Analysis of zz-www.sudokuwiki.org-0119-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=119
level: medium
position: .7.1.42......9......9...48.4....3.....8.4.19....6....5.26...9......3......17.2.5. initial
Autosolve
position: .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,6 => CTR => A1: 5,8 * DIS # D4: 2,5 => CTR => D4: 8,9 * DIS # E4: 2,5 => CTR => E4: 1,7,8 * DIS # E4: 5,7 => CTR => E4: 1,2,8 * PRF # A5: 5,7 => SOL * DIS # F8: 6,8 => CTR => F8: 1,5,9 * DIS # I9: 6,8 => CTR => I9: 3,4 * CNT 7 HDP CHAINS / 29 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,6 => CTR => A1: 5,8 * DIS A1: 5,8 # D4: 2,5 => CTR => D4: 8,9 * DIS A1: 5,8 + D4: 8,9 # E4: 2,5 => CTR => E4: 1,7,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F8: 6,8 => CTR => F8: 1,5,9 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 # A7: 5,8 => CTR => A7: 3,7 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 7 => CTR => A8: 5,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 1 => CTR => E7: 5,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 # A5: 3,6 => CTR => A5: 2,7 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 1 => CTR => E6: 2,7 * PRF A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 4 => SOL * STA A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 + D8: 4 * CNT 10 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7.1.42......9......9...48.4....3.....8.4.19....6....5.26...9......3......17.2.5. | initial |
| .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5. | autosolve |
| 873154269214896537659327481465913728738245196192678345326581974587439612941762853 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) C1: 3,5 H1: 3,6 D5: 2,5 F5: 5,7 E9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,E4: 1.. / B4 = 1 => 13 pairs (_) / E4 = 1 => 11 pairs (_) H8,I8: 2.. / H8 = 2 => 6 pairs (_) / I8 = 2 => 6 pairs (_) H4,H8: 2.. / H4 = 2 => 6 pairs (_) / H8 = 2 => 6 pairs (_) D2,D3: 3.. / D2 = 3 => 9 pairs (_) / D3 = 3 => 6 pairs (_) I5,G6: 3.. / I5 = 3 => 12 pairs (_) / G6 = 3 => 10 pairs (_) G6,G9: 3.. / G6 = 3 => 10 pairs (_) / G9 = 3 => 12 pairs (_) B2,C2: 4.. / B2 = 4 => 9 pairs (_) / C2 = 4 => 6 pairs (_) D7,D8: 4.. / D7 = 4 => 5 pairs (_) / D8 = 4 => 15 pairs (_) D7,I7: 4.. / D7 = 4 => 5 pairs (_) / I7 = 4 => 15 pairs (_) B9,I9: 4.. / B9 = 4 => 16 pairs (_) / I9 = 4 => 5 pairs (_) C2,C8: 4.. / C2 = 4 => 6 pairs (_) / C8 = 4 => 9 pairs (_) F8,E9: 6.. / F8 = 6 => 0 pairs (X) / E9 = 6 => 6 pairs (_) A1,E1: 8.. / A1 = 8 => 8 pairs (_) / E1 = 8 => 13 pairs (_) D4,F6: 9.. / D4 = 9 => 11 pairs (_) / F6 = 9 => 0 pairs (X) A9,B9: 9.. / A9 = 9 => 5 pairs (_) / B9 = 9 => 16 pairs (_) D8,F8: 9.. / D8 = 9 => 0 pairs (X) / F8 = 9 => 11 pairs (_) B4,D4: 9.. / B4 = 9 => 0 pairs (X) / D4 = 9 => 11 pairs (_) A6,A9: 9.. / A6 = 9 => 16 pairs (_) / A9 = 9 => 5 pairs (_) D4,D8: 9.. / D4 = 9 => 11 pairs (_) / D8 = 9 => 0 pairs (X) F6,F8: 9.. / F6 = 9 => 0 pairs (X) / F8 = 9 => 11 pairs (_) * DURATION: 0:00:22.752853 START: 05:40:06.852798 END: 05:40:29.605651 2017-05-01 * CP COUNT: (20) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D5,E9,F5,H1) * .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5. * PAIR C1: 3,5 BLK 1 A1: 3,5,6,8 # reduction candidate for 3,5 A1: 3,5 # 16 pairs A3: 3,5,1,2,6 # reduction candidate for 3,5 A3: 3,5 # 10 pairs B3: 3,5,1,6 # reduction candidate for 3,5 B3: 3,5 # 8 pairs * PAIR H1: 3,6 BLK 3 H2: 3,6,1,7 # reduction candidate for 3,6 H2: 3,6 # 10 pairs I2: 3,6,1,7 # reduction candidate for 3,6 I2: 3,6 # 8 pairs I3: 3,6,1,7 # reduction candidate for 3,6 I3: 3,6 # 9 pairs * PAIR H1: 3,6 ROW 1 A1: 3,6,5,8 # reduction candidate for 3,6 A1: 3,6 => CTR * .751842.9..4.9.5....9...48.45.913.....8.4.19...3628745.26.519..5.7.39.....1762.5. A1: 5,8 # 6 pairs * PAIR D5: 2,5 BLK 5 D4: 2,5,8,9 # reduction candidate for 2,5 D4: 2,5 => CTR * .7.1.42.9....9.5....9...48.49..13.....8.4.19....689.45.2645.9.....93....9.17.2.5. D4: 8,9 # 6 pairs E4: 2,5,1,7,8 # reduction candidate for 2,5 E4: 2,5 => CTR * .7.1.42.9....9.5171.927.48.415923768..8547192.9.6..345.26...97.....396219.176285. E4: 1,7,8 # 5 pairs * PAIR D5: 2,5 ROW 5 A5: 2,5,3,6,7 # reduction candidate for 2,5 A5: 2,5 # 15 pairs A5: 3,6,7 # 5 pairs * PAIR D5: 2,5 COL D D3: 2,5,3 # reduction candidate for 2,5 D3: 2,5 # 9 pairs D3: 3 # 6 pairs * PAIR F5: 5,7 BLK 5 E4: 5,7,1,2,8 # reduction candidate for 5,7 E4: 5,7 => CTR * .731.4269284.9.5....9.2.48.4159738..768245193..26..745326...97...7.396....176235. E4: 1,2,8 # 5 pairs * PAIR F5: 5,7 ROW 5 A5: 5,7,2,3,6 # reduction candidate for 5,7 A5: 5,7 => SOLVED * 873154269214896537659327481465913728738245196192678345326581974587439612941762853 A5: 2,3,6 # 5 pairs * PAIR F5: 5,7 COL F F3: 5,7,6 # reduction candidate for 5,7 F3: 5,7 # 8 pairs F3: 6 # 7 pairs * PAIR E9: 6,8 BLK 8 F8: 6,8,1,5,9 # reduction candidate for 6,8 F8: 6,8 => CTR * 573184269842396517..9...48.495813.....8.4.193...6.9845326451978.5493.6..981762354 F8: 1,5,9 # 6 pairs * PAIR E9: 6,8 ROW 9 G9: 6,8,3 # reduction candidate for 6,8 G9: 6,8 # 10 pairs I9: 6,8,3,4 # reduction candidate for 6,8 I9: 6,8 => CTR * .731.42692.4.9.53...932.48.4....3.26..824.193.326.9.45326...97....9316..941762358 I9: 3,4 # 6 pairs * PAIR E9: 6,8 COL E E1: 6,8,5 # reduction candidate for 6,8 E1: 6,8 # 13 pairs E1: 5 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0119-base-pr-000.dot * REASONING * DIS # A1: 3,6 => CTR => A1: 5,8 * DIS # D4: 2,5 => CTR => D4: 8,9 * DIS # E4: 2,5 => CTR => E4: 1,7,8 * DIS # E4: 5,7 => CTR => E4: 1,2,8 * PRF # A5: 5,7 => SOL * DIS # F8: 6,8 => CTR => F8: 1,5,9 * DIS # I9: 6,8 => CTR => I9: 3,4 * CNT 7 HDP CHAINS / 29 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C1,D5,E9,F5,H1) * .7.1.42.9....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......17.2.5. * PAIR C1: 3,5 BLK 1 A1: 3,5,6,8 # reduction candidate for 3,5 A1: 3,5 # 16 pairs A3: 3,5,1,2,6 # reduction candidate for 3,5 A3: 3,5 # 10 pairs B3: 3,5,1,6 # reduction candidate for 3,5 B3: 3,5 # 8 pairs * PAIR H1: 3,6 BLK 3 H2: 3,6,1,7 # reduction candidate for 3,6 H2: 3,6 # 10 pairs I2: 3,6,1,7 # reduction candidate for 3,6 I2: 3,6 # 8 pairs I3: 3,6,1,7 # reduction candidate for 3,6 I3: 3,6 # 9 pairs * PAIR H1: 3,6 ROW 1 A1: 3,6,5,8 # reduction candidate for 3,6 A1: 3,6 => CTR * .751842.9..4.9.5....9...48.45.913.....8.4.19...3628745.26.519..5.7.39.....1762.5. * PAIR RESTART * PAIR H1: 3,6 BLK 3 H2: 3,6,1,7 # reduction candidate for 3,6 H2: 3,6 # 11 pairs I2: 3,6,1,7 # reduction candidate for 3,6 I2: 3,6 # 9 pairs I3: 3,6,1,7 # reduction candidate for 3,6 I3: 3,6 # 10 pairs * PAIR D5: 2,5 BLK 5 D4: 2,5,8,9 # reduction candidate for 2,5 D4: 2,5 => CTR * .7.1.42.9....9.5....9...48.49..13.....8.4.19....689.45.2645.9.....93....9.17.2.5. E4: 2,5,1,7,8 # reduction candidate for 2,5 E4: 2,5 => CTR * .731.4269....9.5....9.7.48.41.923.76..8547192...6..345.26...937....396....1762.5. * RESTART * PAIR D5: 2,5 COL D D3: 2,5,3 # reduction candidate for 2,5 D3: 2,5 # 11 pairs D3: 3 # 9 pairs * PAIR F5: 5,7 COL F F3: 5,7,6 # reduction candidate for 5,7 F3: 6 # 12 pairs F3: 5,7 # 11 pairs * PAIR E9: 6,8 BLK 8 F8: 6,8,1,5,9 # reduction candidate for 6,8 F8: 6,8 => CTR * 573184269842.9.53...93.548.495813.....8547193.3.629845326451978.5.938612981762354 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A1,B5,C2,C6,D4,D5,E1,F5,G9,H4) * .731.4269....9.5....9...48.4....3.....8.4.19....6...45.26...9......3......1762.5. * PAIR A1: 5,8 COL A A7: 5,8,3,7 # reduction candidate for 5,8 A7: 5,8 => CTR * 873154269.4289.5...5932.48.465913728.38.4519691.6..345.264.19.....539612391762854 A8: 5,8,7 # reduction candidate for 5,8 A8: 5,8 # 14 pairs * RESTART * PAIR A1: 5,8 COL A A8: 5,8,7 # reduction candidate for 5,8 A8: 7 => CTR * .731.4269..2896537.693754814....3.2...854719....62..45326...97.7...39612..1762.5. * PAIR RESTART * PAIR E1: 5,8 COL E E7: 5,8,1 # reduction candidate for 5,8 E7: 1 => CTR * 873154269.64.9.53..593264874159.3.26638.4.19...26.1.45.26.1.97.5.7.396.2..1762.5. * PAIR RESTART * PAIR B5: 3,6 BLK 4 A5: 3,6,2,7 # reduction candidate for 3,6 A5: 3,6 => CTR * .731.4269....9.5....9...48.4....3..8..8.4.19....6.8345.26...9......39..6..176285. * PAIR C6: 2,7 ROW 6 E6: 2,7,1 # reduction candidate for 2,7 E6: 1 => CTR * .731.4269....9.5....9.2.48.4.5.73.2.7.824519...261.745326...9....7.3..129.1762.5. * PAIR RESTART * PAIR D4: 8,9 COL D D8: 8,9,4 # reduction candidate for 8,9 D8: 4 => SOLVED * 873154269214896537659327481465913728738245196192678345326581974587439612941762853 * DURATION: 0:00:25.403627 START: 05:40:48.394585 END: 05:41:13.798212 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0119-base-pr-001.dot * REASONING * DIS # A1: 3,6 => CTR => A1: 5,8 * DIS A1: 5,8 # D4: 2,5 => CTR => D4: 8,9 * DIS A1: 5,8 + D4: 8,9 # E4: 2,5 => CTR => E4: 1,7,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F8: 6,8 => CTR => F8: 1,5,9 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 # A7: 5,8 => CTR => A7: 3,7 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 7 => CTR => A8: 5,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 1 => CTR => E7: 5,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 # A5: 3,6 => CTR => A5: 2,7 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 1 => CTR => E6: 2,7 * PRF A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 4 => SOL * STA A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 + D8: 4 * CNT 10 HDP CHAINS / 28 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=119
Solution
position: 873154269214896537659327481465913728738245196192678345326581974587439612941762853 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 * INC # A3: 3,5 => UNS * INC # B3: 3,5 => UNS * INC # H2: 3,6 => UNS * INC # I2: 3,6 => UNS * INC # I3: 3,6 => UNS * DIS # A1: 3,6 => CTR => A1: 5,8 * INC # A1: 5,8 => UNS * DIS # D4: 2,5 => CTR => D4: 8,9 * INC # D4: 8,9 => UNS * DIS # E4: 2,5 => CTR => E4: 1,7,8 * INC # E4: 1,7,8 => UNS * INC # A5: 2,5 => UNS * INC # A5: 3,6,7 => UNS * INC # D3: 2,5 => UNS * INC # D3: 3 => UNS * DIS # E4: 5,7 => CTR => E4: 1,2,8 * INC # E4: 1,2,8 => UNS * PRF # A5: 5,7 => SOL * INC # A5: 2,3,6 => UNS * INC # F3: 5,7 => UNS * INC # F3: 6 => UNS * DIS # F8: 6,8 => CTR => F8: 1,5,9 * INC # F8: 1,5,9 => UNS * INC # G9: 6,8 => UNS * DIS # I9: 6,8 => CTR => I9: 3,4 * INC # I9: 3,4 => UNS * INC # E1: 6,8 => UNS * INC # E1: 5 => UNS * CNT 29 HDP CHAINS / 29 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 3,5 => UNS * INC # A3: 3,5 => UNS * INC # B3: 3,5 => UNS * INC # H2: 3,6 => UNS * INC # I2: 3,6 => UNS * INC # I3: 3,6 => UNS * DIS # A1: 3,6 => CTR => A1: 5,8 * INC A1: 5,8 # H2: 3,6 => UNS * INC A1: 5,8 # I2: 3,6 => UNS * INC A1: 5,8 # I3: 3,6 => UNS * DIS A1: 5,8 # D4: 2,5 => CTR => D4: 8,9 * DIS A1: 5,8 + D4: 8,9 # E4: 2,5 => CTR => E4: 1,7,8 * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # D3: 2,5 => UNS * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # D3: 3 => UNS * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F3: 5,7 => UNS * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F3: 6 => UNS * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 # F8: 6,8 => CTR => F8: 1,5,9 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 # A7: 5,8 => CTR => A7: 3,7 * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 5,8 => UNS * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 5,8 => UNS * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 # A8: 7 => CTR => A8: 5,8 * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 5,8 => UNS * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 # E7: 1 => CTR => E7: 5,8 * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 # A5: 3,6 => CTR => A5: 2,7 * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 2,7 => UNS * DIS A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 # E6: 1 => CTR => E6: 2,7 * INC A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 8,9 => UNS * PRF A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 # D8: 4 => SOL * STA A1: 5,8 + D4: 8,9 + E4: 1,7,8 + F8: 1,5,9 + A7: 3,7 + A8: 5,8 + E7: 5,8 + A5: 2,7 + E6: 2,7 + D8: 4 * CNT 28 HDP CHAINS / 28 HYP OPENED