Analysis of zz-www.sudokuwiki.org-0021-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=21
level: medium
position: .34....1...26.........9......6....258...3...9.7....4.8....5...3.....79...6....24. initial
Autosolve
position: 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I3: 4,7 => CTR => I3: 2 * DIS # B5: 1,5 => CTR => B5: 2,4 * PRF # H7: 6,7 => SOL * DIS # E8: 1,8 => CTR => E8: 2,4,6 * PRF # D9: 1,8 => SOL * DIS # F9: 1,8 => CTR => F9: 3,9 * DIS # C9: 1,8 => CTR => C9: 3,5,7,9 * DIS # E8: 2,4,8 => CTR => E8: 1,6 * DIS # A9: 1,7 => CTR => A9: 3,5 * CNT 9 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I3: 4,7 => CTR => I3: 2 * DIS I3: 2 # B5: 1,5 => CTR => B5: 2,4 * DIS I3: 2 + B5: 2,4 # A6: 1,5 => CTR => A6: 2,3 * PRF I3: 2 + B5: 2,4 + A6: 2,3 # H7: 6,7 => SOL * STA I3: 2 + B5: 2,4 + A6: 2,3 + H7: 6,7 * CNT 4 HDP CHAINS / 11 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .34....1...26.........9......6....258...3...9.7....4.8....5...3.....79...6....24. | initial |
| 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24. | autosolve |
| 934825716182673594657491382396748125841532679275916438719254863428367951563189247 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) I2: 4,7 C5: 1,5 H5: 6,7 H6: 3,6 E9: 1,8 I8: 1,6 I9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G4,G5: 1.. / G4 = 1 => 9 pairs (_) / G5 = 1 => 10 pairs (_) I8,I9: 1.. / I8 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) I1,I3: 2.. / I1 = 2 => 0 pairs (X) / I3 = 2 => 7 pairs (_) B5,A6: 2.. / B5 = 2 => 8 pairs (_) / A6 = 2 => 8 pairs (_) G4,H6: 3.. / G4 = 3 => 0 pairs (X) / H6 = 3 => 8 pairs (_) F2,G2: 3.. / F2 = 3 => 7 pairs (_) / G2 = 3 => 11 pairs (_) A4,G4: 3.. / A4 = 3 => 8 pairs (_) / G4 = 3 => 0 pairs (X) H3,H6: 3.. / H3 = 3 => 0 pairs (X) / H6 = 3 => 8 pairs (_) I2,I3: 4.. / I2 = 4 => 7 pairs (_) / I3 = 4 => 0 pairs (X) A9,C9: 5.. / A9 = 5 => 8 pairs (_) / C9 = 5 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) F7,E8: 6.. / F7 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) E8,I8: 6.. / E8 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) E6,E8: 6.. / E6 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) I1,I8: 6.. / I1 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) A2,C3: 7.. / A2 = 7 => 11 pairs (_) / C3 = 7 => 11 pairs (_) G7,H7: 8.. / G7 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) H3,H7: 8.. / H3 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) B4,C6: 9.. / B4 = 9 => 7 pairs (_) / C6 = 9 => 9 pairs (_) B4,B7: 9.. / B4 = 9 => 7 pairs (_) / B7 = 9 => 9 pairs (_) * DURATION: 0:00:26.776714 START: 03:47:33.123061 END: 03:47:59.899775 2017-05-01 * CP COUNT: (20) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E9,H5,H6,I2,I8,I9) * 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24. * PAIR I2: 4,7 BLK 3 I3: 4,7,2 # reduction candidate for 4,7 I3: 4,7 => CTR * 934.7.612.826...9.6...9..8.3.6....258...3..69.7..6.438....56873.18327956.6398.241 I3: 2 # 7 pairs * PAIR I2: 4,7 ROW 2 E2: 4,7,1,8 # reduction candidate for 4,7 E2: 4,7 # 12 pairs E2: 1,8 # 11 pairs * PAIR C5: 1,5 BLK 4 B5: 1,5,2,4 # reduction candidate for 1,5 B5: 1,5 => CTR * 934.2.617..26...946...9..82346...1258...3.769279.6.43849..5687312..47956.6....241 B5: 2,4 # 9 pairs A6: 1,5,2,3 # reduction candidate for 1,5 A6: 1,5 # 12 pairs C6: 1,5,3,9 # reduction candidate for 1,5 C6: 1,5 # 15 pairs * PAIR C5: 1,5 ROW 5 D5: 1,5,2,4,7 # reduction candidate for 1,5 D5: 1,5 # 13 pairs F5: 1,5,2,4,6 # reduction candidate for 1,5 F5: 1,5 # 13 pairs * PAIR C5: 1,5 COL C C3: 1,5,7,8 # reduction candidate for 1,5 C3: 1,5 # 15 pairs C9: 1,5,3,7,8,9 # reduction candidate for 1,5 C9: 1,5 # 12 pairs * PAIR H5: 6,7 BLK 6 G5: 6,7,1 # reduction candidate for 6,7 G5: 1 # 10 pairs G5: 6,7 # 9 pairs * PAIR H5: 6,7 COL H H7: 6,7,8 # reduction candidate for 6,7 H7: 6,7 => SOLVED * 934825716182673594657491382396748125841532679275916438719254863428367951563189247 H7: 8 # 10 pairs * PAIR E9: 1,8 BLK 8 D8: 1,8,2,3,4 # reduction candidate for 1,8 D8: 1,8 # 13 pairs E8: 1,8,2,4,6 # reduction candidate for 1,8 E8: 1,8 => CTR * 934.2.617.8267..94657.943823.6.4..2584..32.6927..6.438....56873..8..7956.6..8.241 E8: 2,4,6 # 7 pairs D9: 1,8,3,9 # reduction candidate for 1,8 D9: 1,8 => SOLVED * 934825716182673594657491382396748125841532679275916438719254863428367951563189247 D9: 3,9 # 8 pairs F9: 1,8,3,9 # reduction candidate for 1,8 F9: 1,8 => CTR * 934.2.716..2673.946.7194..2..6748.2584.23..7927.5194687.9452683428367951.6.981247 F9: 3,9 # 8 pairs * PAIR E9: 1,8 ROW 9 C9: 1,8,3,5,7,9 # reduction candidate for 1,8 C9: 1,8 => CTR * 934.2..16..267..946.7.9...2..6.4..2584..3..7927..1.4.87...5...34...6795156..8.247 C9: 3,5,7,9 # 7 pairs * PAIR E9: 1,8 COL E E2: 1,8,4,7 # reduction candidate for 1,8 E2: 1,8 # 11 pairs E4: 1,8,4,7 # reduction candidate for 1,8 E4: 1,8 # 15 pairs * PAIR I8: 1,6 ROW 8 E8: 1,6,2,4,8 # reduction candidate for 1,6 E8: 2,4,8 => CTR * 934...61..826...9.6...9..8.3.6....258...3..69.7..6.438....56873..83.7956.6398.241 E8: 1,6 # 9 pairs * PAIR I9: 1,7 ROW 9 A9: 1,7,3,5 # reduction candidate for 1,7 A9: 1,7 => CTR * 934....1.7.26...946.8.9..72346.7.125821.3.769579...438.97.5.683.83..795.165.8.247 A9: 3,5 # 8 pairs C9: 1,7,3,5,8,9 # reduction candidate for 1,7 C9: 1,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0021-base-pr-000.dot * REASONING * DIS # I3: 4,7 => CTR => I3: 2 * DIS # B5: 1,5 => CTR => B5: 2,4 * PRF # H7: 6,7 => SOL * DIS # E8: 1,8 => CTR => E8: 2,4,6 * PRF # D9: 1,8 => SOL * DIS # F9: 1,8 => CTR => F9: 3,9 * DIS # C9: 1,8 => CTR => C9: 3,5,7,9 * DIS # E8: 2,4,8 => CTR => E8: 1,6 * DIS # A9: 1,7 => CTR => A9: 3,5 * CNT 9 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,E9,H5,H6,I2,I8,I9) * 934....1...26...9.6...9......6....258...3...9.7....4.8....5...3.....795..6....24. * PAIR I2: 4,7 BLK 3 I3: 4,7,2 # reduction candidate for 4,7 I3: 4,7 => CTR * 934.7.612.826...9.6...9..8.3.6....258...3..69.7..6.438....56873.18327956.6398.241 * PAIR C5: 1,5 BLK 4 B5: 1,5,2,4 # reduction candidate for 1,5 B5: 1,5 => CTR * 934.2.617..26...946...9..82346....258...32.69279.6.43849.2568731...47956.6..8.241 A6: 1,5,2,3 # reduction candidate for 1,5 A6: 1,5 => CTR * 934.2.617..26...946...9..82346....2582..3..69.79.6243849.2568732.8.47956.6..8.241 C6: 1,5,3,9 # reduction candidate for 1,5 C6: 1,5 # 15 pairs * RESTART * PAIR C5: 1,5 BLK 4 C6: 1,5,3,9 # reduction candidate for 1,5 C6: 1,5 # 15 pairs C6: 3,9 # 12 pairs * PAIR C5: 1,5 ROW 5 D5: 1,5,2,4,7 # reduction candidate for 1,5 D5: 1,5 # 21 pairs F5: 1,5,2,4,6 # reduction candidate for 1,5 F5: 1,5 # 23 pairs * PAIR H5: 6,7 BLK 6 G5: 6,7,1 # reduction candidate for 6,7 G5: 6,7 # 19 pairs G5: 1 # 11 pairs * PAIR H5: 6,7 COL H H7: 6,7,8 # reduction candidate for 6,7 H7: 6,7 => SOLVED * 934825716182673594657491382396748125841532679275916438719254863428367951563189247 * DURATION: 0:00:11.589824 START: 03:48:22.470459 END: 03:48:34.060283 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0021-base-pr-001.dot * REASONING * DIS # I3: 4,7 => CTR => I3: 2 * DIS I3: 2 # B5: 1,5 => CTR => B5: 2,4 * DIS I3: 2 + B5: 2,4 # A6: 1,5 => CTR => A6: 2,3 * PRF I3: 2 + B5: 2,4 + A6: 2,3 # H7: 6,7 => SOL * STA I3: 2 + B5: 2,4 + A6: 2,3 + H7: 6,7 * CNT 4 HDP CHAINS / 11 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=21
Solution
position: 934825716182673594657491382396748125841532679275916438719254863428367951563189247 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:
* DIS # I3: 4,7 => CTR => I3: 2 * INC # I3: 2 => UNS * INC # E2: 4,7 => UNS * INC # E2: 1,8 => UNS * DIS # B5: 1,5 => CTR => B5: 2,4 * INC # B5: 2,4 => UNS * INC # A6: 1,5 => UNS * INC # C6: 1,5 => UNS * INC # D5: 1,5 => UNS * INC # F5: 1,5 => UNS * INC # C3: 1,5 => UNS * INC # C9: 1,5 => UNS * INC # G5: 6,7 => UNS * INC # G5: 1 => UNS * PRF # H7: 6,7 => SOL * INC # H7: 8 => UNS * INC # D8: 1,8 => UNS * DIS # E8: 1,8 => CTR => E8: 2,4,6 * INC # E8: 2,4,6 => UNS * PRF # D9: 1,8 => SOL * INC # D9: 3,9 => UNS * DIS # F9: 1,8 => CTR => F9: 3,9 * INC # F9: 3,9 => UNS * DIS # C9: 1,8 => CTR => C9: 3,5,7,9 * INC # C9: 3,5,7,9 => UNS * INC # E2: 1,8 => UNS * INC # E4: 1,8 => UNS * INC # E8: 1,6 => UNS * DIS # E8: 2,4,8 => CTR => E8: 1,6 * DIS # A9: 1,7 => CTR => A9: 3,5 * INC # A9: 3,5 => UNS * INC # C9: 1,7 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I3: 4,7 => CTR => I3: 2 * DIS I3: 2 # B5: 1,5 => CTR => B5: 2,4 * DIS I3: 2 + B5: 2,4 # A6: 1,5 => CTR => A6: 2,3 * INC I3: 2 + B5: 2,4 + A6: 2,3 # C6: 1,5 => UNS * INC I3: 2 + B5: 2,4 + A6: 2,3 # C6: 1,5 => UNS * INC I3: 2 + B5: 2,4 + A6: 2,3 # C6: 3,9 => UNS * INC I3: 2 + B5: 2,4 + A6: 2,3 # D5: 1,5 => UNS * INC I3: 2 + B5: 2,4 + A6: 2,3 # F5: 1,5 => UNS * INC I3: 2 + B5: 2,4 + A6: 2,3 # G5: 6,7 => UNS * INC I3: 2 + B5: 2,4 + A6: 2,3 # G5: 1 => UNS * PRF I3: 2 + B5: 2,4 + A6: 2,3 # H7: 6,7 => SOL * STA I3: 2 + B5: 2,4 + A6: 2,3 + H7: 6,7 * CNT 11 HDP CHAINS / 11 HYP OPENED