Analysis of zz-www.sudokuwiki.org-0048-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=48

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=48

position: ..6...5...3.2...9.1....7.36..27...6.6..5.1..2.1...67..89.1....4.6...8.7...4...8.. initial

Autosolve

position: ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B3: 5,8 => CTR => B3: 2,4
* CNT   1 HDP CHAINS /  22 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 # B3: 5,8 => CTR => B3: 2,4
* DIS B3: 2,4 # H1: 8 => CTR => H1: 2,4
* DIS B3: 2,4 + H1: 2,4 # H6: 5 => CTR => H6: 4,8
* DIS B3: 2,4 + H1: 2,4 + H6: 4,8 # E5: 4,8 => CTR => E5: 3,9
* DIS B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 7 => CTR => B5: 4,8
* PRF B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 # D1: 4,8 => SOL
* STA B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 + D1: 4,8
* CNT   6 HDP CHAINS /  23 HYP OPENED

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

Details

Positions

..6...5...3.2...9.1....7.36..27...6.6..5.1..2.1...67..89.1....4.6...8.7...4...8.. initial
..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81. autosolve
946813527735264198128957436452789361687531942319426785893172654561348279274695813 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
F2: 4,5
I1: 7,8
G2: 1,4
G3: 2,4
H5: 4,8
H7: 2,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,I2: 1.. / G2 = 1  =>  7 pairs (_) / I2 = 1  => 16 pairs (_)
G4,I4: 1.. / G4 = 1  => 16 pairs (_) / I4 = 1  =>  7 pairs (_)
G2,G4: 1.. / G2 = 1  =>  7 pairs (_) / G4 = 1  => 16 pairs (_)
I2,I4: 1.. / I2 = 1  => 16 pairs (_) / I4 = 1  =>  7 pairs (_)
H1,G3: 2.. / H1 = 2  => 17 pairs (_) / G3 = 2  =>  8 pairs (_)
F7,F9: 2.. / F7 = 2  => 17 pairs (_) / F9 = 2  =>  8 pairs (_)
H7,G8: 2.. / H7 = 2  =>  8 pairs (_) / G8 = 2  => 17 pairs (_)
B3,G3: 2.. / B3 = 2  => 17 pairs (_) / G3 = 2  =>  8 pairs (_)
F7,H7: 2.. / F7 = 2  => 17 pairs (_) / H7 = 2  =>  8 pairs (_)
A8,G8: 2.. / A8 = 2  =>  8 pairs (_) / G8 = 2  => 17 pairs (_)
G3,G8: 2.. / G3 = 2  =>  8 pairs (_) / G8 = 2  => 17 pairs (_)
H1,H7: 2.. / H1 = 2  => 17 pairs (_) / H7 = 2  =>  8 pairs (_)
D1,F1: 3.. / D1 = 3  =>  9 pairs (_) / F1 = 3  => 10 pairs (_)
D8,E8: 4.. / D8 = 4  =>  7 pairs (_) / E8 = 4  =>  7 pairs (_)
F2,E3: 5.. / F2 = 5  =>  8 pairs (_) / E3 = 5  => 13 pairs (_)
H6,H7: 5.. / H6 = 5  =>  8 pairs (_) / H7 = 5  => 17 pairs (_)
I1,I2: 7.. / I1 = 7  =>  6 pairs (_) / I2 = 7  =>  8 pairs (_)
B5,C5: 7.. / B5 = 7  =>  7 pairs (_) / C5 = 7  => 11 pairs (_)
E7,E9: 7.. / E7 = 7  =>  7 pairs (_) / E9 = 7  => 10 pairs (_)
C7,E7: 7.. / C7 = 7  => 10 pairs (_) / E7 = 7  =>  7 pairs (_)
C2,I2: 8.. / C2 = 8  =>  8 pairs (_) / I2 = 8  =>  6 pairs (_)
A1,C3: 9.. / A1 = 9  =>  9 pairs (_) / C3 = 9  =>  9 pairs (_)
* DURATION: 0:00:27.377512  START: 04:22:36.930729  END: 04:23:04.308241 2017-05-01
* CP COUNT: (22)
* INCONCLUSIVE

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F2,G2,G3,H5,H7,I1)
* ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81.
* PAIR F2: 4,5 BLK 2
E3: 4,5,8,9                              # reduction candidate for 4,5
E3: 8,9                                  #  9 pairs
E3: 4,5                                  #  9 pairs
* PAIR F2: 4,5 ROW 2
A2: 4,5,7                                # reduction candidate for 4,5
A2: 4,5                                  #  9 pairs
A2: 7                                    #  7 pairs
* PAIR I1: 7,8 BLK 3
I2: 7,8,1                                # reduction candidate for 7,8
I2: 1                                    # 16 pairs
I2: 7,8                                  #  7 pairs
* PAIR I1: 7,8 ROW 1
B1: 7,8,2,4                              # reduction candidate for 7,8
B1: 7,8                                  #  9 pairs
B1: 2,4                                  #  7 pairs
* PAIR G2: 1,4 COL G
G4: 1,4,3,9                              # reduction candidate for 1,4
G4: 1,4                                  # 10 pairs
G4: 3,9                                  #  8 pairs
* PAIR G3: 2,4 BLK 3
H1: 2,4,8                                # reduction candidate for 2,4
H1: 8                                    # 16 pairs
H1: 2,4                                  #  7 pairs
* PAIR G3: 2,4 ROW 3
B3: 2,4,5,8                              # reduction candidate for 2,4
B3: 5,8 => CTR
* .26.1.5...3.26..9.1....7236..27...6.6..5.1..2.1..2675.89.1..624261..8.7...46.281.
B3: 2,4                                  #  8 pairs
* PAIR H5: 4,8 BLK 6
H6: 4,8,5                                # reduction candidate for 4,8
H6: 4,8                                  # 17 pairs
H6: 5                                    #  8 pairs
* PAIR H5: 4,8 ROW 5
B5: 4,8,7                                # reduction candidate for 4,8
B5: 4,8                                  # 11 pairs
E5: 4,8,3,9                              # reduction candidate for 4,8
E5: 4,8                                  # 10 pairs
* PAIR H5: 4,8 COL H
H1: 4,8,2                                # reduction candidate for 4,8
H1: 2                                    # 17 pairs
H1: 4,8                                  #  8 pairs
* PAIR H7: 2,5 ROW 7
F7: 2,5,3                                # reduction candidate for 2,5
F7: 3                                    # 19 pairs
F7: 2,5                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0048-base-pr-000.dot
* REASONING
* DIS # B3: 5,8 => CTR => B3: 2,4
* CNT   1 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F2,G2,G3,H5,H7,I1)
* ..6.1.5...3.26..9.1....7.36..27...6.6..5.1..2.1..267..89.1..6.4.61..8.7...46..81.
* PAIR F2: 4,5 BLK 2
E3: 4,5,8,9                              # reduction candidate for 4,5
E3: 8,9                                  #  9 pairs
E3: 4,5                                  #  9 pairs
* PAIR F2: 4,5 ROW 2
A2: 4,5,7                                # reduction candidate for 4,5
A2: 4,5                                  #  9 pairs
A2: 7                                    #  7 pairs
* PAIR I1: 7,8 BLK 3
I2: 7,8,1                                # reduction candidate for 7,8
I2: 1                                    # 16 pairs
I2: 7,8                                  #  7 pairs
* PAIR I1: 7,8 ROW 1
B1: 7,8,2,4                              # reduction candidate for 7,8
B1: 7,8                                  #  9 pairs
B1: 2,4                                  #  7 pairs
* PAIR G2: 1,4 COL G
G4: 1,4,3,9                              # reduction candidate for 1,4
G4: 1,4                                  # 10 pairs
G4: 3,9                                  #  8 pairs
* PAIR G3: 2,4 BLK 3
H1: 2,4,8                                # reduction candidate for 2,4
H1: 8                                    # 16 pairs
H1: 2,4                                  #  7 pairs
* PAIR G3: 2,4 ROW 3
B3: 2,4,5,8                              # reduction candidate for 2,4
B3: 5,8 => CTR
* .26.1.5...3.26..9.1....7236..27...6.6..5.1..2.1..2675.89.1..624261..8.7...46.281.
* PAIR RESTART
* PAIR G3: 2,4 BLK 3
H1: 2,4,8                                # reduction candidate for 2,4
H1: 8 => CTR
* 926314587738265491145..723658274916.6..5.1.42.1..2675.89.153624261..8.75354672819
* PAIR H5: 4,8 BLK 6
H6: 4,8,5                                # reduction candidate for 4,8
H6: 5 => CTR
* .26.1.54..3.26419.14..57236.827...6167.5.1.82.1.82675.89.1.56242614.8.75.546.281.
* PAIR H5: 4,8 ROW 5
B5: 4,8,7                                # reduction candidate for 4,8
B5: 4,8                                  # 18 pairs
E5: 4,8,3,9                              # reduction candidate for 4,8
E5: 4,8 => CTR
* 9.6.14527.3.26519.125..74365.27...6167.5.1..2.1..267.5897132654361458279254679813
* RESTART
* PAIR H5: 4,8 ROW 5
B5: 4,8,7                                # reduction candidate for 4,8
B5: 7 => CTR
* ..6.1.52..3.26.19.12...7436..27...616785.1.42.1..26785897132654361.5827925467.81.
* PAIR RESTART

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,B1,B5,C2,C6,D3,D8,E3,E5,F2,G4,G5,H5,H6,I1,I2,I8,I9)
* ..6.1.52..3.26.19.12...7436.5278..616.75.1..2.1..267.5893172654561.4827.2746..81.
* PAIR B1: 4,8 ROW 1
D1: 4,8,3,9                              # reduction candidate for 4,8
D1: 4,8 => SOLVED
* 946813527735264198128957436452789361687531942319426785893172654561348279274695813
* DURATION: 0:00:20.182836  START: 04:23:19.557515  END: 04:23:39.740351 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0048-base-pr-001.dot
* REASONING
* DIS # B3: 5,8 => CTR => B3: 2,4
* DIS B3: 2,4 # H1: 8 => CTR => H1: 2,4
* DIS B3: 2,4 + H1: 2,4 # H6: 5 => CTR => H6: 4,8
* DIS B3: 2,4 + H1: 2,4 + H6: 4,8 # E5: 4,8 => CTR => E5: 3,9
* DIS B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 7 => CTR => B5: 4,8
* PRF B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 # D1: 4,8 => SOL
* STA B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 + D1: 4,8
* CNT   6 HDP CHAINS /  23 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=48

Solution

position: 946813527735264198128957436452789361687531942319426785893172654561348279274695813 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 # E3: 4,5 => UNS
* INC # E3: 8,9 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 7 => UNS
* INC # I2: 7,8 => UNS
* INC # I2: 1 => UNS
* INC # B1: 7,8 => UNS
* INC # B1: 2,4 => UNS
* INC # G4: 1,4 => UNS
* INC # G4: 3,9 => UNS
* INC # H1: 2,4 => UNS
* INC # H1: 8 => UNS
* INC # B3: 2,4 => UNS
* DIS # B3: 5,8 => CTR => B3: 2,4
* INC # H6: 4,8 => UNS
* INC # H6: 5 => UNS
* INC # B5: 4,8 => UNS
* INC # E5: 4,8 => UNS
* INC # H1: 4,8 => UNS
* INC # H1: 2 => UNS
* INC # F7: 2,5 => UNS
* INC # F7: 3 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 4,5 => UNS
* INC # E3: 8,9 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 7 => UNS
* INC # I2: 7,8 => UNS
* INC # I2: 1 => UNS
* INC # B1: 7,8 => UNS
* INC # B1: 2,4 => UNS
* INC # G4: 1,4 => UNS
* INC # G4: 3,9 => UNS
* INC # H1: 2,4 => UNS
* INC # H1: 8 => UNS
* INC # B3: 2,4 => UNS
* DIS # B3: 5,8 => CTR => B3: 2,4
* INC B3: 2,4 # H1: 2,4 => UNS
* DIS B3: 2,4 # H1: 8 => CTR => H1: 2,4
* INC B3: 2,4 + H1: 2,4 # H6: 4,8 => UNS
* DIS B3: 2,4 + H1: 2,4 # H6: 5 => CTR => H6: 4,8
* INC B3: 2,4 + H1: 2,4 + H6: 4,8 # B5: 4,8 => UNS
* DIS B3: 2,4 + H1: 2,4 + H6: 4,8 # E5: 4,8 => CTR => E5: 3,9
* INC B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 4,8 => UNS
* DIS B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 # B5: 7 => CTR => B5: 4,8
* PRF B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 # D1: 4,8 => SOL
* STA B3: 2,4 + H1: 2,4 + H6: 4,8 + E5: 3,9 + B5: 4,8 + D1: 4,8
* CNT  23 HDP CHAINS /  23 HYP OPENED