Analysis of zz-www.sudokuwiki.org-0012-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=12
level: medium
position: 9..851.....79.6.....5.2....82.....3...1...8...4.....27....6.2.....1.53.....782..6 initial
Autosolve
position: 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C1: 3,6 => SOL * DIS # H3: 4,6 => CTR => H3: 1,8,9 * DIS # H5: 5,9 => CTR => H5: 4,6 * PRF # C6: 6,9 => SOL * DIS # C8: 6,9 => CTR => C8: 2,4,8 * PRF # G4: 4,9 => SOL * DIS # I4: 4,9 => CTR => I4: 1,5 * PRF # G6: 5,6 => SOL * DIS # C8: 4,9 => CTR => C8: 2,6,8 * CNT 9 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C1: 3,6 => SOL * STA C1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 9..851.....79.6.....5.2....82.....3...1...8...4.....27....6.2.....1.53.....782..6 | initial |
| 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6 | autosolve |
| 963851742287946153415327698826579431751234869349618527198463275672195384534782916 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B1: 3,6 E2: 3,4 D3: 3,4 H1: 4,6 C4: 6,9 D4: 5,6 F4: 4,9 D6: 5,6 D7: 3,4 E8: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,I4: 1.. / G4 = 1 => 11 pairs (_) / I4 = 1 => 10 pairs (_) C1,A2: 2.. / C1 = 2 => 12 pairs (_) / A2 = 2 => 11 pairs (_) I1,I2: 2.. / I1 = 2 => 11 pairs (_) / I2 = 2 => 12 pairs (_) A8,C8: 2.. / A8 = 2 => 12 pairs (_) / C8 = 2 => 11 pairs (_) C1,I1: 2.. / C1 = 2 => 12 pairs (_) / I1 = 2 => 11 pairs (_) A2,I2: 2.. / A2 = 2 => 11 pairs (_) / I2 = 2 => 12 pairs (_) A2,A8: 2.. / A2 = 2 => 11 pairs (_) / A8 = 2 => 12 pairs (_) C1,C8: 2.. / C1 = 2 => 12 pairs (_) / C8 = 2 => 11 pairs (_) E2,D3: 3.. / E2 = 3 => 12 pairs (_) / D3 = 3 => 13 pairs (_) A6,C6: 3.. / A6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) E5,F5: 3.. / E5 = 3 => 13 pairs (_) / F5 = 3 => 12 pairs (_) D7,F7: 3.. / D7 = 3 => 12 pairs (_) / F7 = 3 => 13 pairs (_) D3,D7: 3.. / D3 = 3 => 13 pairs (_) / D7 = 3 => 12 pairs (_) E2,E5: 3.. / E2 = 3 => 12 pairs (_) / E5 = 3 => 13 pairs (_) F5,F7: 3.. / F5 = 3 => 12 pairs (_) / F7 = 3 => 13 pairs (_) E2,D3: 4.. / E2 = 4 => 13 pairs (_) / D3 = 4 => 12 pairs (_) D3,D7: 4.. / D3 = 4 => 12 pairs (_) / D7 = 4 => 13 pairs (_) D4,D6: 5.. / D4 = 5 => 11 pairs (_) / D6 = 5 => 0 pairs (X) D4,D6: 6.. / D4 = 6 => 0 pairs (X) / D6 = 6 => 11 pairs (_) A5,B5: 7.. / A5 = 7 => 10 pairs (_) / B5 = 7 => 14 pairs (_) H7,H8: 7.. / H7 = 7 => 12 pairs (_) / H8 = 7 => 11 pairs (_) B2,B3: 8.. / B2 = 8 => 10 pairs (_) / B3 = 8 => 11 pairs (_) C7,C8: 8.. / C7 = 8 => 10 pairs (_) / C8 = 8 => 0 pairs (X) F7,E8: 9.. / F7 = 9 => 12 pairs (_) / E8 = 9 => 14 pairs (_) C6,G6: 9.. / C6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) E5,E8: 9.. / E5 = 9 => 12 pairs (_) / E8 = 9 => 14 pairs (_) * DURATION: 0:00:34.672572 START: 03:35:37.370408 END: 03:36:12.042980 2017-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C4,D3,D4,D6,D7,E2,E8,F4,H1) * 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6 * PAIR B1: 3,6 BLK 1 C1: 3,6,2,4 # reduction candidate for 3,6 C1: 3,6 => SOLVED * 963851742287946153415327698826579431751234869349618527198463275672195384534782916 C1: 2,4 # 11 pairs A3: 3,6,1,4 # reduction candidate for 3,6 A3: 3,6 # 15 pairs B3: 3,6,1,8 # reduction candidate for 3,6 B3: 3,6 # 16 pairs * PAIR E2: 3,4 ROW 2 A2: 3,4,1,2 # reduction candidate for 3,4 A2: 3,4 # 14 pairs I2: 3,4,1,2,5,8 # reduction candidate for 3,4 I2: 3,4 # 13 pairs * PAIR E2: 3,4 COL E E5: 3,4,9 # reduction candidate for 3,4 E5: 3,4 # 14 pairs E5: 9 # 12 pairs * PAIR D3: 3,4 ROW 3 A3: 3,4,1,6 # reduction candidate for 3,4 A3: 3,4 # 13 pairs I3: 3,4,1,8,9 # reduction candidate for 3,4 I3: 3,4 # 14 pairs * PAIR H1: 4,6 BLK 3 G3: 4,6,1,9 # reduction candidate for 4,6 G3: 4,6 # 13 pairs H3: 4,6,1,8,9 # reduction candidate for 4,6 H3: 4,6 => CTR * 9..8517....79.6.....5.27...829.74.3...12..8.4.43.18927....6.2.....1.53....4782..6 H3: 1,8,9 # 10 pairs * PAIR H1: 4,6 ROW 1 C1: 4,6,2,3 # reduction candidate for 4,6 C1: 2,3 # 12 pairs C1: 4,6 # 11 pairs * PAIR H1: 4,6 COL H H5: 4,6,5,9 # reduction candidate for 4,6 H5: 5,9 => CTR * 9..85174...79.6.....5.27169829.74631..12..854543618927..84632.5...1.53....4782..6 H5: 4,6 # 11 pairs * PAIR C4: 6,9 BLK 4 B5: 6,9,5,7 # reduction candidate for 6,9 B5: 6,9 # 13 pairs C6: 6,9,3 # reduction candidate for 6,9 C6: 6,9 => SOLVED * 963851742287946153415327698826579431751234869349618527198463275672195384534782916 C6: 3 # 13 pairs * PAIR C4: 6,9 ROW 4 G4: 6,9,1,4,5 # reduction candidate for 6,9 G4: 6,9 # 17 pairs G4: 1,4,5 # 10 pairs * PAIR C4: 6,9 COL C C8: 6,9,2,4,8 # reduction candidate for 6,9 C8: 6,9 => CTR * 962851743..79.6..2..5.276..8265794317912..8655436189271.8.6.2..27914538...4782..6 C8: 2,4,8 # 10 pairs * PAIR D4: 5,6 ROW 4 G4: 5,6,1,4,9 # reduction candidate for 5,6 G4: 5,6 # 16 pairs G4: 1,4,9 # 10 pairs * PAIR F4: 4,9 BLK 5 E5: 4,9,3 # reduction candidate for 4,9 E5: 4,9 # 12 pairs F5: 4,9,3 # reduction candidate for 4,9 F5: 4,9 # 13 pairs * PAIR F4: 4,9 ROW 4 G4: 4,9,1,5,6 # reduction candidate for 4,9 G4: 4,9 => SOLVED * 963851742287946153415327698826579431751234869349618527198463275672195384534782916 G4: 1,5,6 # 10 pairs I4: 4,9,1,5 # reduction candidate for 4,9 I4: 4,9 => CTR * 96.8517422.79465..4.53276..82657.13...123.865543618.27....6.2..6.21.53.....782..6 I4: 1,5 # 11 pairs * PAIR F4: 4,9 COL F F7: 4,9,3 # reduction candidate for 4,9 F7: 3 # 13 pairs F7: 4,9 # 12 pairs * PAIR D6: 5,6 ROW 6 A6: 5,6,3 # reduction candidate for 5,6 A6: 5,6 # 13 pairs G6: 5,6,9 # reduction candidate for 5,6 G6: 5,6 => SOLVED * 963851742287946153415327698826579431751234869349618527198463275672195384534782916 G6: 9 # 12 pairs * PAIR D7: 3,4 BLK 8 F7: 3,4,9 # reduction candidate for 3,4 F7: 3,4 # 14 pairs F7: 9 # 12 pairs * PAIR E8: 4,9 BLK 8 F7: 4,9,3 # reduction candidate for 4,9 F7: 3 # 13 pairs F7: 4,9 # 12 pairs * PAIR E8: 4,9 ROW 8 C8: 4,9,2,6,8 # reduction candidate for 4,9 C8: 4,9 => CTR * 932851764..7936..26.5427..382..7..3...12.38...4..18.27..836.2..26.1.5378...782..6 C8: 2,6,8 # 10 pairs H8: 4,9,7,8 # reduction candidate for 4,9 H8: 4,9 # 13 pairs I8: 4,9,8 # reduction candidate for 4,9 I8: 4,9 # 13 pairs * PAIR E8: 4,9 COL E E5: 4,9,3 # reduction candidate for 4,9 E5: 3 # 13 pairs E5: 4,9 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0012-base-pr-000.dot * REASONING * PRF # C1: 3,6 => SOL * DIS # H3: 4,6 => CTR => H3: 1,8,9 * DIS # H5: 5,9 => CTR => H5: 4,6 * PRF # C6: 6,9 => SOL * DIS # C8: 6,9 => CTR => C8: 2,4,8 * PRF # G4: 4,9 => SOL * DIS # I4: 4,9 => CTR => I4: 1,5 * PRF # G6: 5,6 => SOL * DIS # C8: 4,9 => CTR => C8: 2,6,8 * CNT 9 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,C4,D3,D4,D6,D7,E2,E8,F4,H1) * 9..8517....79.6.....5.27...82..7..3...12..8...4..18.27....6.2.....1.53.....782..6 * PAIR B1: 3,6 BLK 1 C1: 3,6,2,4 # reduction candidate for 3,6 C1: 3,6 => SOLVED * 963851742287946153415327698826579431751234869349618527198463275672195384534782916 * DURATION: 0:00:02.536880 START: 03:36:49.953972 END: 03:36:52.490852 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0012-base-pr-001.dot * REASONING * PRF # C1: 3,6 => SOL * STA C1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=12
Solution
position: 963851742287946153415327698826579431751234869349618527198463275672195384534782916 solved
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:
* PRF # C1: 3,6 => SOL * INC # C1: 2,4 => UNS * INC # A3: 3,6 => UNS * INC # B3: 3,6 => UNS * INC # A2: 3,4 => UNS * INC # I2: 3,4 => UNS * INC # E5: 3,4 => UNS * INC # E5: 9 => UNS * INC # A3: 3,4 => UNS * INC # I3: 3,4 => UNS * INC # G3: 4,6 => UNS * DIS # H3: 4,6 => CTR => H3: 1,8,9 * INC # H3: 1,8,9 => UNS * INC # C1: 4,6 => UNS * INC # C1: 2,3 => UNS * INC # H5: 4,6 => UNS * DIS # H5: 5,9 => CTR => H5: 4,6 * INC # B5: 6,9 => UNS * PRF # C6: 6,9 => SOL * INC # C6: 3 => UNS * INC # G4: 6,9 => UNS * INC # G4: 1,4,5 => UNS * DIS # C8: 6,9 => CTR => C8: 2,4,8 * INC # C8: 2,4,8 => UNS * INC # G4: 5,6 => UNS * INC # G4: 1,4,9 => UNS * INC # E5: 4,9 => UNS * INC # F5: 4,9 => UNS * PRF # G4: 4,9 => SOL * INC # G4: 1,5,6 => UNS * DIS # I4: 4,9 => CTR => I4: 1,5 * INC # I4: 1,5 => UNS * INC # F7: 4,9 => UNS * INC # F7: 3 => UNS * INC # A6: 5,6 => UNS * PRF # G6: 5,6 => SOL * INC # G6: 9 => UNS * INC # F7: 3,4 => UNS * INC # F7: 9 => UNS * INC # F7: 4,9 => UNS * INC # F7: 3 => UNS * DIS # C8: 4,9 => CTR => C8: 2,6,8 * INC # C8: 2,6,8 => UNS * INC # H8: 4,9 => UNS * INC # I8: 4,9 => UNS * INC # E5: 4,9 => UNS * INC # E5: 3 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C1: 3,6 => SOL * STA C1: 3,6 * CNT 1 HDP CHAINS / 1 HYP OPENED