..7348562..38691.4468721953...4538.6
* PAIR F6: 4,8 ROW 6
H6: 4,8,6                                # reduction candidate for 4,8
H6: 6 => CTR
* ..1.3.68.34.1862978.6...3412....5.3963..9..18..731..62..3...1.4.687219531...538.6
* PAIR F6: 4,8 COL F
F1: 4,8,2,7,9                            # reduction candidate for 4,8
F1: 4,8                                  # 10 pairs
F1: 2,7,9                                #  7 pairs
* PAIR RESTART
* PAIR F6: 4,8 BLK 5
D4: 4,8,6                                # reduction candidate for 4,8
D4: 4,8                                  # 10 pairs
E4: 4,8,1,6,7                            # reduction candidate for 4,8
E4: 4,8 => CTR
* ..1.3....34.1.6.988.....3.121..45.3..3.297.1...7318..2.83.6.1.4.6.781.531..4538..
D5: 4,8,2,6                              # reduction candidate for 4,8
D5: 4,8 => CTR
* ..1.3....34.126.988...473.1218675439.3.892.1...7314.82583269174.6.781953179453826
F5: 4,8,2,7                              # reduction candidate for 4,8
F5: 4,8 => CTR
* 7.183....34.126.988.6547321218675439.3.298.17..7314.82583962174.6.781.5317.4538..
* RESTART
* PAIR F6: 4,8 COL F
F1: 4,8,2,7,9                            # reduction candidate for 4,8
F1: 4,8                                  # 12 pairs
F1: 2,7,9                                # 10 pairs
* PAIR A8: 4,9 BLK 7
C8: 4,9,2,8                              # reduction candidate for 4,9
C8: 4,9 => SOLVED
* 721938645345126798896547321219875436438692517657314982583269174964781253172453869
* DURATION: 0:00:18.847842  START: 05:33:26.956401  END: 05:33:45.804243 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0114-base-pr-001.dot
* REASONING
* DIS # C3: 2,5 => CTR => C3: 6,9
* DIS C3: 6,9 # E6: 4,8 => CTR => E6: 1,6
* DIS C3: 6,9 + E6: 1,6 # H6: 6 => CTR => H6: 4,8
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 # E4: 4,8 => CTR => E4: 1,6,7
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 # D5: 4,8 => CTR => D5: 2,6
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 # F5: 4,8 => CTR => F5: 2,7
* PRF C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # C8: 4,9 => SOL
* STA C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 + C8: 4,9
* CNT   7 HDP CHAINS /  25 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=114

Solution

position: 721938645345126798896547321219875436438692517657314982583269174964781253172453869 solved
Solution

See section Pair Reduction for the HDP chains leading to this result.

Appendix: Full HDP Chains

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # B3: 2,5 => UNS
* DIS # C3: 2,5 => CTR => C3: 6,9
* INC # C3: 6,9 => UNS
* INC # G2: 2,5 => UNS
* INC # G2: 7 => UNS
* INC # D4: 4,8 => UNS
* INC # E4: 4,8 => UNS
* INC # D5: 4,8 => UNS
* INC # F5: 4,8 => UNS
* DIS # E6: 4,8 => CTR => E6: 1,6
* INC # E6: 1,6 => UNS
* INC # H6: 4,8 => UNS
* DIS # H6: 6 => CTR => H6: 4,8
* INC # F1: 4,8 => UNS
* INC # F1: 2,7,9 => UNS
* PRF # C8: 4,9 => SOL
* INC # C8: 2,8 => UNS
* DIS # A9: 4,9 => CTR => A9: 1,7
* INC # A9: 1,7 => UNS
* INC # C9: 4,9 => UNS
* INC # A6: 4,9 => UNS
* INC # A6: 1,5,6 => UNS
* DIS # C8: 2,9 => CTR => C8: 4,8
* INC # C8: 4,8 => UNS
* CNT  25 HDP CHAINS /  25 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # B3: 2,5 => UNS
* DIS # C3: 2,5 => CTR => C3: 6,9
* INC C3: 6,9 # G2: 2,5 => UNS
* INC C3: 6,9 # G2: 7 => UNS
* INC C3: 6,9 # B1: 2,5 => UNS
* INC C3: 6,9 # B3: 2,5 => UNS
* INC C3: 6,9 # G2: 2,5 => UNS
* INC C3: 6,9 # G2: 7 => UNS
* INC C3: 6,9 # D4: 4,8 => UNS
* INC C3: 6,9 # E4: 4,8 => UNS
* INC C3: 6,9 # D5: 4,8 => UNS
* INC C3: 6,9 # F5: 4,8 => UNS
* DIS C3: 6,9 # E6: 4,8 => CTR => E6: 1,6
* INC C3: 6,9 + E6: 1,6 # H6: 4,8 => UNS
* DIS C3: 6,9 + E6: 1,6 # H6: 6 => CTR => H6: 4,8
* INC C3: 6,9 + E6: 1,6 + H6: 4,8 # F1: 4,8 => UNS
* INC C3: 6,9 + E6: 1,6 + H6: 4,8 # F1: 2,7,9 => UNS
* INC C3: 6,9 + E6: 1,6 + H6: 4,8 # D4: 4,8 => UNS
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 # E4: 4,8 => CTR => E4: 1,6,7
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 # D5: 4,8 => CTR => D5: 2,6
* DIS C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 # F5: 4,8 => CTR => F5: 2,7
* INC C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # F1: 4,8 => UNS
* INC C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # F1: 2,7,9 => UNS
* PRF C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 # C8: 4,9 => SOL
* STA C3: 6,9 + E6: 1,6 + H6: 4,8 + E4: 1,6,7 + D5: 2,6 + F5: 2,7 + C8: 4,9
* CNT  25 HDP CHAINS /  25 HYP OPENED