Analysis of zz-www.sudokuwiki.org-0001-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=1
level: medium
position: ......9...7.2.65...8...9.4....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1...... initial
Autosolve
position: ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B1: 3,5 => CTR => B1: 4,6 * DIS # A3: 3,5 => CTR => A3: 1,6 * DIS # E3: 1,7 => CTR => E3: 3,5 * DIS # C5: 3,5 => CTR => C5: 2,9 * PRF # D1: 1,7 => SOL * DIS # D1: 4 => CTR => D1: 1,7 * DIS # E1: 1,7 => CTR => E1: 3,4,5,8 * DIS # E3: 1,7 => CTR => E3: 3,5 * DIS # D6: 1,7 => CTR => D6: 9 * PRF # D6: 9 => SOL * DIS # A4: 3,9 => CTR => A4: 7,8 * DIS # C4: 3,9 => CTR => C4: 7 * DIS # A5: 3,9 => CTR => A5: 2,5,8 * DIS # C5: 3,9 => CTR => C5: 2,5 * PRF # B6: 3,9 => SOL * DIS # B6: 5 => CTR => B6: 3,9 * DIS # B9: 3,9 => CTR => B9: 4,5,6 * DIS # E8: 4,5 => CTR => E8: 1,6,9 * PRF # B9: 4,5 => SOL * DIS # I9: 4,5 => CTR => I9: 3,6,8 * DIS # E8: 1,6 => CTR => E8: 4,5,9 * CNT 21 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B1: 3,5 => CTR => B1: 4,6 * DIS B1: 4,6 # A3: 3,5 => CTR => A3: 1,6 * DIS B1: 4,6 + A3: 1,6 # E3: 1,7 => CTR => E3: 3,5 * DIS B1: 4,6 + A3: 1,6 + E3: 3,5 # C5: 3,5 => CTR => C5: 2,9 * DIS B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # A1: 3,5 => CTR => A1: 1,2,6 * PRF B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 2,4 => SOL * STA B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 + C1: 2,4 * CNT 6 HDP CHAINS / 14 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......9...7.2.65...8...9.4....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1...... | initial |
| ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... | autosolve |
| 264185937379246518185739246897513462512468379436972851723851694648397125951624783 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C3: 3,5 D3: 1,7 B4: 3,9 F9: 4,5 G8: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,C1: 2.. / A1 = 2 => 5 pairs (_) / C1 = 2 => 6 pairs (_) A5,C5: 2.. / A5 = 2 => 6 pairs (_) / C5 = 2 => 5 pairs (_) A1,A5: 2.. / A1 = 2 => 5 pairs (_) / A5 = 2 => 6 pairs (_) C1,C5: 2.. / C1 = 2 => 6 pairs (_) / C5 = 2 => 5 pairs (_) C2,E2: 4.. / C2 = 4 => 0 pairs (X) / E2 = 4 => 0 pairs (_) H6,H9: 5.. / H6 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) A3,I3: 6.. / A3 = 6 => 6 pairs (_) / I3 = 6 => 6 pairs (_) E4,H4: 6.. / E4 = 6 => 8 pairs (_) / H4 = 6 => 9 pairs (_) D5,D9: 6.. / D5 = 6 => 10 pairs (_) / D9 = 6 => 8 pairs (_) I1,I3: 7.. / I1 = 7 => 6 pairs (_) / I3 = 7 => 8 pairs (_) A4,C4: 7.. / A4 = 7 => 0 pairs (X) / C4 = 7 => 5 pairs (_) D6,E6: 7.. / D6 = 7 => 0 pairs (X) / E6 = 7 => 7 pairs (_) G7,G9: 7.. / G7 = 7 => 5 pairs (_) / G9 = 7 => 5 pairs (_) A9,G9: 7.. / A9 = 7 => 5 pairs (_) / G9 = 7 => 5 pairs (_) C4,C7: 7.. / C4 = 7 => 5 pairs (_) / C7 = 7 => 0 pairs (X) A4,A5: 8.. / A4 = 8 => 6 pairs (_) / A5 = 8 => 0 pairs (X) A2,C2: 9.. / A2 = 9 => 0 pairs (X) / C2 = 9 => 0 pairs (_) I5,I6: 9.. / I5 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) E8,D9: 9.. / E8 = 9 => 8 pairs (_) / D9 = 9 => 0 pairs (X) * DURATION: 0:00:24.329093 START: 03:20:16.875435 END: 03:20:41.204528 2017-05-01 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C3,D3,F9,G8) * ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... * PAIR C3: 3,5 BLK 1 A1: 3,5,1,2,6 # reduction candidate for 3,5 A1: 3,5 # 11 pairs B1: 3,5,4,6 # reduction candidate for 3,5 B1: 3,5 => CTR * 2.4...9..1792465..68...924..9.5..4.2.12....794.6972....2.8...9.5.8397.2.9.1.2.7.. B1: 4,6 # 6 pairs C1: 3,5,2,4 # reduction candidate for 3,5 C1: 3,5 # 12 pairs A3: 3,5,1,6 # reduction candidate for 3,5 A3: 3,5 => CTR * 1624..9.79742.65...8...92468375914622196...754567.2..9.2.8...9..983.7.2..4192..5. A3: 1,6 # 6 pairs * PAIR C3: 3,5 ROW 3 E3: 3,5,1,7 # reduction candidate for 3,5 E3: 1,7 => CTR * 1.24..9.79742.65...8...924.8375914622196...754567.2..9.2.8...9..983.7.2..4192..5. E3: 3,5 # 7 pairs * PAIR C3: 3,5 COL C C5: 3,5,2,9 # reduction candidate for 3,5 C5: 3,5 => CTR * .42...9...792465...8...924.8975..4.221.....794.6972...7248...9.568397124931.2.7.. C5: 2,9 # 6 pairs C7: 3,5,4,7 # reduction candidate for 3,5 C7: 3,5 # 9 pairs * PAIR D3: 1,7 BLK 2 D1: 1,7,4 # reduction candidate for 1,7 D1: 1,7 => SOLVED * 264185937379246518185739246897513462512468379436972851723851694648397125951624783 D1: 4 => CTR * .6.4..9.79742.65...8...9246.3.5..462.1..4..75456..2..9.2.8...94.48397.21.91624.5. E1: 1,7,3,4,5,8 # reduction candidate for 1,7 E1: 1,7 => CTR * .6.4..9..9742.65..18.7.9246.3.5..462.1.....75456172..9.2.8.1.9...83.7124.41.2..5. E1: 3,4,5,8 # 5 pairs E3: 1,7,3,5 # reduction candidate for 1,7 E3: 1,7 => CTR * 1.24..9.79742.65...8...924.8375914622196...754567.2..9.2.8...9..983.7.2..4192..5. E3: 3,5 # 7 pairs * PAIR D3: 1,7 ROW 3 I3: 1,7,3,6 # reduction candidate for 1,7 I3: 1,7 # 8 pairs I3: 3,6 # 7 pairs * PAIR D3: 1,7 COL D D6: 1,7,9 # reduction candidate for 1,7 D6: 1,7 => CTR * .6.4..9.79742.65...8...9246.3.5..462.1..4..75456..2..9.2.8...94.48397.21.91624.5. D6: 9 => SOLVED * 264185937379246518185739246897513462512468379436972851723851694648397125951624783 * PAIR B4: 3,9 BLK 4 A4: 3,9,7,8 # reduction candidate for 3,9 A4: 3,9 => CTR * 2.....9...792465...8...924...75..4.2812493675456..2..9.2.8...9...83.712...1.24.5. A4: 7,8 # 6 pairs C4: 3,9,7 # reduction candidate for 3,9 C4: 3,9 => CTR * 26....9...7.2.65...8...924.7..568412812943675456..28396278..394548397126..1624758 C4: 7 # 5 pairs A5: 3,9,2,5,8 # reduction candidate for 3,9 A5: 3,9 => CTR * 2.....9...792465...8...924.8.75..4.2.124...75456..2..9.2.8...9...83.7.2...1.24.5. A5: 2,5,8 # 5 pairs C5: 3,9,2,5 # reduction candidate for 3,9 C5: 3,9 => CTR * ..24..9...742.65...8...924.8.75..4.221964..75456..2..9.2.8...94.483.7.2..91.24.5. C5: 2,5 # 6 pairs B6: 3,9,5 # reduction candidate for 3,9 B6: 3,9 => SOLVED * 264185937379246518185739246897513462512468379436972851723851694648397125951624783 B6: 5 => CTR * .6.4..9..9742.65...8...9246.3956.4.2.1294.675456..2..962.8...94.48397.2..91624.5. * PAIR B4: 3,9 ROW 4 E4: 3,9,1,6,8 # reduction candidate for 3,9 E4: 3,9 # 18 pairs E4: 1,6,8 # 6 pairs * PAIR B4: 3,9 COL B B9: 3,9,4,5,6 # reduction candidate for 3,9 B9: 3,9 => CTR * .6.4..9..9742.65...8...9246...5..462.1.64..75456..2..9.2.861.945483.7.2...1.24.5. B9: 4,5,6 # 5 pairs * PAIR F9: 4,5 BLK 8 E7: 4,5,1,6 # reduction candidate for 4,5 E7: 4,5 # 12 pairs F7: 4,5,1 # reduction candidate for 4,5 F7: 4,5 # 9 pairs E8: 4,5,1,6,9 # reduction candidate for 4,5 E8: 4,5 => CTR * .6.4..9..9742.65...8.1.9246.395184628126.4375456732..9.27861.94.98347.2..41925... E8: 1,6,9 # 5 pairs * PAIR F9: 4,5 ROW 9 B9: 4,5,3,6,9 # reduction candidate for 4,5 B9: 4,5 => SOLVED * 264185937379246518185739246897513462512468379436972851723851694648397125951624783 B9: 3,6,9 # 5 pairs I9: 4,5,3,6,8 # reduction candidate for 4,5 I9: 4,5 => CTR * ......9...792465...8...924.8.75..4.2.1.4...7.4.6..2.5..2.8...9...83.7.2..6192.... I9: 3,6,8 # 5 pairs * PAIR F9: 4,5 COL F F1: 4,5,1,3,8 # reduction candidate for 4,5 F1: 4,5 # 12 pairs F1: 1,3,8 # 5 pairs * PAIR G8: 1,6 BLK 9 G7: 1,6,3,7 # reduction candidate for 1,6 G7: 1,6 # 11 pairs I7: 1,6,3,4,5 # reduction candidate for 1,6 I7: 1,6 # 8 pairs I8: 1,6,4,5 # reduction candidate for 1,6 I8: 1,6 # 8 pairs * PAIR G8: 1,6 ROW 8 E8: 1,6,4,5,9 # reduction candidate for 1,6 E8: 1,6 => CTR * .6.4..9..9742.65...8...9246.3.5..462.1.6...7.456..2....2.8...955983.7.24.41925... E8: 4,5,9 # 5 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0001-base-pr-000.dot * REASONING * DIS # B1: 3,5 => CTR => B1: 4,6 * DIS # A3: 3,5 => CTR => A3: 1,6 * DIS # E3: 1,7 => CTR => E3: 3,5 * DIS # C5: 3,5 => CTR => C5: 2,9 * PRF # D1: 1,7 => SOL * DIS # D1: 4 => CTR => D1: 1,7 * DIS # E1: 1,7 => CTR => E1: 3,4,5,8 * DIS # E3: 1,7 => CTR => E3: 3,5 * DIS # D6: 1,7 => CTR => D6: 9 * PRF # D6: 9 => SOL * DIS # A4: 3,9 => CTR => A4: 7,8 * DIS # C4: 3,9 => CTR => C4: 7 * DIS # A5: 3,9 => CTR => A5: 2,5,8 * DIS # C5: 3,9 => CTR => C5: 2,5 * PRF # B6: 3,9 => SOL * DIS # B6: 5 => CTR => B6: 3,9 * DIS # B9: 3,9 => CTR => B9: 4,5,6 * DIS # E8: 4,5 => CTR => E8: 1,6,9 * PRF # B9: 4,5 => SOL * DIS # I9: 4,5 => CTR => I9: 3,6,8 * DIS # E8: 1,6 => CTR => E8: 4,5,9 * CNT 21 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C3,D3,F9,G8) * ......9...7.2.65...8...924....5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... * PAIR C3: 3,5 BLK 1 A1: 3,5,1,2,6 # reduction candidate for 3,5 A1: 3,5 # 11 pairs B1: 3,5,4,6 # reduction candidate for 3,5 B1: 3,5 => CTR * 2.4...9..1792465..68...924..9.5..4.2.12....794.6972....2.8...9.5.8397.2.9.1.2.7.. C1: 3,5,2,4 # reduction candidate for 3,5 C1: 3,5 # 12 pairs A3: 3,5,1,6 # reduction candidate for 3,5 A3: 3,5 => CTR * 1624..9.79742.65...8...92468375914622196...754567.2..9.2.8...9..983.7.2..4192..5. * PAIR C3: 3,5 ROW 3 E3: 3,5,1,7 # reduction candidate for 3,5 E3: 1,7 => CTR * .4.1..9671792.65..685..9243...5..4.2.1.....7.4.6..2....2.8...9...83.7.2...1.2.... * PAIR C3: 3,5 COL C C5: 3,5,2,9 # reduction candidate for 3,5 C5: 3,5 => CTR * .42...9...792465...8...924.8975..4.221.....794.6972...7248...9.568397124931.2.7.. C7: 3,5,4,7 # reduction candidate for 3,5 C7: 3,5 # 13 pairs * RESTART * PAIR C3: 3,5 COL C C7: 3,5,4,7 # reduction candidate for 3,5 C7: 3,5 # 13 pairs C7: 4,7 # 10 pairs * PAIR RESTART * PAIR C3: 3,5 BLK 1 A1: 3,5,1,2,6 # reduction candidate for 3,5 A1: 3,5 => CTR * ..2...9..97.2.65..18.7.92468375914.2219....75456..2..9.2.8...9...83.7.2...192..5. C1: 3,5,2,4 # reduction candidate for 3,5 C1: 3,5 # 13 pairs * RESTART * PAIR C3: 3,5 BLK 1 C1: 3,5,2,4 # reduction candidate for 3,5 C1: 2,4 => SOLVED * 264185937379246518185739246897513462512468379436972851723851694648397125951624783 * DURATION: 0:00:12.353030 START: 03:21:16.432863 END: 03:21:28.785893 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0001-base-pr-001.dot * REASONING * DIS # B1: 3,5 => CTR => B1: 4,6 * DIS B1: 4,6 # A3: 3,5 => CTR => A3: 1,6 * DIS B1: 4,6 + A3: 1,6 # E3: 1,7 => CTR => E3: 3,5 * DIS B1: 4,6 + A3: 1,6 + E3: 3,5 # C5: 3,5 => CTR => C5: 2,9 * DIS B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # A1: 3,5 => CTR => A1: 1,2,6 * PRF B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 2,4 => SOL * STA B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 + C1: 2,4 * CNT 6 HDP CHAINS / 14 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=1
Solution
position: 264185937379246518185739246897513462512468379436972851723851694648397125951624783 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:
* INC # A1: 3,5 => UNS * DIS # B1: 3,5 => CTR => B1: 4,6 * INC # B1: 4,6 => UNS * INC # C1: 3,5 => UNS * DIS # A3: 3,5 => CTR => A3: 1,6 * INC # A3: 1,6 => UNS * INC # E3: 3,5 => UNS * DIS # E3: 1,7 => CTR => E3: 3,5 * DIS # C5: 3,5 => CTR => C5: 2,9 * INC # C5: 2,9 => UNS * INC # C7: 3,5 => UNS * PRF # D1: 1,7 => SOL * DIS # D1: 4 => CTR => D1: 1,7 * DIS # E1: 1,7 => CTR => E1: 3,4,5,8 * INC # E1: 3,4,5,8 => UNS * DIS # E3: 1,7 => CTR => E3: 3,5 * INC # E3: 3,5 => UNS * INC # I3: 1,7 => UNS * INC # I3: 3,6 => UNS * DIS # D6: 1,7 => CTR => D6: 9 * PRF # D6: 9 => SOL * DIS # A4: 3,9 => CTR => A4: 7,8 * INC # A4: 7,8 => UNS * DIS # C4: 3,9 => CTR => C4: 7 * INC # C4: 7 => UNS * DIS # A5: 3,9 => CTR => A5: 2,5,8 * INC # A5: 2,5,8 => UNS * DIS # C5: 3,9 => CTR => C5: 2,5 * INC # C5: 2,5 => UNS * PRF # B6: 3,9 => SOL * DIS # B6: 5 => CTR => B6: 3,9 * INC # E4: 3,9 => UNS * INC # E4: 1,6,8 => UNS * DIS # B9: 3,9 => CTR => B9: 4,5,6 * INC # B9: 4,5,6 => UNS * INC # E7: 4,5 => UNS * INC # F7: 4,5 => UNS * DIS # E8: 4,5 => CTR => E8: 1,6,9 * INC # E8: 1,6,9 => UNS * PRF # B9: 4,5 => SOL * INC # B9: 3,6,9 => UNS * DIS # I9: 4,5 => CTR => I9: 3,6,8 * INC # I9: 3,6,8 => UNS * INC # F1: 4,5 => UNS * INC # F1: 1,3,8 => UNS * INC # G7: 1,6 => UNS * INC # I7: 1,6 => UNS * INC # I8: 1,6 => UNS * DIS # E8: 1,6 => CTR => E8: 4,5,9 * INC # E8: 4,5,9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,5 => UNS * DIS # B1: 3,5 => CTR => B1: 4,6 * INC B1: 4,6 # C1: 3,5 => UNS * DIS B1: 4,6 # A3: 3,5 => CTR => A3: 1,6 * INC B1: 4,6 + A3: 1,6 # E3: 3,5 => UNS * DIS B1: 4,6 + A3: 1,6 # E3: 1,7 => CTR => E3: 3,5 * DIS B1: 4,6 + A3: 1,6 + E3: 3,5 # C5: 3,5 => CTR => C5: 2,9 * INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # C7: 3,5 => UNS * INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # C7: 3,5 => UNS * INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # C7: 4,7 => UNS * DIS B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 # A1: 3,5 => CTR => A1: 1,2,6 * INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 3,5 => UNS * INC B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 3,5 => UNS * PRF B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 # C1: 2,4 => SOL * STA B1: 4,6 + A3: 1,6 + E3: 3,5 + C5: 2,9 + A1: 1,2,6 + C1: 2,4 * CNT 14 HDP CHAINS / 14 HYP OPENED