Analysis of xx-top500-228-base.sdk
Contents
Original Sudoku
level: medium
position: 5..1............72...8.....1..5..3...6..2..4..........3.......1.4..7........4.5.. initial
Autosolve
position: 52.1.7.34.1345..7279483261517.5.432..6572314.432.1.75.3572..4.1.41.7528328.3415.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E7: 6,9 => SOL * PRF # F6: 6,9 => SOL * DIS # I4: 8,9 => CTR => I4: 6 * PRF # F6: 6,9 => SOL * PRF # I6: 8 => SOL * DIS # I4: 8,9 => CTR => I4: 6 * PRF # E7: 6,9 => SOL * PRF # E7: 6,9 => SOL * CNT 8 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E7: 6,9 => SOL * STA E7: 6,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5..1............72...8.....1..5..3...6..2..4..........3.......1.4..7........4.5.. | initial |
| 52.1.7.34.1345..7279483261517.5.432..6572314.432.1.75.3572..4.1.41.7528328.3415.7 | autosolve |
| 528167934613459872794832615179584326865723149432916758357298461941675283286341597 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 6,8 A2: 6,8 E1: 6,9 F2: 6,9 G1: 8,9 G2: 8,9 C4: 8,9 A5: 8,9 D6: 6,9 I5: 8,9 A8: 6,9 C9: 6,9 D8: 6,9 H7: 6,9 H9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,A2: 6.. / C1 = 6 => 0 pairs (X) / A2 = 6 => 0 pairs (_) E1,F2: 6.. / E1 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) I4,I6: 6.. / I4 = 6 => 17 pairs (_) / I6 = 6 => 0 pairs (X) A8,C9: 6.. / A8 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) H7,H9: 6.. / H7 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) C1,E1: 6.. / C1 = 6 => 0 pairs (X) / E1 = 6 => 0 pairs (_) A2,F2: 6.. / A2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) E4,I4: 6.. / E4 = 6 => 0 pairs (X) / I4 = 6 => 17 pairs (_) A8,D8: 6.. / A8 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) C9,H9: 6.. / C9 = 6 => 0 pairs (*) / H9 = 6 => 0 pairs (X) A2,A8: 6.. / A2 = 6 => 0 pairs (*) / A8 = 6 => 0 pairs (X) C1,C9: 6.. / C1 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) D6,D8: 6.. / D6 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) C1,A2: 8.. / C1 = 8 => 0 pairs (*) / A2 = 8 => 0 pairs (X) G1,G2: 8.. / G1 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) C4,A5: 8.. / C4 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) E4,F6: 8.. / E4 = 8 => 0 pairs (*) / F6 = 8 => 0 pairs (X) E7,F7: 8.. / E7 = 8 => 18 pairs (_) / F7 = 8 => 0 pairs (*) C1,G1: 8.. / C1 = 8 => 0 pairs (*) / G1 = 8 => 0 pairs (X) A2,G2: 8.. / A2 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) A5,I5: 8.. / A5 = 8 => 0 pairs (*) / I5 = 8 => 0 pairs (X) F6,I6: 8.. / F6 = 8 => 18 pairs (_) / I6 = 8 => 0 pairs (*) A2,A5: 8.. / A2 = 8 => 0 pairs (X) / A5 = 8 => 0 pairs (_) C1,C4: 8.. / C1 = 8 => 0 pairs (*) / C4 = 8 => 0 pairs (X) E4,E7: 8.. / E4 = 8 => 0 pairs (*) / E7 = 8 => 0 pairs (X) F6,F7: 8.. / F6 = 8 => 18 pairs (_) / F7 = 8 => 0 pairs (*) E1,F2: 9.. / E1 = 9 => 0 pairs (X) / F2 = 9 => 0 pairs (_) G1,G2: 9.. / G1 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) C4,A5: 9.. / C4 = 9 => 0 pairs (*) / A5 = 9 => 0 pairs (X) A8,C9: 9.. / A8 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) H7,H9: 9.. / H7 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) E1,G1: 9.. / E1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) F2,G2: 9.. / F2 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) A5,I5: 9.. / A5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) A8,D8: 9.. / A8 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) C9,H9: 9.. / C9 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) A5,A8: 9.. / A5 = 9 => 0 pairs (X) / A8 = 9 => 0 pairs (_) C4,C9: 9.. / C4 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D6,D8: 9.. / D6 = 9 => 0 pairs (*) / D8 = 9 => 0 pairs (X) * DURATION: 0:01:04.070318 START: 10:38:30.050741 END: 10:39:34.121059 2017-05-04 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A8,C1,C4,C9,D6,D8,E1,F2,G1,G2,H7,H9,I5) * 52.1.7.34.1345..7279483261517.5.432..6572314.432.1.75.3572..4.1.41.7528328.3415.7 * PAIR E1: 6,9 COL E E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 # 18 pairs E7: 6,9,8 # reduction candidate for 6,9 E7: 6,9 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 E7: 8 # 18 pairs * PAIR F2: 6,9 COL F F6: 6,9,8 # reduction candidate for 6,9 F6: 6,9 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 F6: 8 # 18 pairs F7: 6,9,8 # reduction candidate for 6,9 F7: 6,9 # 18 pairs * PAIR C4: 8,9 ROW 4 E4: 8,9,6 # reduction candidate for 8,9 E4: 8,9 # 17 pairs I4: 8,9,6 # reduction candidate for 8,9 I4: 8,9 => CTR * 52.1.7.34.1345..7279483261517.56432..6572314.432918756357289461941675283286341597 I4: 6 # 17 pairs * PAIR D6: 6,9 BLK 5 E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 # 18 pairs F6: 6,9,8 # reduction candidate for 6,9 F6: 6,9 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 F6: 8 # 18 pairs * PAIR D6: 6,9 ROW 6 I6: 6,9,8 # reduction candidate for 6,9 I6: 8 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 I6: 6,9 # 18 pairs * PAIR I5: 8,9 BLK 6 I4: 8,9,6 # reduction candidate for 8,9 I4: 8,9 => CTR * 52.1.7.34.1345..7279483261517.56432..6572314.432918756357289461941675283286341597 I4: 6 # 17 pairs I6: 8,9,6 # reduction candidate for 8,9 I6: 8,9 # 17 pairs * PAIR D8: 6,9 BLK 8 E7: 6,9,8 # reduction candidate for 6,9 E7: 6,9 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 E7: 8 # 18 pairs F7: 6,9,8 # reduction candidate for 6,9 F7: 6,9 # 18 pairs * PAIR H7: 6,9 ROW 7 E7: 6,9,8 # reduction candidate for 6,9 E7: 6,9 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 E7: 8 # 18 pairs F7: 6,9,8 # reduction candidate for 6,9 F7: 6,9 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-228-base-pr-000.dot * REASONING * PRF # E7: 6,9 => SOL * PRF # F6: 6,9 => SOL * DIS # I4: 8,9 => CTR => I4: 6 * PRF # F6: 6,9 => SOL * PRF # I6: 8 => SOL * DIS # I4: 8,9 => CTR => I4: 6 * PRF # E7: 6,9 => SOL * PRF # E7: 6,9 => SOL * CNT 8 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,A8,C1,C4,C9,D6,D8,E1,F2,G1,G2,H7,H9,I5) * 52.1.7.34.1345..7279483261517.5.432..6572314.432.1.75.3572..4.1.41.7528328.3415.7 * PAIR E1: 6,9 COL E E4: 6,9,8 # reduction candidate for 6,9 E4: 6,9 # 18 pairs E7: 6,9,8 # reduction candidate for 6,9 E7: 6,9 => SOLVED * 528167934613459872794832615179584326865723149432916758357298461941675283286341597 * DURATION: 0:00:02.778797 START: 10:39:57.868784 END: 10:40:00.647581 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-228-base-pr-001.dot * REASONING * PRF # E7: 6,9 => SOL * STA E7: 6,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 228 solution: 528167934613459872794832615179584326865723149432916758357298461941675283286341597 info: 2064 FNWXY S8.f 32649 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 528167934613459872794832615179584326865723149432916758357298461941675283286341597 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 # E4: 6,9 => UNS * PRF # E7: 6,9 => SOL * INC # E7: 8 => UNS * PRF # F6: 6,9 => SOL * INC # F6: 8 => UNS * INC # F7: 6,9 => UNS * INC # E4: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 6 * INC # I4: 6 => UNS * INC # E4: 6,9 => UNS * PRF # F6: 6,9 => SOL * INC # F6: 8 => UNS * INC # I6: 6,9 => UNS * PRF # I6: 8 => SOL * DIS # I4: 8,9 => CTR => I4: 6 * INC # I4: 6 => UNS * INC # I6: 8,9 => UNS * PRF # E7: 6,9 => SOL * INC # E7: 8 => UNS * INC # F7: 6,9 => UNS * PRF # E7: 6,9 => SOL * INC # E7: 8 => UNS * INC # F7: 6,9 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E4: 6,9 => UNS * PRF # E7: 6,9 => SOL * STA E7: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED