Analysis of xx-top500-344-base.sdk
Contents
Original Sudoku
level: medium
position: ..6....8479.................4.86....5.....9.1...3.....1....9......4...6.......2.. initial
Autosolve
position: 3.69...8479..486.348..36.9.943861...568..49312..39584613.6.94.88.941.36.6.4.83219 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 2,7 => CTR => E1: 5 * PRF # E1: 5 => SOL * PRF # D3: 2,7 => SOL * PRF # H4: 7 => SOL * PRF # D3: 2,7 => SOL * DIS # E1: 2,7 => CTR => E1: 5 * PRF # E1: 5 => SOL * PRF # E7: 2,7 => SOL * DIS # E7: 5 => CTR => E7: 2,7 * DIS # G1: 5,7 => CTR => G1: 1 * DIS # C7: 5,7 => CTR => C7: 2 * PRF # C7: 2 => SOL * PRF # B8: 5,7 => SOL * DIS # B8: 2 => CTR => B8: 5,7 * PRF # E7: 2,7 => SOL * DIS # E7: 5 => CTR => E7: 2,7 * PRF # B8: 5 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 2 => CTR => E7: 5,7 * DIS # D3: 5,7 => CTR => D3: 1,2 * DIS # C7: 5,7 => CTR => C7: 2 * PRF # C7: 2 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 2 => CTR => E7: 5,7 * PRF # B8: 5,7 => SOL * DIS # B8: 2 => CTR => B8: 5,7 * CNT 26 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 2,7 => CTR => E1: 5 * PRF E1: 5 => SOL * STA E1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..6....8479.................4.86....5.....9.1...3.....1....9......4...6.......2.. | initial |
| 3.69...8479..486.348..36.9.943861...568..49312..39584613.6.94.88.941.36.6.4.83219 | autosolve |
| 326957184795148623481236795943861572568724931217395846132679458859412367674583219 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) F1: 2,7 H2: 2,5 B6: 1,7 C6: 1,7 D5: 2,7 E5: 2,7 G4: 5,7 B9: 5,7 F8: 2,7 D9: 5,7 H7: 5,7 I8: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D2,D3: 1.. / D2 = 1 => 13 pairs (_) / D3 = 1 => 15 pairs (_) G1,G3: 1.. / G1 = 1 => 13 pairs (_) / G3 = 1 => 0 pairs (X) B6,C6: 1.. / B6 = 1 => 13 pairs (_) / C6 = 1 => 0 pairs (X) B1,G1: 1.. / B1 = 1 => 0 pairs (X) / G1 = 1 => 13 pairs (_) C2,D2: 1.. / C2 = 1 => 15 pairs (_) / D2 = 1 => 13 pairs (_) B1,B6: 1.. / B1 = 1 => 0 pairs (X) / B6 = 1 => 13 pairs (_) H2,I3: 2.. / H2 = 2 => 15 pairs (_) / I3 = 2 => 14 pairs (_) D5,E5: 2.. / D5 = 2 => 0 pairs (X) / E5 = 2 => 0 pairs (_) H4,I4: 2.. / H4 = 2 => 14 pairs (_) / I4 = 2 => 15 pairs (_) C7,B8: 2.. / C7 = 2 => 0 pairs (*) / B8 = 2 => 0 pairs (X) E7,F8: 2.. / E7 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) C7,E7: 2.. / C7 = 2 => 0 pairs (*) / E7 = 2 => 0 pairs (X) B8,F8: 2.. / B8 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) B1,B8: 2.. / B1 = 2 => 0 pairs (*) / B8 = 2 => 0 pairs (X) F1,F8: 2.. / F1 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) H2,H4: 2.. / H2 = 2 => 15 pairs (_) / H4 = 2 => 14 pairs (_) I3,I4: 2.. / I3 = 2 => 14 pairs (_) / I4 = 2 => 15 pairs (_) E7,D9: 5.. / E7 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) H7,I8: 5.. / H7 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) B8,I8: 5.. / B8 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) B9,D9: 5.. / B9 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) E1,E7: 5.. / E1 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) B6,C6: 7.. / B6 = 7 => 0 pairs (X) / C6 = 7 => 13 pairs (_) D5,E5: 7.. / D5 = 7 => 0 pairs (*) / E5 = 7 => 0 pairs (X) H7,I8: 7.. / H7 = 7 => 16 pairs (_) / I8 = 7 => 0 pairs (*) B9,D9: 7.. / B9 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) C6,C7: 7.. / C6 = 7 => 13 pairs (_) / C7 = 7 => 0 pairs (X) F1,F8: 7.. / F1 = 7 => 0 pairs (*) / F8 = 7 => 0 pairs (X) H4,H7: 7.. / H4 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) * DURATION: 0:01:01.794875 START: 14:29:10.572512 END: 14:30:12.367387 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,C6,D5,D9,E5,F1,F8,G4,H2,H7,I8) * 3.69...8479..486.348..36.9.943861...568..49312..39584613.6.94.88.941.36.6.4.83219 * PAIR F1: 2,7 BLK 2 E1: 2,7,5 # reduction candidate for 2,7 E1: 2,7 => CTR * 32697..8479..486.348..36.9.943861...568..49312..39584613.6594788.9412365654783219 E1: 5 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 D3: 2,7,1,5 # reduction candidate for 2,7 D3: 2,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 D3: 1,5 # 14 pairs * PAIR H2: 2,5 BLK 3 I3: 2,5,7 # reduction candidate for 2,5 I3: 2,5 # 16 pairs I3: 7 # 14 pairs * PAIR H2: 2,5 ROW 2 C2: 2,5,1 # reduction candidate for 2,5 C2: 2,5 # 13 pairs D2: 2,5,1 # reduction candidate for 2,5 D2: 2,5 # 15 pairs * PAIR H2: 2,5 COL H H4: 2,5,7 # reduction candidate for 2,5 H4: 7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 H4: 2,5 # 16 pairs * PAIR D5: 2,7 COL D D3: 2,7,1,5 # reduction candidate for 2,7 D3: 2,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 D3: 1,5 # 14 pairs * PAIR E5: 2,7 COL E E1: 2,7,5 # reduction candidate for 2,7 E1: 2,7 => CTR * 32697..8479..486.348..36.9.943861...568..49312..39584613.6594788.9412365654783219 E1: 5 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 E7: 2,7,5 # reduction candidate for 2,7 E7: 2,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 E7: 5 => CTR * 32697..8479..486.348..36.9.943861...568..49312..3958461326594788.9412365654783219 * PAIR G4: 5,7 BLK 6 H4: 5,7,2 # reduction candidate for 5,7 H4: 5,7 # 15 pairs I4: 5,7,2 # reduction candidate for 5,7 I4: 5,7 # 14 pairs * PAIR G4: 5,7 COL G G1: 5,7,1 # reduction candidate for 5,7 G1: 5,7 => CTR * 3169...8479.1486.348..3619.943861...568..49312713958461376294588.941.36.6.4.83219 G1: 1 # 13 pairs G3: 5,7,1 # reduction candidate for 5,7 G3: 5,7 # 13 pairs * PAIR B9: 5,7 BLK 7 C7: 5,7,2 # reduction candidate for 5,7 C7: 5,7 => CTR * 35697..8479..486.348..36.9.943861...568..49312..39584613.6294.8829417365674583219 C7: 2 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 B8: 5,7,2 # reduction candidate for 5,7 B8: 5,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 B8: 2 => CTR * 3569.218479.148653481736.9.943861...568..49312..39584613.6.94.8829417365674583219 * PAIR F8: 2,7 BLK 8 E7: 2,7,5 # reduction candidate for 2,7 E7: 2,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 E7: 5 => CTR * 32697..8479..486.348..36.9.943861...568..49312..3958461326594788.9412365654783219 * PAIR F8: 2,7 ROW 8 B8: 2,7,5 # reduction candidate for 2,7 B8: 5 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 B8: 2,7 # 16 pairs * PAIR D9: 5,7 BLK 8 E7: 5,7,2 # reduction candidate for 5,7 E7: 5,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 E7: 2 => CTR * 3.695..8479..486.348..36.9.943861...568.749312..39584613.6294.88294173656.4.83219 * PAIR D9: 5,7 COL D D3: 5,7,1,2 # reduction candidate for 5,7 D3: 5,7 => CTR * 3569...8479.1486.348..36.9.943861...5682749312..39584613.6294.8829417365674583219 D3: 1,2 # 14 pairs * PAIR H7: 5,7 ROW 7 C7: 5,7,2 # reduction candidate for 5,7 C7: 5,7 => CTR * 35697..8479..486.348..36.9.943861...568..49312..39584613.6294.8829417365674583219 C7: 2 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 E7: 5,7,2 # reduction candidate for 5,7 E7: 5,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 E7: 2 => CTR * 3.695..8479..486.348..36.9.943861...568.749312..39584613.6294.88294173656.4.83219 * PAIR H7: 5,7 COL H H4: 5,7,2 # reduction candidate for 5,7 H4: 5,7 # 15 pairs H4: 2 # 14 pairs * PAIR I8: 5,7 ROW 8 B8: 5,7,2 # reduction candidate for 5,7 B8: 5,7 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 B8: 2 => CTR * 3569.218479.148653481736.9.943861...568..49312..39584613.6.94.8829417365674583219 * PAIR I8: 5,7 COL I I3: 5,7,2 # reduction candidate for 5,7 I3: 5,7 # 15 pairs I4: 5,7,2 # reduction candidate for 5,7 I4: 5,7 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-344-base-pr-000.dot * REASONING * DIS # E1: 2,7 => CTR => E1: 5 * PRF # E1: 5 => SOL * PRF # D3: 2,7 => SOL * PRF # H4: 7 => SOL * PRF # D3: 2,7 => SOL * DIS # E1: 2,7 => CTR => E1: 5 * PRF # E1: 5 => SOL * PRF # E7: 2,7 => SOL * DIS # E7: 5 => CTR => E7: 2,7 * DIS # G1: 5,7 => CTR => G1: 1 * DIS # C7: 5,7 => CTR => C7: 2 * PRF # C7: 2 => SOL * PRF # B8: 5,7 => SOL * DIS # B8: 2 => CTR => B8: 5,7 * PRF # E7: 2,7 => SOL * DIS # E7: 5 => CTR => E7: 2,7 * PRF # B8: 5 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 2 => CTR => E7: 5,7 * DIS # D3: 5,7 => CTR => D3: 1,2 * DIS # C7: 5,7 => CTR => C7: 2 * PRF # C7: 2 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 2 => CTR => E7: 5,7 * PRF # B8: 5,7 => SOL * DIS # B8: 2 => CTR => B8: 5,7 * CNT 26 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B6,B9,C6,D5,D9,E5,F1,F8,G4,H2,H7,I8) * 3.69...8479..486.348..36.9.943861...568..49312..39584613.6.94.88.941.36.6.4.83219 * PAIR F1: 2,7 BLK 2 E1: 2,7,5 # reduction candidate for 2,7 E1: 2,7 => CTR * 32697..8479..486.348..36.9.943861...568..49312..39584613.6594788.9412365654783219 E1: 5 => SOLVED * 326957184795148623481236795943861572568724931217395846132679458859412367674583219 * DURATION: 0:00:01.939969 START: 14:31:10.563373 END: 14:31:12.503342 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-344-base-pr-001.dot * REASONING * DIS # E1: 2,7 => CTR => E1: 5 * PRF E1: 5 => SOL * STA E1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 344 solution: 326957184795148623481236795943861572568724931217395846132679458859412367674583219 info: 3422 FNBHWXY S8.f 42260 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 326957184795148623481236795943861572568724931217395846132679458859412367674583219 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 # E1: 2,7 => CTR => E1: 5 * PRF # E1: 5 => SOL * PRF # D3: 2,7 => SOL * INC # D3: 1,5 => UNS * INC # I3: 2,5 => UNS * INC # I3: 7 => UNS * INC # C2: 2,5 => UNS * INC # D2: 2,5 => UNS * INC # H4: 2,5 => UNS * PRF # H4: 7 => SOL * PRF # D3: 2,7 => SOL * INC # D3: 1,5 => UNS * DIS # E1: 2,7 => CTR => E1: 5 * PRF # E1: 5 => SOL * PRF # E7: 2,7 => SOL * DIS # E7: 5 => CTR => E7: 2,7 * INC # H4: 5,7 => UNS * INC # I4: 5,7 => UNS * DIS # G1: 5,7 => CTR => G1: 1 * INC # G1: 1 => UNS * INC # G3: 5,7 => UNS * DIS # C7: 5,7 => CTR => C7: 2 * PRF # C7: 2 => SOL * PRF # B8: 5,7 => SOL * DIS # B8: 2 => CTR => B8: 5,7 * PRF # E7: 2,7 => SOL * DIS # E7: 5 => CTR => E7: 2,7 * INC # B8: 2,7 => UNS * PRF # B8: 5 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 2 => CTR => E7: 5,7 * DIS # D3: 5,7 => CTR => D3: 1,2 * INC # D3: 1,2 => UNS * DIS # C7: 5,7 => CTR => C7: 2 * PRF # C7: 2 => SOL * PRF # E7: 5,7 => SOL * DIS # E7: 2 => CTR => E7: 5,7 * INC # H4: 5,7 => UNS * INC # H4: 2 => UNS * PRF # B8: 5,7 => SOL * DIS # B8: 2 => CTR => B8: 5,7 * INC # I3: 5,7 => UNS * INC # I4: 5,7 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 2,7 => CTR => E1: 5 * PRF E1: 5 => SOL * STA E1: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED