Analysis of zz-www.sudokuwiki.org-0142-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=142

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=142

position: ..7...3...9...6..58....5..21.85.........7.........87.94..8....13......4...2.9.6.. initial

Autosolve

position: ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 5,6 => CTR => B1: 1,4
* DIS # B5: 5,6 => CTR => B5: 2,3,4
* DIS # B6: 5,6 => CTR => B6: 2,3,4
* DIS # G5: 2,4 => CTR => G5: 1,5,8
* DIS # B8: 5,6 => CTR => B8: 1,8
* DIS # C8: 5,6 => CTR => C8: 1,9
* DIS # E7: 5,6 => CTR => E7: 2,3
* DIS # B1: 5,6 => CTR => B1: 1,4
* DIS # B5: 5,6 => CTR => B5: 2,3,4
* DIS # B6: 5,6 => CTR => B6: 2,3,4
* DIS # D8: 1,2 => CTR => D8: 6
* DIS # E8: 1,2 => CTR => E8: 5,6
* DIS # F5: 1,2 => CTR => F5: 3,4
* PRF # H9: 3,8 => SOL
* CNT  14 HDP CHAINS /  38 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 # B1: 5,6 => CTR => B1: 1,4
* DIS B1: 1,4 # G5: 2,4 => CTR => G5: 1,5,8
* DIS B1: 1,4 + G5: 1,5,8 # E4: 2,4 => CTR => E4: 3,6
* DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 # C7: 5,6 => CTR => C7: 9
* DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 # C8: 5,6 => CTR => C8: 1
* PRF B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 => SOL
* STA B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1
* CNT   6 HDP CHAINS /   5 HYP OPENED

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

Details

Positions

..7...3...9...6..58....5..21.85.........7.........87.94..8....13......4...2.9.6.. initial
..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6.. autosolve
517924368294386175836715492178569234945273816623148759469837521381652947752491683 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
A1: 5,6
A6: 5,6
G4: 2,4
B7: 5,6
F8: 1,2
I9: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,B6: 2.. / B5 = 2  =>  6 pairs (_) / B6 = 2  =>  6 pairs (_)
E7,H7: 3.. / E7 = 3  => 18 pairs (_) / H7 = 3  =>  0 pairs (X)
F5,F9: 3.. / F5 = 3  =>  7 pairs (_) / F9 = 3  =>  0 pairs (X)
D9,F9: 4.. / D9 = 4  =>  7 pairs (_) / F9 = 4  =>  8 pairs (_)
A1,B1: 5.. / A1 = 5  =>  4 pairs (_) / B1 = 5  =>  0 pairs (X)
E7,E8: 5.. / E7 = 5  =>  0 pairs (X) / E8 = 5  =>  6 pairs (_)
B9,H9: 5.. / B9 = 5  =>  0 pairs (*) / H9 = 5  =>  0 pairs (X)
A1,A6: 5.. / A1 = 5  =>  4 pairs (_) / A6 = 5  =>  0 pairs (X)
A1,A6: 6.. / A1 = 6  =>  0 pairs (X) / A6 = 6  =>  4 pairs (_)
D2,D3: 7.. / D2 = 7  =>  6 pairs (_) / D3 = 7  =>  6 pairs (_)
H2,H3: 7.. / H2 = 7  =>  6 pairs (_) / H3 = 7  =>  6 pairs (_)
D2,H2: 7.. / D2 = 7  =>  6 pairs (_) / H2 = 7  =>  6 pairs (_)
D3,H3: 7.. / D3 = 7  =>  6 pairs (_) / H3 = 7  =>  6 pairs (_)
E1,E2: 8.. / E1 = 8  =>  7 pairs (_) / E2 = 8  =>  8 pairs (_)
B8,B9: 8.. / B8 = 8  =>  7 pairs (_) / B9 = 8  =>  0 pairs (X)
B8,G8: 8.. / B8 = 8  =>  7 pairs (_) / G8 = 8  =>  0 pairs (X)
D1,D3: 9.. / D1 = 9  =>  6 pairs (_) / D3 = 9  =>  0 pairs (X)
C7,C8: 9.. / C7 = 9  => 10 pairs (_) / C8 = 9  => 14 pairs (_)
D1,H1: 9.. / D1 = 9  =>  6 pairs (_) / H1 = 9  =>  0 pairs (X)
C8,G8: 9.. / C8 = 9  => 14 pairs (_) / G8 = 9  => 10 pairs (_)
* DURATION: 0:00:23.780562  START: 06:09:18.918695  END: 06:09:42.699257 2017-05-01
* CP COUNT: (20)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B7,F8,G4,I9)
* ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6..
* PAIR A1: 5,6 BLK 1
B1: 5,6,1,4                              # reduction candidate for 5,6
B1: 5,6 => CTR
* ..79..3..29.3861758.17459621785.94369...735.8..3.687.94.5837291319652847782.94653
B1: 1,4                                  #  5 pairs
* PAIR A6: 5,6 BLK 4
B5: 5,6,2,3,4                            # reduction candidate for 5,6
B5: 5,6 => CTR
* 547...3..291..6..5836..5..21785.9...95..7....62...875946.8.7..13......477.2.9.6..
B5: 2,3,4                                #  6 pairs
C5: 5,6,3,4                              # reduction candidate for 5,6
C5: 5,6                                  #  8 pairs
B6: 5,6,2,3,4                            # reduction candidate for 5,6
B6: 5,6 => CTR
* 547...3..291..64.5836.451.217856923492..735..65342871946583792131965284778219.653
B6: 2,3,4                                #  6 pairs
C6: 5,6,3,4                              # reduction candidate for 5,6
C6: 5,6                                  #  8 pairs
* PAIR A6: 5,6 ROW 6
H6: 5,6,1,2,3                            # reduction candidate for 5,6
H6: 5,6                                  #  8 pairs
H6: 1,2,3                                #  6 pairs
* PAIR G4: 2,4 BLK 6
G5: 2,4,1,5,8                            # reduction candidate for 2,4
G5: 2,4 => CTR
* 5179..3..29...68758.67.51921785.9...9...7....6....87.94698.7521381652947752.9.6..
G5: 1,5,8                                #  6 pairs
* PAIR G4: 2,4 ROW 4
E4: 2,4,3,6                              # reduction candidate for 2,4
E4: 2,4                                  # 10 pairs
E4: 3,6                                  #  7 pairs
* PAIR B7: 5,6 BLK 7
C7: 5,6,9                                # reduction candidate for 5,6
C7: 5,6                                  # 14 pairs
B8: 5,6,1,8                              # reduction candidate for 5,6
B8: 5,6 => CTR
* ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13.....847782.9.653
B8: 1,8                                  #  7 pairs
C8: 5,6,1,9                              # reduction candidate for 5,6
C8: 5,6 => CTR
* ..798.3..29...68758..7.51921785.942.9...7.58......87194.98.723138....947712.9.658
C8: 1,9                                  #  7 pairs
* PAIR B7: 5,6 ROW 7
E7: 5,6,2,3                              # reduction candidate for 5,6
E7: 5,6 => CTR
* ..798.3.429...68758..7.51921785.942.9...7.58......87194.98.723138....947712.9.658
E7: 2,3                                  #  9 pairs
* PAIR B7: 5,6 COL B
B1: 5,6,1,4                              # reduction candidate for 5,6
B1: 5,6 => CTR
* ..79..3..29.3861758.17459621785.94369...735.8..3.687.94.5837291319652847782.94653
B1: 1,4                                  #  5 pairs
B5: 5,6,2,3,4                            # reduction candidate for 5,6
B5: 5,6 => CTR
* 547...3..291..6..5836..5..21785.9...95..7....62...875946.8.7..13......477.2.9.6..
B5: 2,3,4                                #  6 pairs
B6: 5,6,2,3,4                            # reduction candidate for 5,6
B6: 5,6 => CTR
* 547...3..291..64.5836.451.217856923492..735..65342871946583792131965284778219.653
B6: 2,3,4                                #  6 pairs
* PAIR F8: 1,2 BLK 8
D8: 1,2,6                                # reduction candidate for 1,2
D8: 1,2 => CTR
* ..798.3.429...68758..7.51921785394269...74583....287194.98.723138....947712493658
D8: 6                                    #  6 pairs
E8: 1,2,5,6                              # reduction candidate for 1,2
E8: 1,2 => CTR
* .5798.3.429...68758..7.51921785.942.9...7.58......87194698572313856..947712.9.658
E8: 5,6                                  #  7 pairs
* PAIR F8: 1,2 COL F
F1: 1,2,4                                # reduction candidate for 1,2
F1: 1,2                                  #  9 pairs
F5: 1,2,3,4                              # reduction candidate for 1,2
F5: 1,2 => CTR
* 517..43.629...6..58....5..21785.9...9...7....6....87.94..8.7.3138.....477.2493658
F5: 3,4                                  #  7 pairs
* PAIR I9: 3,8 BLK 9
H9: 3,8,5                                # reduction candidate for 3,8
H9: 3,8 => SOLVED
* 517924368294386175836715492178569234945273816623148759469837521381652947752491683
H9: 5                                    #  9 pairs
* PAIR I9: 3,8 COL I
I5: 3,8,4,6                              # reduction candidate for 3,8
I5: 4,6                                  #  9 pairs
I5: 3,8                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0142-base-pr-000.dot
* REASONING
* DIS # B1: 5,6 => CTR => B1: 1,4
* DIS # B5: 5,6 => CTR => B5: 2,3,4
* DIS # B6: 5,6 => CTR => B6: 2,3,4
* DIS # G5: 2,4 => CTR => G5: 1,5,8
* DIS # B8: 5,6 => CTR => B8: 1,8
* DIS # C8: 5,6 => CTR => C8: 1,9
* DIS # E7: 5,6 => CTR => E7: 2,3
* DIS # B1: 5,6 => CTR => B1: 1,4
* DIS # B5: 5,6 => CTR => B5: 2,3,4
* DIS # B6: 5,6 => CTR => B6: 2,3,4
* DIS # D8: 1,2 => CTR => D8: 6
* DIS # E8: 1,2 => CTR => E8: 5,6
* DIS # F5: 1,2 => CTR => F5: 3,4
* PRF # H9: 3,8 => SOL
* CNT  14 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B7,F8,G4,I9)
* ..7...3..29...6..58....5..21785.9...9...7.........87.94..8.7..13......477.2.9.6..
* PAIR A1: 5,6 BLK 1
B1: 5,6,1,4                              # reduction candidate for 5,6
B1: 5,6 => CTR
* ..79..3..29.3861758.17459621785.94369...735.8..3.687.94.5837291319652847782.94653
* PAIR G4: 2,4 BLK 6
G5: 2,4,1,5,8                            # reduction candidate for 2,4
G5: 2,4 => CTR
* 5179..3..29...68758.67.51921785.9...9...7....6....87.94698.7521381652947752.9.6..
* PAIR G4: 2,4 ROW 4
E4: 2,4,3,6                              # reduction candidate for 2,4
E4: 2,4 => CTR
* 5.7...3..29...6..58....5..21785.9..39..67....6....87.94.98.72313.....947712.9.658
* PAIR RESTART
* PAIR B7: 5,6 BLK 7
C7: 5,6,9                                # reduction candidate for 5,6
C7: 5,6 => CTR
* 547..13..29...6..58...451.21785692349241735..6....87194..837921319652847782.94653
C8: 5,6,1                                # reduction candidate for 5,6
C8: 5,6 => CTR
* 547...3.629...6..58....5..21785.9..49...7.5836....87194.98.72.138....947712.9.658
C8: 1 => SOLVED
* 517924368294386175836715492178569234945273816623148759469837521381652947752491683
* DURATION: 0:00:07.490682  START: 06:10:07.450921  END: 06:10:14.941603 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0142-base-pr-001.dot
* REASONING
* DIS # B1: 5,6 => CTR => B1: 1,4
* DIS B1: 1,4 # G5: 2,4 => CTR => G5: 1,5,8
* DIS B1: 1,4 + G5: 1,5,8 # E4: 2,4 => CTR => E4: 3,6
* DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 # C7: 5,6 => CTR => C7: 9
* DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 # C8: 5,6 => CTR => C8: 1
* PRF B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 => SOL
* STA B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1
* CNT   6 HDP CHAINS /   5 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=142

Solution

position: 517924368294386175836715492178569234945273816623148759469837521381652947752491683 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 # B1: 5,6 => CTR => B1: 1,4
* INC # B1: 1,4 => UNS
* DIS # B5: 5,6 => CTR => B5: 2,3,4
* INC # B5: 2,3,4 => UNS
* INC # C5: 5,6 => UNS
* DIS # B6: 5,6 => CTR => B6: 2,3,4
* INC # B6: 2,3,4 => UNS
* INC # C6: 5,6 => UNS
* INC # H6: 5,6 => UNS
* INC # H6: 1,2,3 => UNS
* DIS # G5: 2,4 => CTR => G5: 1,5,8
* INC # G5: 1,5,8 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 3,6 => UNS
* INC # C7: 5,6 => UNS
* DIS # B8: 5,6 => CTR => B8: 1,8
* INC # B8: 1,8 => UNS
* DIS # C8: 5,6 => CTR => C8: 1,9
* INC # C8: 1,9 => UNS
* DIS # E7: 5,6 => CTR => E7: 2,3
* INC # E7: 2,3 => UNS
* DIS # B1: 5,6 => CTR => B1: 1,4
* INC # B1: 1,4 => UNS
* DIS # B5: 5,6 => CTR => B5: 2,3,4
* INC # B5: 2,3,4 => UNS
* DIS # B6: 5,6 => CTR => B6: 2,3,4
* INC # B6: 2,3,4 => UNS
* DIS # D8: 1,2 => CTR => D8: 6
* INC # D8: 6 => UNS
* DIS # E8: 1,2 => CTR => E8: 5,6
* INC # E8: 5,6 => UNS
* INC # F1: 1,2 => UNS
* DIS # F5: 1,2 => CTR => F5: 3,4
* INC # F5: 3,4 => UNS
* PRF # H9: 3,8 => SOL
* INC # H9: 5 => UNS
* INC # I5: 3,8 => UNS
* INC # I5: 4,6 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 5,6 => CTR => B1: 1,4
* DIS B1: 1,4 # G5: 2,4 => CTR => G5: 1,5,8
* DIS B1: 1,4 + G5: 1,5,8 # E4: 2,4 => CTR => E4: 3,6
* DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 # C7: 5,6 => CTR => C7: 9
* DIS B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 # C8: 5,6 => CTR => C8: 1
* PRF B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1 => SOL
* STA B1: 1,4 + G5: 1,5,8 + E4: 3,6 + C7: 9 + C8: 1
* CNT   6 HDP CHAINS /   5 HYP OPENED