Analysis of zz-www.sudokuwiki.org-0081-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=81

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=81

position: ..4.3...22..1..9.........7.7.2..5....4.....9....7..5.6.8.........5..4..31...9.6.. initial

Autosolve

position: ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS # G3: 1,8 => CTR => G3: 3,4
* DIS # G4: 1,8 => CTR => G4: 3,4
* CNT   3 HDP CHAINS /  19 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 # H1: 1,8 => CTR => H1: 5,6
* DIS H1: 5,6 # G3: 1,8 => CTR => G3: 3,4
* PRF H1: 5,6 + G3: 3,4 # I3: 4,5 => SOL
* STA H1: 5,6 + G3: 3,4 + I3: 4,5
* CNT   3 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

..4.3...22..1..9.........7.7.2..5....4.....9....7..5.6.8.........5..4..31...9.6.. initial
..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6.. autosolve
874539162253176948619428375762985431541263897398741526486357219925614783137892654 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
G1: 1,8
A8: 6,9
C9: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,H6: 2.. / G5 = 2  =>  6 pairs (_) / H6 = 2  =>  6 pairs (_)
B8,B9: 2.. / B8 = 2  => 18 pairs (_) / B9 = 2  =>  3 pairs (_)
H2,G3: 3.. / H2 = 3  =>  4 pairs (_) / G3 = 3  =>  8 pairs (_)
A3,A6: 3.. / A3 = 3  =>  0 pairs (X) / A6 = 3  =>  8 pairs (_)
H9,I9: 4.. / H9 = 4  =>  4 pairs (_) / I9 = 4  =>  8 pairs (_)
E6,H6: 4.. / E6 = 4  =>  4 pairs (_) / H6 = 4  =>  0 pairs (X)
D3,D4: 4.. / D3 = 4  =>  4 pairs (_) / D4 = 4  =>  0 pairs (X)
G3,G4: 4.. / G3 = 4  =>  0 pairs (X) / G4 = 4  =>  4 pairs (_)
H1,H2: 6.. / H1 = 6  =>  4 pairs (_) / H2 = 6  => 17 pairs (_)
B4,C5: 6.. / B4 = 6  =>  7 pairs (_) / C5 = 6  =>  0 pairs (X)
G5,I5: 7.. / G5 = 7  =>  0 pairs (X) / I5 = 7  =>  3 pairs (_)
B1,F1: 7.. / B1 = 7  =>  4 pairs (_) / F1 = 7  =>  4 pairs (_)
I5,I9: 7.. / I5 = 7  =>  3 pairs (_) / I9 = 7  =>  0 pairs (X)
D4,F6: 9.. / D4 = 9  =>  4 pairs (_) / F6 = 9  =>  0 pairs (X)
A8,B8: 9.. / A8 = 9  =>  4 pairs (_) / B8 = 9  =>  8 pairs (_)
B4,D4: 9.. / B4 = 9  =>  0 pairs (X) / D4 = 9  =>  4 pairs (_)
C3,C6: 9.. / C3 = 9  =>  5 pairs (_) / C6 = 9  =>  6 pairs (_)
* DURATION: 0:00:18.864306  START: 04:53:27.698399  END: 04:53:46.562705 2017-05-01
* CP COUNT: (17)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C9,G1)
* ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6..
* PAIR G1: 1,8 BLK 3
H1: 1,8,5,6                              # reduction candidate for 1,8
H1: 1,8 => CTR
* 6549371822..1589648..4263757.2..543154.....973..74.5.6486....59925..4.131..592648
H1: 5,6                                  #  4 pairs
G3: 1,8,3,4                              # reduction candidate for 1,8
G3: 1,8 => CTR
* .54.37162278156934...4298757.2.65481546...397...74.5264836...59..5..4.131.7593648
G3: 3,4                                  #  4 pairs
I3: 1,8,4,5                              # reduction candidate for 1,8
I3: 1,8                                  #  7 pairs
* PAIR G1: 1,8 COL G
G4: 1,8,3,4                              # reduction candidate for 1,8
G4: 1,8 => CTR
* ..4.3...22..1..9........47.7.24.5...54....397...7..5.648......9..5..4..31...9.6..
G4: 3,4                                  #  4 pairs
G5: 1,8,2,3,7                            # reduction candidate for 1,8
G5: 1,8                                  # 15 pairs
G8: 1,8,2,7                              # reduction candidate for 1,8
G8: 1,8                                  #  8 pairs
* PAIR A8: 6,9 BLK 7
B8: 6,9,2,7                              # reduction candidate for 6,9
B8: 2,7                                  # 15 pairs
B8: 6,9                                  #  7 pairs
* PAIR A8: 6,9 COL A
A1: 6,9,8                                # reduction candidate for 6,9
A1: 6,9                                  #  6 pairs
A3: 6,9,3,8                              # reduction candidate for 6,9
A3: 6,9                                  # 15 pairs
* PAIR C9: 3,7 BLK 7
C7: 3,7,6                                # reduction candidate for 3,7
C7: 3,7                                  #  7 pairs
B9: 3,7,2                                # reduction candidate for 3,7
B9: 3,7                                  # 18 pairs
* PAIR C9: 3,7 ROW 9
F9: 3,7,2,8                              # reduction candidate for 3,7
F9: 3,7                                  #  5 pairs
F9: 2,8                                  #  4 pairs
* PAIR C9: 3,7 COL C
C2: 3,7,6,8                              # reduction candidate for 3,7
C2: 3,7                                  # 15 pairs
C2: 6,8                                  #  5 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0081-base-pr-000.dot
* REASONING
* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS # G3: 1,8 => CTR => G3: 3,4
* DIS # G4: 1,8 => CTR => G4: 3,4
* CNT   3 HDP CHAINS /  19 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C9,G1)
* ..4.3...22..1..9.........7.7.2..5...54.....9....7..5.648......9..5..4..31...9.6..
* PAIR G1: 1,8 BLK 3
H1: 1,8,5,6                              # reduction candidate for 1,8
H1: 1,8 => CTR
* 6549371822..1589648..4263757.2..543154.....973..74.5.6486....59925..4.131..592648
G3: 1,8,3,4                              # reduction candidate for 1,8
G3: 1,8 => CTR
* .54.37162278156934...4298757.2.65481546...397...74.5264836...59..5..4.131.7593648
I3: 1,8,4,5                              # reduction candidate for 1,8
I3: 1,8                                  #  7 pairs
* RESTART
* PAIR G1: 1,8 BLK 3
I3: 1,8,4,5                              # reduction candidate for 1,8
I3: 4,5 => SOLVED
* 874539162253176948619428375762985431541263897398741526486357219925614783137892654
* DURATION: 0:00:05.954842  START: 04:53:58.587629  END: 04:54:04.542471 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0081-base-pr-001.dot
* REASONING
* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS H1: 5,6 # G3: 1,8 => CTR => G3: 3,4
* PRF H1: 5,6 + G3: 3,4 # I3: 4,5 => SOL
* STA H1: 5,6 + G3: 3,4 + I3: 4,5
* CNT   3 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=81

Solution

position: 874539162253176948619428375762985431541263897398741526486357219925614783137892654 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 # H1: 1,8 => CTR => H1: 5,6
* INC # H1: 5,6 => UNS
* DIS # G3: 1,8 => CTR => G3: 3,4
* INC # G3: 3,4 => UNS
* INC # I3: 1,8 => UNS
* DIS # G4: 1,8 => CTR => G4: 3,4
* INC # G4: 3,4 => UNS
* INC # G5: 1,8 => UNS
* INC # G8: 1,8 => UNS
* INC # B8: 6,9 => UNS
* INC # B8: 2,7 => UNS
* INC # A1: 6,9 => UNS
* INC # A3: 6,9 => UNS
* INC # C7: 3,7 => UNS
* INC # B9: 3,7 => UNS
* INC # F9: 3,7 => UNS
* INC # F9: 2,8 => UNS
* INC # C2: 3,7 => UNS
* INC # C2: 6,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # H1: 1,8 => CTR => H1: 5,6
* DIS H1: 5,6 # G3: 1,8 => CTR => G3: 3,4
* INC H1: 5,6 + G3: 3,4 # I3: 1,8 => UNS
* INC H1: 5,6 + G3: 3,4 # I3: 1,8 => UNS
* PRF H1: 5,6 + G3: 3,4 # I3: 4,5 => SOL
* STA H1: 5,6 + G3: 3,4 + I3: 4,5
* CNT   5 HDP CHAINS /   5 HYP OPENED