Analysis of zz-www.sudokuwiki.org-0010-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=10

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=10

position: ..1.7.......8..4..8.......31.3.2..8...45.37...5..1.3.22.......9..6..4.......9.1.. initial

Autosolve

position: ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A2: 6,7 => CTR => A2: 3,5
* DIS # B4: 6,7 => CTR => B4: 9
* DIS # A6: 6,9 => CTR => A6: 7
* DIS # H5: 1 => CTR => H5: 6,9
* DIS # H5: 1,6 => CTR => H5: 9
* DIS # F7: 5,7 => CTR => F7: 1,6,8
* DIS # H7: 5,7 => CTR => H7: 3,4,6
* DIS # B8: 3,9 => CTR => B8: 1,8
* PRF # B7: 3,4 => SOL
* DIS # B9: 3,4 => CTR => B9: 8
* DIS # H9: 3,4 => CTR => H9: 2,5,6,7
* CNT  11 HDP CHAINS /  45 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 # A2: 6,7 => CTR => A2: 3,5
* DIS A2: 3,5 # H5: 1 => CTR => H5: 6,9
* DIS A2: 3,5 + H5: 6,9 # F7: 5,7 => CTR => F7: 1,6,8
* DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 # H7: 5,7 => CTR => H7: 3,4,6
* DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 # B8: 3,9 => CTR => B8: 1,8
* PRF A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 # B7: 3,4 => SOL
* STA A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 + B7: 3,4
* CNT   6 HDP CHAINS /  18 HYP OPENED

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

Details

Positions

..1.7.......8..4..8.......31.3.2..8...45.37...5..1.3.22.......9..6..4.......9.1.. initial
..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1.. autosolve
431279856569831427872645913193427685624583791758916342247168539916354278385792164 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
C2: 2,9
B3: 6,7
C3: 2,9
A5: 6,9
I5: 1,6
C7: 5,7
A8: 3,9
A9: 3,4
C9: 5,7
E8: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H5,I5: 1.. / H5 = 1  =>  0 pairs (X) / I5 = 1  => 10 pairs (_)
B7,B8: 1.. / B7 = 1  => 19 pairs (_) / B8 = 1  => 17 pairs (_)
B8,D8: 1.. / B8 = 1  => 17 pairs (_) / D8 = 1  => 19 pairs (_)
I2,I5: 1.. / I2 = 1  =>  0 pairs (X) / I5 = 1  => 10 pairs (_)
C2,C3: 2.. / C2 = 2  =>  8 pairs (_) / C3 = 2  =>  8 pairs (_)
D1,E2: 3.. / D1 = 3  => 12 pairs (_) / E2 = 3  => 18 pairs (_)
A1,B1: 4.. / A1 = 4  => 16 pairs (_) / B1 = 4  => 13 pairs (_)
D4,D6: 4.. / D4 = 4  =>  0 pairs (*) / D6 = 4  =>  0 pairs (X)
I4,H6: 4.. / I4 = 4  => 13 pairs (_) / H6 = 4  =>  0 pairs (*)
D4,I4: 4.. / D4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
D6,H6: 4.. / D6 = 4  => 13 pairs (_) / H6 = 4  =>  0 pairs (*)
B7,H7: 4.. / B7 = 4  =>  0 pairs (*) / H7 = 4  =>  0 pairs (X)
A1,A9: 4.. / A1 = 4  => 16 pairs (_) / A9 = 4  => 13 pairs (_)
I4,I9: 4.. / I4 = 4  => 13 pairs (_) / I9 = 4  =>  0 pairs (*)
A1,A2: 5.. / A1 = 5  => 21 pairs (_) / A2 = 5  => 13 pairs (_)
G4,I4: 5.. / G4 = 5  => 13 pairs (_) / I4 = 5  =>  0 pairs (*)
C7,C9: 5.. / C7 = 5  => 10 pairs (_) / C9 = 5  =>  8 pairs (_)
E2,E7: 6.. / E2 = 6  => 13 pairs (_) / E7 = 6  => 12 pairs (_)
B4,A6: 7.. / B4 = 7  =>  0 pairs (X) / A6 = 7  => 12 pairs (_)
C7,C9: 7.. / C7 = 7  =>  8 pairs (_) / C9 = 7  => 10 pairs (_)
B3,H3: 7.. / B3 = 7  => 13 pairs (_) / H3 = 7  => 12 pairs (_)
A2,A6: 7.. / A2 = 7  =>  0 pairs (X) / A6 = 7  => 12 pairs (_)
G1,I1: 8.. / G1 = 8  => 13 pairs (_) / I1 = 8  => 11 pairs (_)
F7,F9: 8.. / F7 = 8  => 11 pairs (_) / F9 = 8  =>  0 pairs (X)
C2,C3: 9.. / C2 = 9  =>  8 pairs (_) / C3 = 9  =>  8 pairs (_)
A8,B8: 9.. / A8 = 9  => 13 pairs (_) / B8 = 9  =>  0 pairs (X)
A5,H5: 9.. / A5 = 9  =>  0 pairs (X) / H5 = 9  => 13 pairs (_)
B4,B8: 9.. / B4 = 9  => 13 pairs (_) / B8 = 9  =>  0 pairs (X)
* DURATION: 0:00:44.616984  START: 03:32:24.475795  END: 03:33:09.092779 2017-05-01
* CP COUNT: (28)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,A9,B3,C2,C3,C7,C9,E8,I5)
* ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1..
* PAIR C2: 2,9 ROW 2
F2: 2,9,1,5,6                            # reduction candidate for 2,9
F2: 2,9                                  # 11 pairs
H2: 2,9,1,5,6,7                          # reduction candidate for 2,9
H2: 2,9                                  # 13 pairs
* PAIR B3: 6,7 BLK 1
A2: 6,7,3,5                              # reduction candidate for 6,7
A2: 6,7 => CTR
* 54137.....3.86.4..86..4..73173.2.584.245837...584173.221..38.49396154...48..9.13.
A2: 3,5                                  # 13 pairs
B2: 6,7,3                                # reduction candidate for 6,7
B2: 6,7                                  # 15 pairs
* PAIR B3: 6,7 ROW 3
H3: 6,7,1,2,5,9                          # reduction candidate for 6,7
H3: 1,2,5,9                              # 13 pairs
H3: 6,7                                  # 11 pairs
* PAIR B3: 6,7 COL B
B4: 6,7,9                                # reduction candidate for 6,7
B4: 6,7 => CTR
* .4137.....3.86.4..8...4...31.3.2.584.245837...5841.3.2215738649396154...487.9.135
B4: 9                                    # 13 pairs
* PAIR C3: 2,9 ROW 3
D3: 2,9,1,6                              # reduction candidate for 2,9
D3: 2,9                                  # 12 pairs
F3: 2,9,1,5,6                            # reduction candidate for 2,9
F3: 2,9                                  # 14 pairs
G3: 2,9,5,6                              # reduction candidate for 2,9
G3: 2,9                                  # 12 pairs
H3: 2,9,1,5,6,7                          # reduction candidate for 2,9
H3: 2,9                                  # 18 pairs
* PAIR A5: 6,9 BLK 4
B4: 6,9,7                                # reduction candidate for 6,9
B4: 6,9                                  # 12 pairs
A6: 6,9,7                                # reduction candidate for 6,9
A6: 6,9 => CTR
* 54137....73.8..4..86..41573173.2..85.245837...58.1.34221......939615482748..9.136
A6: 7                                    # 12 pairs
* PAIR A5: 6,9 ROW 5
H5: 6,9,1                                # reduction candidate for 6,9
H5: 1 => CTR
* .4137...8.3.86.4.18...41.531.3.2.584924583716.5841.392215738649396154827487.9.135
H5: 6,9                                  # 10 pairs
* PAIR I5: 1,6 BLK 6
H5: 1,6,9                                # reduction candidate for 1,6
H5: 1,6 => CTR
* .4137.....3.86.4..8...4...31.3.2.5849245837...5841.392215738649396154...487.9.135
H5: 9                                    # 13 pairs
* PAIR I5: 1,6 COL I
I2: 1,6,5,7                              # reduction candidate for 1,6
I2: 1,6                                  # 13 pairs
I2: 5,7                                  # 11 pairs
* PAIR C7: 5,7 ROW 7
F7: 5,7,1,6,8                            # reduction candidate for 5,7
F7: 5,7 => CTR
* ..1.7..285.98.24168.2.4...31937265846245837917584193622.5..7.499.6.54.37..7.981..
F7: 1,6,8                                # 10 pairs
H7: 5,7,3,4,6                            # reduction candidate for 5,7
H7: 5,7 => CTR
* 4.137....53.86.4.787..4..63193.2.586624583791758.1.34224.1386.991675423838..9.1.4
H7: 3,4,6                                # 10 pairs
* PAIR A8: 3,9 BLK 7
B8: 3,9,1,8                              # reduction candidate for 3,9
B8: 3,9 => CTR
* .4137.......86.4..8...4...31.3.2.584.245837...5841.3.2215738649..6154...487.9.135
B8: 1,8                                  # 14 pairs
* PAIR A9: 3,4 BLK 7
B7: 3,4,1,8                              # reduction candidate for 3,4
B7: 3,4 => SOLVED
* 431279856569831427872645913193427685624583791758916342247168539916354278385792164
B7: 1,8                                  # 16 pairs
B9: 3,4,8                                # reduction candidate for 3,4
B9: 3,4 => CTR
* ..1.7......98.241.8.2.45.73193.2.5846245837917584193622.5..1.49916254837..76981..
B9: 8                                    # 11 pairs
* PAIR A9: 3,4 ROW 9
H9: 3,4,2,5,6,7                          # reduction candidate for 3,4
H9: 3,4 => CTR
* ..137.......86.4..8...4...31.3.2.584.245837...5841.3.22....86.9..6..4....8..9.1..
H9: 2,5,6,7                              # 10 pairs
* PAIR A9: 3,4 COL A
A1: 3,4,5,6                              # reduction candidate for 3,4
A1: 5,6                                  # 15 pairs
A1: 3,4                                  # 15 pairs
* PAIR C9: 5,7 ROW 9
F9: 5,7,2,6,8                            # reduction candidate for 5,7
F9: 5,7                                  # 13 pairs
H9: 5,7,2,3,4,6                          # reduction candidate for 5,7
H9: 5,7                                  # 11 pairs
I9: 5,7,4,6,8                            # reduction candidate for 5,7
I9: 5,7                                  # 14 pairs
* PAIR E8: 3,5 BLK 8
E7: 3,5,6                                # reduction candidate for 3,5
E7: 3,5                                  # 13 pairs
E7: 6                                    # 12 pairs
* PAIR E8: 3,5 ROW 8
H8: 3,5,2,7                              # reduction candidate for 3,5
H8: 3,5                                  # 17 pairs
H8: 2,7                                  # 11 pairs
* PAIR E8: 3,5 COL E
E2: 3,5,6                                # reduction candidate for 3,5
E2: 6                                    # 13 pairs
E2: 3,5                                  # 12 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0010-base-pr-000.dot
* REASONING
* DIS # A2: 6,7 => CTR => A2: 3,5
* DIS # B4: 6,7 => CTR => B4: 9
* DIS # A6: 6,9 => CTR => A6: 7
* DIS # H5: 1 => CTR => H5: 6,9
* DIS # H5: 1,6 => CTR => H5: 9
* DIS # F7: 5,7 => CTR => F7: 1,6,8
* DIS # H7: 5,7 => CTR => H7: 3,4,6
* DIS # B8: 3,9 => CTR => B8: 1,8
* PRF # B7: 3,4 => SOL
* DIS # B9: 3,4 => CTR => B9: 8
* DIS # H9: 3,4 => CTR => H9: 2,5,6,7
* CNT  11 HDP CHAINS /  45 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,A9,B3,C2,C3,C7,C9,E8,I5)
* ..1.7.......8..4..8...4...31.3.2..8..245837...58.1.3.22.......9..6..4.......9.1..
* PAIR C2: 2,9 ROW 2
F2: 2,9,1,5,6                            # reduction candidate for 2,9
F2: 2,9                                  # 11 pairs
H2: 2,9,1,5,6,7                          # reduction candidate for 2,9
H2: 2,9                                  # 13 pairs
* PAIR B3: 6,7 BLK 1
A2: 6,7,3,5                              # reduction candidate for 6,7
A2: 6,7 => CTR
* 54137.....3.86.4..86..4..73173.2.584.245837...584173.221..38.49396154...48..9.13.
B2: 6,7,3                                # reduction candidate for 6,7
B2: 6,7                                  # 15 pairs
* RESTART
* PAIR B3: 6,7 BLK 1
B2: 6,7,3                                # reduction candidate for 6,7
B2: 3                                    # 17 pairs
B2: 6,7                                  # 15 pairs
* PAIR B3: 6,7 ROW 3
H3: 6,7,1,2,5,9                          # reduction candidate for 6,7
H3: 6,7                                  # 14 pairs
H3: 1,2,5,9                              # 14 pairs
* PAIR C3: 2,9 ROW 3
D3: 2,9,1,6                              # reduction candidate for 2,9
D3: 2,9                                  # 15 pairs
F3: 2,9,1,5,6                            # reduction candidate for 2,9
F3: 2,9                                  # 17 pairs
G3: 2,9,5,6                              # reduction candidate for 2,9
G3: 2,9                                  # 15 pairs
H3: 2,9,1,5,6,7                          # reduction candidate for 2,9
H3: 2,9                                  # 19 pairs
* PAIR A5: 6,9 ROW 5
H5: 6,9,1                                # reduction candidate for 6,9
H5: 1 => CTR
* 6413759..53.86.4.187..41..3163.2..8492458371675841639221..38.49396154...48..9.13.
* PAIR RESTART
* PAIR C7: 5,7 ROW 7
F7: 5,7,1,6,8                            # reduction candidate for 5,7
F7: 5,7 => CTR
* ..1.7...8.798..4..86294...3193.2.5846245837917584193622.5..7.499.6.54.37..7.981..
H7: 5,7,3,4,6                            # reduction candidate for 5,7
H7: 5,7 => CTR
* 4.137....53.86.4.787..4..63193.2.586624583791758.1.34224.1386.991675423838..9.1.4
* RESTART
* PAIR RESTART
* PAIR A8: 3,9 BLK 7
B8: 3,9,1,8                              # reduction candidate for 3,9
B8: 3,9 => CTR
* .4137...6...86.4..86..4..73193.2.5846245837917584193.221...8649..61.4...48..9.1..
* PAIR A9: 3,4 BLK 7
B7: 3,4,1,8                              # reduction candidate for 3,4
B7: 3,4 => SOLVED
* 431279856569831427872645913193427685624583791758916342247168539916354278385792164
* DURATION: 0:00:18.926699  START: 03:33:45.691683  END: 03:34:04.618382 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0010-base-pr-001.dot
* REASONING
* DIS # A2: 6,7 => CTR => A2: 3,5
* DIS A2: 3,5 # H5: 1 => CTR => H5: 6,9
* DIS A2: 3,5 + H5: 6,9 # F7: 5,7 => CTR => F7: 1,6,8
* DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 # H7: 5,7 => CTR => H7: 3,4,6
* DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 # B8: 3,9 => CTR => B8: 1,8
* PRF A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 # B7: 3,4 => SOL
* STA A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 + B7: 3,4
* CNT   6 HDP CHAINS /  18 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=10

Solution

position: 431279856569831427872645913193427685624583791758916342247168539916354278385792164 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 # F2: 2,9 => UNS
* INC # H2: 2,9 => UNS
* DIS # A2: 6,7 => CTR => A2: 3,5
* INC # A2: 3,5 => UNS
* INC # B2: 6,7 => UNS
* INC # H3: 6,7 => UNS
* INC # H3: 1,2,5,9 => UNS
* DIS # B4: 6,7 => CTR => B4: 9
* INC # B4: 9 => UNS
* INC # D3: 2,9 => UNS
* INC # F3: 2,9 => UNS
* INC # G3: 2,9 => UNS
* INC # H3: 2,9 => UNS
* INC # B4: 6,9 => UNS
* DIS # A6: 6,9 => CTR => A6: 7
* INC # A6: 7 => UNS
* INC # H5: 6,9 => UNS
* DIS # H5: 1 => CTR => H5: 6,9
* DIS # H5: 1,6 => CTR => H5: 9
* INC # H5: 9 => UNS
* INC # I2: 1,6 => UNS
* INC # I2: 5,7 => UNS
* DIS # F7: 5,7 => CTR => F7: 1,6,8
* INC # F7: 1,6,8 => UNS
* DIS # H7: 5,7 => CTR => H7: 3,4,6
* INC # H7: 3,4,6 => UNS
* DIS # B8: 3,9 => CTR => B8: 1,8
* INC # B8: 1,8 => UNS
* PRF # B7: 3,4 => SOL
* INC # B7: 1,8 => UNS
* DIS # B9: 3,4 => CTR => B9: 8
* INC # B9: 8 => UNS
* DIS # H9: 3,4 => CTR => H9: 2,5,6,7
* INC # H9: 2,5,6,7 => UNS
* INC # A1: 3,4 => UNS
* INC # A1: 5,6 => UNS
* INC # F9: 5,7 => UNS
* INC # H9: 5,7 => UNS
* INC # I9: 5,7 => UNS
* INC # E7: 3,5 => UNS
* INC # E7: 6 => UNS
* INC # H8: 3,5 => UNS
* INC # H8: 2,7 => UNS
* INC # E2: 3,5 => UNS
* INC # E2: 6 => UNS
* CNT  45 HDP CHAINS /  45 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F2: 2,9 => UNS
* INC # H2: 2,9 => UNS
* DIS # A2: 6,7 => CTR => A2: 3,5
* INC A2: 3,5 # B2: 6,7 => UNS
* INC A2: 3,5 # B2: 6,7 => UNS
* INC A2: 3,5 # B2: 3 => UNS
* INC A2: 3,5 # H3: 6,7 => UNS
* INC A2: 3,5 # H3: 1,2,5,9 => UNS
* INC A2: 3,5 # D3: 2,9 => UNS
* INC A2: 3,5 # F3: 2,9 => UNS
* INC A2: 3,5 # G3: 2,9 => UNS
* INC A2: 3,5 # H3: 2,9 => UNS
* INC A2: 3,5 # H5: 6,9 => UNS
* DIS A2: 3,5 # H5: 1 => CTR => H5: 6,9
* DIS A2: 3,5 + H5: 6,9 # F7: 5,7 => CTR => F7: 1,6,8
* DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 # H7: 5,7 => CTR => H7: 3,4,6
* DIS A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 # B8: 3,9 => CTR => B8: 1,8
* PRF A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 # B7: 3,4 => SOL
* STA A2: 3,5 + H5: 6,9 + F7: 1,6,8 + H7: 3,4,6 + B8: 1,8 + B7: 3,4
* CNT  18 HDP CHAINS /  18 HYP OPENED