Analysis of zz-menneske-no-05925446-base.sdk

Contents

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=5925446

level: medium

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=5925446

position: .1......47...5.......3.8.......3....9...6.8....3..7.2.46.....7.......2..57..2.31. initial

Autosolve

position: .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 2,6 => CTR => A1: 3,8
* PRF # I5: 1,7 => SOL
* DIS # C8: 8,9 => CTR => C8: 1
* DIS # G3: 5,9 => CTR => G3: 1,6,7
* DIS # G4: 5,9 => CTR => G4: 1,4,6,7
* DIS # G6: 5,9 => CTR => G6: 1,4,6
* CNT   6 HDP CHAINS /  32 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 # A1: 2,6 => CTR => A1: 3,8
* PRF A1: 3,8 # I5: 1,7 => SOL
* STA A1: 3,8 + I5: 1,7
* CNT   2 HDP CHAINS /  11 HYP OPENED

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

Details

Positions

.1......47...5.......3.8.......3....9...6.8....3..7.2.46.....7.......2..57..2.31. initial
.1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31. autosolve
315276984728459163694318752256831497947562831183947625462183579831795246579624318 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
A3: 2,6
E1: 7,9
H5: 3,5
C9: 8,9
G7: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A8,C8: 1.. / A8 = 1  =>  0 pairs (X) / C8 = 1  =>  6 pairs (_)
D7,E7: 1.. / D7 = 1  =>  8 pairs (_) / E7 = 1  =>  6 pairs (_)
I2,I3: 2.. / I2 = 2  => 10 pairs (_) / I3 = 2  =>  0 pairs (*)
A1,B2: 3.. / A1 = 3  =>  6 pairs (_) / B2 = 3  =>  9 pairs (_)
H5,I5: 3.. / H5 = 3  =>  0 pairs (*) / I5 = 3  =>  0 pairs (X)
A8,B8: 3.. / A8 = 3  =>  9 pairs (_) / B8 = 3  =>  6 pairs (_)
A1,H1: 3.. / A1 = 3  =>  6 pairs (_) / H1 = 3  =>  9 pairs (_)
A1,A8: 3.. / A1 = 3  =>  6 pairs (_) / A8 = 3  =>  9 pairs (_)
B2,B8: 3.. / B2 = 3  =>  9 pairs (_) / B8 = 3  =>  6 pairs (_)
I2,I5: 3.. / I2 = 3  =>  0 pairs (*) / I5 = 3  =>  0 pairs (X)
G4,G6: 4.. / G4 = 4  =>  5 pairs (_) / G6 = 4  =>  0 pairs (X)
D9,F9: 4.. / D9 = 4  =>  6 pairs (_) / F9 = 4  =>  5 pairs (_)
E3,E6: 4.. / E3 = 4  =>  0 pairs (X) / E6 = 4  =>  6 pairs (_)
I8,I9: 6.. / I8 = 6  =>  9 pairs (_) / I9 = 6  =>  6 pairs (_)
A6,G6: 6.. / A6 = 6  => 12 pairs (_) / G6 = 6  => 11 pairs (_)
C4,C5: 7.. / C4 = 7  =>  0 pairs (X) / C5 = 7  =>  5 pairs (_)
D8,E8: 7.. / D8 = 7  =>  8 pairs (_) / E8 = 7  =>  8 pairs (_)
C5,I5: 7.. / C5 = 7  =>  5 pairs (_) / I5 = 7  =>  0 pairs (X)
D1,D8: 7.. / D1 = 7  =>  8 pairs (_) / D8 = 7  =>  8 pairs (_)
H1,H2: 8.. / H1 = 8  =>  7 pairs (_) / H2 = 8  =>  5 pairs (_)
* DURATION: 0:00:17.869254  START: 01:26:06.845532  END: 01:26:24.714786 2019-05-01
* CP COUNT: (20)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C9,E1,G7,H5)
* .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31.
* PAIR A3: 2,6 BLK 1
A1: 2,6,3,8                              # reduction candidate for 2,6
A1: 2,6 => CTR
* .18...534734.5.18929534876.....3..9.9.7.6.853..3..7.21462.1397.381...24.579.2.31.
A1: 3,8                                  #  6 pairs
* PAIR A3: 2,6 COL A
A4: 2,6,1,8                              # reduction candidate for 2,6
A4: 2,6                                  # 13 pairs
A4: 1,8                                  #  6 pairs
* PAIR E1: 7,9 BLK 2
D1: 7,9,2,6                              # reduction candidate for 7,9
D1: 7,9                                  #  9 pairs
E3: 7,9,1,4                              # reduction candidate for 7,9
E3: 7,9                                  # 32 pairs
* PAIR E1: 7,9 ROW 1
G1: 7,9,5,6                              # reduction candidate for 7,9
G1: 7,9                                  # 13 pairs
G1: 5,6                                  #  6 pairs
* PAIR E1: 7,9 COL E
E8: 7,9,8                                # reduction candidate for 7,9
E8: 8                                    # 19 pairs
E8: 7,9                                  #  8 pairs
* PAIR H5: 3,5 BLK 6
I5: 3,5,1,7                              # reduction candidate for 3,5
I5: 1,7 => SOLVED
* 315276984728459163694318752256831497947562831183947625462183579831795246579624318
I5: 3,5                                  #  9 pairs
* PAIR H5: 3,5 COL H
H1: 3,5,6,8,9                            # reduction candidate for 3,5
H1: 3,5                                  #  8 pairs
H1: 6,8,9                                #  6 pairs
* PAIR C9: 8,9 BLK 7
B8: 8,9,3                                # reduction candidate for 8,9
B8: 8,9                                  #  9 pairs
C8: 8,9,1                                # reduction candidate for 8,9
C8: 8,9 => CTR
* 31579..84786.5..322943.8.656.183.497947.6.8538539476214621.357.13.57.24.57..2.31.
C8: 1                                    #  6 pairs
* PAIR C9: 8,9 ROW 9
D9: 8,9,4,6                              # reduction candidate for 8,9
D9: 8,9                                  #  6 pairs
I9: 8,9,6                                # reduction candidate for 8,9
I9: 8,9                                  #  9 pairs
* PAIR C9: 8,9 COL C
C1: 8,9,5,6                              # reduction candidate for 8,9
C1: 8,9                                  #  9 pairs
C2: 8,9,4,6                              # reduction candidate for 8,9
C2: 8,9                                  # 12 pairs
* PAIR G7: 5,9 BLK 9
I7: 5,9,8                                # reduction candidate for 5,9
I7: 5,9                                  # 12 pairs
I8: 5,9,6,8                              # reduction candidate for 5,9
I8: 5,9                                  #  8 pairs
* PAIR G7: 5,9 ROW 7
D7: 5,9,1,8                              # reduction candidate for 5,9
D7: 5,9                                  #  8 pairs
D7: 1,8                                  #  6 pairs
* PAIR G7: 5,9 COL G
G1: 5,9,6,7                              # reduction candidate for 5,9
G1: 5,9                                  #  7 pairs
G3: 5,9,1,6,7                            # reduction candidate for 5,9
G3: 5,9 => CTR
* .15.9.7.47...5.6.2..4378591..6.3.4.7947.6.853..3.47129462.1397....78.24.578.2.316
G3: 1,6,7                                #  5 pairs
G4: 5,9,1,4,6,7                          # reduction candidate for 5,9
G4: 5,9 => CTR
* .1......47...5...22..348.......3..679.7.6.8536.3..7421462.13.7.......24.57..2.31.
G4: 1,4,6,7                              #  5 pairs
G6: 5,9,1,4,6                            # reduction candidate for 5,9
G6: 5,9 => CTR
* .15.....47...5...22463.8.95....3.467927.6.8536.3.47921462..357.......24.57..2.31.
G6: 1,4,6                                #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-05925446-base-pr-000.dot
* REASONING
* DIS # A1: 2,6 => CTR => A1: 3,8
* PRF # I5: 1,7 => SOL
* DIS # C8: 8,9 => CTR => C8: 1
* DIS # G3: 5,9 => CTR => G3: 1,6,7
* DIS # G4: 5,9 => CTR => G4: 1,4,6,7
* DIS # G6: 5,9 => CTR => G6: 1,4,6
* CNT   6 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,C9,E1,G7,H5)
* .1......47...5.......3.8.......3....9...6.8....3..7.2.462..3.7.......24.57..2.31.
* PAIR A3: 2,6 BLK 1
A1: 2,6,3,8                              # reduction candidate for 2,6
A1: 2,6 => CTR
* .18...534734.5.18929534876.....3..9.9.7.6.853..3..7.21462.1397.381...24.579.2.31.
* PAIR A3: 2,6 COL A
A4: 2,6,1,8                              # reduction candidate for 2,6
A4: 2,6                                  # 13 pairs
A4: 1,8                                  # 12 pairs
* PAIR E1: 7,9 BLK 2
D1: 7,9,2,6                              # reduction candidate for 7,9
D1: 7,9                                  # 10 pairs
E3: 7,9,1,4                              # reduction candidate for 7,9
E3: 7,9                                  # 32 pairs
* PAIR E1: 7,9 ROW 1
G1: 7,9,5,6                              # reduction candidate for 7,9
G1: 7,9                                  # 13 pairs
G1: 5,6                                  #  7 pairs
* PAIR E1: 7,9 COL E
E8: 7,9,8                                # reduction candidate for 7,9
E8: 8                                    # 19 pairs
E8: 7,9                                  #  9 pairs
* PAIR H5: 3,5 BLK 6
I5: 3,5,1,7                              # reduction candidate for 3,5
I5: 1,7 => SOLVED
* 315276984728459163694318752256831497947562831183947625462183579831795246579624318
* DURATION: 0:00:07.477717  START: 01:26:40.633630  END: 01:26:48.111347 2019-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-05925446-base-pr-001.dot
* REASONING
* DIS # A1: 2,6 => CTR => A1: 3,8
* PRF A1: 3,8 # I5: 1,7 => SOL
* STA A1: 3,8 + I5: 1,7
* CNT   2 HDP CHAINS /  11 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=5925446
umulig

Solution

position: 315276984728459163694318752256831497947562831183947625462183579831795246579624318 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:

* DIS # A1: 2,6 => CTR => A1: 3,8
* INC # A1: 3,8 => UNS
* INC # A4: 2,6 => UNS
* INC # A4: 1,8 => UNS
* INC # D1: 7,9 => UNS
* INC # E3: 7,9 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 5,6 => UNS
* INC # E8: 7,9 => UNS
* INC # E8: 8 => UNS
* INC # I5: 3,5 => UNS
* PRF # I5: 1,7 => SOL
* INC # H1: 3,5 => UNS
* INC # H1: 6,8,9 => UNS
* INC # B8: 8,9 => UNS
* DIS # C8: 8,9 => CTR => C8: 1
* INC # C8: 1 => UNS
* INC # D9: 8,9 => UNS
* INC # I9: 8,9 => UNS
* INC # C1: 8,9 => UNS
* INC # C2: 8,9 => UNS
* INC # I7: 5,9 => UNS
* INC # I8: 5,9 => UNS
* INC # D7: 5,9 => UNS
* INC # D7: 1,8 => UNS
* INC # G1: 5,9 => UNS
* DIS # G3: 5,9 => CTR => G3: 1,6,7
* INC # G3: 1,6,7 => UNS
* DIS # G4: 5,9 => CTR => G4: 1,4,6,7
* INC # G4: 1,4,6,7 => UNS
* DIS # G6: 5,9 => CTR => G6: 1,4,6
* INC # G6: 1,4,6 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 2,6 => CTR => A1: 3,8
* INC A1: 3,8 # A4: 2,6 => UNS
* INC A1: 3,8 # A4: 1,8 => UNS
* INC A1: 3,8 # D1: 7,9 => UNS
* INC A1: 3,8 # E3: 7,9 => UNS
* INC A1: 3,8 # G1: 7,9 => UNS
* INC A1: 3,8 # G1: 5,6 => UNS
* INC A1: 3,8 # E8: 7,9 => UNS
* INC A1: 3,8 # E8: 8 => UNS
* INC A1: 3,8 # I5: 3,5 => UNS
* PRF A1: 3,8 # I5: 1,7 => SOL
* STA A1: 3,8 + I5: 1,7
* CNT  11 HDP CHAINS /  11 HYP OPENED