Analysis of xx-top500-008-base.sdk
Contents
Original Sudoku
level: medium
position: ....25.1..3...........1.....4.3..6...7....4..5........8..6........4..3..1......2. initial
Autosolve
position: 469.25.13231...5..7859132649423..6.137.1.94.251.2..93.8536.214.6274.13.519453..26 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H2: 7,8 => SOL * DIS # H2: 9 => CTR => H2: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * DIS # E6: 4,6 => CTR => E6: 7,8 * PRF # H2: 7,8 => SOL * DIS # H2: 9 => CTR => H2: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * DIS # E5: 5 => CTR => E5: 6,8 * DIS # E6: 6,8 => CTR => E6: 4,7 * DIS # E4: 7,8 => CTR => E4: 5 * DIS # H4: 5 => CTR => H4: 7,8 * DIS # E6: 4,6 => CTR => E6: 7,8 * DIS # H4: 5,8 => CTR => H4: 7 * PRF # H4: 7 => SOL * DIS # E5: 5,8 => CTR => E5: 6 * DIS # H4: 5 => CTR => H4: 7,8 * DIS # E6: 4,6 => CTR => E6: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # I2: 7,9 => SOL * DIS # I2: 8 => CTR => I2: 7,9 * PRF # H2: 8,9 => SOL * DIS # H2: 7 => CTR => H2: 8,9 * CNT 25 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H2: 7,8 => SOL * STA H2: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....25.1..3...........1.....4.3..6...7....4..5........8..6........4..3..1......2. | initial |
| 469.25.13231...5..7859132649423..6.137.1.94.251.2..93.8536.214.6274.13.519453..26 | autosolve |
| 469825713231746589785913264942358671378169452516274938853692147627481395194537826 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) D1: 7,8 D2: 7,8 E2: 4,6 F2: 4,6 G1: 7,8 C5: 6,8 C6: 6,8 F4: 7,8 F6: 4,6 H5: 5,8 I6: 7,8 E7: 7,9 E8: 8,9 F9: 7,8 I7: 7,9 H8: 8,9 G9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 4.. / E2 = 4 => 14 pairs (_) / F2 = 4 => 0 pairs (X) E6,F6: 4.. / E6 = 4 => 0 pairs (X) / F6 = 4 => 14 pairs (_) E2,E6: 4.. / E2 = 4 => 14 pairs (_) / E6 = 4 => 0 pairs (X) F2,F6: 4.. / F2 = 4 => 0 pairs (X) / F6 = 4 => 14 pairs (_) E4,E5: 5.. / E4 = 5 => 18 pairs (_) / E5 = 5 => 0 pairs (X) H4,H5: 5.. / H4 = 5 => 0 pairs (X) / H5 = 5 => 18 pairs (_) E4,H4: 5.. / E4 = 5 => 18 pairs (_) / H4 = 5 => 0 pairs (X) E5,H5: 5.. / E5 = 5 => 0 pairs (X) / H5 = 5 => 18 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (X) / F2 = 6 => 14 pairs (_) C5,C6: 6.. / C5 = 6 => 0 pairs (X) / C6 = 6 => 13 pairs (_) C5,E5: 6.. / C5 = 6 => 0 pairs (X) / E5 = 6 => 13 pairs (_) F2,F6: 6.. / F2 = 6 => 14 pairs (_) / F6 = 6 => 0 pairs (X) D1,D2: 7.. / D1 = 7 => 0 pairs (X) / D2 = 7 => 0 pairs (_) H4,I6: 7.. / H4 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) E7,F9: 7.. / E7 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) I7,G9: 7.. / I7 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) D1,G1: 7.. / D1 = 7 => 0 pairs (X) / G1 = 7 => 0 pairs (_) E6,I6: 7.. / E6 = 7 => 0 pairs (*) / I6 = 7 => 0 pairs (X) E7,I7: 7.. / E7 = 7 => 0 pairs (X) / I7 = 7 => 0 pairs (_) F9,G9: 7.. / F9 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) F4,F9: 7.. / F4 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) G1,G9: 7.. / G1 = 7 => 0 pairs (*) / G9 = 7 => 0 pairs (X) H2,H4: 7.. / H2 = 7 => 0 pairs (X) / H4 = 7 => 0 pairs (_) D1,D2: 8.. / D1 = 8 => 0 pairs (*) / D2 = 8 => 0 pairs (X) C5,C6: 8.. / C5 = 8 => 13 pairs (_) / C6 = 8 => 0 pairs (X) E8,F9: 8.. / E8 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) H8,G9: 8.. / H8 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) D1,G1: 8.. / D1 = 8 => 0 pairs (*) / G1 = 8 => 0 pairs (X) E8,H8: 8.. / E8 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) F9,G9: 8.. / F9 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) F4,F9: 8.. / F4 = 8 => 0 pairs (*) / F9 = 8 => 0 pairs (X) G1,G9: 8.. / G1 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) I2,I6: 8.. / I2 = 8 => 0 pairs (X) / I6 = 8 => 0 pairs (_) H2,I2: 9.. / H2 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) E7,E8: 9.. / E7 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) I7,H8: 9.. / I7 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) E7,I7: 9.. / E7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) E8,H8: 9.. / E8 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) H2,H8: 9.. / H2 = 9 => 0 pairs (X) / H8 = 9 => 0 pairs (_) I2,I7: 9.. / I2 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:28.846744 START: 02:51:33.275448 END: 02:53:02.122192 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C6,D1,D2,E2,E7,E8,F2,F4,F6,F9,G1,G9,H5,H8,I6,I7) * 469.25.13231...5..7859132649423..6.137.1.94.251.2..93.8536.214.6274.13.519453..26 * PAIR D2: 7,8 ROW 2 H2: 7,8,9 # reduction candidate for 7,8 H2: 7,8 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 H2: 9 => CTR * 469.25.13231...59.7859132649423..67137.1.945251.2749388536.214.6274.13.519453..26 I2: 7,8,9 # reduction candidate for 7,8 I2: 7,8 => CTR * 469.25.13231...59.7859132649423..67137.1.945251.2749388536.214.6274.13.519453..26 I2: 9 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 * PAIR E2: 4,6 COL E E6: 4,6,7,8 # reduction candidate for 4,6 E6: 4,6 => CTR * 469.25.13231...5..7859132649423..6.137.1.94.251.2..93785367214962749138519453..26 E6: 7,8 # 13 pairs * PAIR G1: 7,8 BLK 3 H2: 7,8,9 # reduction candidate for 7,8 H2: 7,8 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 H2: 9 => CTR * 469.25.13231...59.7859132649423..67137.1.945251.2749388536.214.6274.13.519453..26 I2: 7,8,9 # reduction candidate for 7,8 I2: 7,8 => CTR * 469.25.13231...59.7859132649423..67137.1.945251.2749388536.214.6274.13.519453..26 I2: 9 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 * PAIR C5: 6,8 ROW 5 E5: 6,8,5 # reduction candidate for 6,8 E5: 5 => CTR * 469.25.13231...5..7859132649423..6.13761594825182..9378536721496274.13.519453..26 E5: 6,8 # 18 pairs * PAIR C6: 6,8 ROW 6 E6: 6,8,4,7 # reduction candidate for 6,8 E6: 6,8 => CTR * 469.25.13231.465..7859132649423..6.137.1.94.251.2.493785367214962749138519453..26 E6: 4,7 # 18 pairs * PAIR F4: 7,8 BLK 5 E4: 7,8,5 # reduction candidate for 7,8 E4: 7,8 => CTR * 469.25.13231...5..7859132649423..65137.1594825182..9378536721496274.13.519453..26 E4: 5 # 18 pairs E6: 7,8,4,6 # reduction candidate for 7,8 E6: 7,8 # 13 pairs * PAIR F4: 7,8 ROW 4 H4: 7,8,5 # reduction candidate for 7,8 H4: 5 => CTR * 469.25.13231...5797859132649423..65137.1.94.251.2..93.8536.214.6274.13.519453..26 H4: 7,8 # 18 pairs * PAIR F6: 4,6 BLK 5 E6: 4,6,7,8 # reduction candidate for 4,6 E6: 4,6 => CTR * 469.25.13231...5..7859132649423..6.137.1.94.251.2..93785367214962749138519453..26 E6: 7,8 # 13 pairs * PAIR H5: 5,8 BLK 6 H4: 5,8,7 # reduction candidate for 5,8 H4: 5,8 => CTR * 469.25.13231...5797859132649423..6.137.1.94.251.2..93.8536.214.6274.13.519453..26 H4: 7 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 * PAIR H5: 5,8 ROW 5 E5: 5,8,6 # reduction candidate for 5,8 E5: 5,8 => CTR * 469.25.13231...5..7859132649423..6.13761.94.25182..93785367214962749138519453..26 E5: 6 # 13 pairs * PAIR I6: 7,8 BLK 6 H4: 7,8,5 # reduction candidate for 7,8 H4: 5 => CTR * 469.25.13231...5797859132649423..65137.1.94.251.2..93.8536.214.6274.13.519453..26 H4: 7,8 # 18 pairs * PAIR I6: 7,8 ROW 6 E6: 7,8,4,6 # reduction candidate for 7,8 E6: 4,6 => CTR * 469.25.13231...5..7859132649423..6.137.1.94.251.2..93785367214962749138519453..26 E6: 7,8 # 13 pairs * PAIR I6: 7,8 COL I I2: 7,8,9 # reduction candidate for 7,8 I2: 7,8 => CTR * 469.25.13231...59.7859132649423..67137.1.945251.2749388536.214.6274.13.519453..26 I2: 9 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 * PAIR I7: 7,9 COL I I2: 7,9,8 # reduction candidate for 7,9 I2: 7,9 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 I2: 8 => CTR * 469.25.13231...5987859132649423..67137.1.94.251.2..93.8536.214.6274.13.519453..26 * PAIR H8: 8,9 COL H H2: 8,9,7 # reduction candidate for 8,9 H2: 8,9 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 H2: 7 => CTR * 469.25.13231...5797859132649423..6.137.1.94.251.2..93.8536.214.6274.13.519453..26 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-008-base-pr-000.dot * REASONING * PRF # H2: 7,8 => SOL * DIS # H2: 9 => CTR => H2: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * DIS # E6: 4,6 => CTR => E6: 7,8 * PRF # H2: 7,8 => SOL * DIS # H2: 9 => CTR => H2: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * DIS # E5: 5 => CTR => E5: 6,8 * DIS # E6: 6,8 => CTR => E6: 4,7 * DIS # E4: 7,8 => CTR => E4: 5 * DIS # H4: 5 => CTR => H4: 7,8 * DIS # E6: 4,6 => CTR => E6: 7,8 * DIS # H4: 5,8 => CTR => H4: 7 * PRF # H4: 7 => SOL * DIS # E5: 5,8 => CTR => E5: 6 * DIS # H4: 5 => CTR => H4: 7,8 * DIS # E6: 4,6 => CTR => E6: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # I2: 7,9 => SOL * DIS # I2: 8 => CTR => I2: 7,9 * PRF # H2: 8,9 => SOL * DIS # H2: 7 => CTR => H2: 8,9 * CNT 25 HDP CHAINS / 35 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C5,C6,D1,D2,E2,E7,E8,F2,F4,F6,F9,G1,G9,H5,H8,I6,I7) * 469.25.13231...5..7859132649423..6.137.1.94.251.2..93.8536.214.6274.13.519453..26 * PAIR D2: 7,8 ROW 2 H2: 7,8,9 # reduction candidate for 7,8 H2: 7,8 => SOLVED * 469825713231746589785913264942358671378169452516274938853692147627481395194537826 * DURATION: 0:00:02.282889 START: 02:53:49.154574 END: 02:53:51.437463 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-008-base-pr-001.dot * REASONING * PRF # H2: 7,8 => SOL * STA H2: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 008 solution: 469825713231746589785913264942358671378169452516274938853692147627481395194537826 info: 1307 FNBTWXY S8.f 3595 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 469825713231746589785913264942358671378169452516274938853692147627481395194537826 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:
* PRF # H2: 7,8 => SOL * DIS # H2: 9 => CTR => H2: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * DIS # E6: 4,6 => CTR => E6: 7,8 * INC # E6: 7,8 => UNS * PRF # H2: 7,8 => SOL * DIS # H2: 9 => CTR => H2: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * INC # E5: 6,8 => UNS * DIS # E5: 5 => CTR => E5: 6,8 * DIS # E6: 6,8 => CTR => E6: 4,7 * INC # E6: 4,7 => UNS * DIS # E4: 7,8 => CTR => E4: 5 * INC # E4: 5 => UNS * INC # E6: 7,8 => UNS * INC # H4: 7,8 => UNS * DIS # H4: 5 => CTR => H4: 7,8 * DIS # E6: 4,6 => CTR => E6: 7,8 * INC # E6: 7,8 => UNS * DIS # H4: 5,8 => CTR => H4: 7 * PRF # H4: 7 => SOL * DIS # E5: 5,8 => CTR => E5: 6 * INC # E5: 6 => UNS * INC # H4: 7,8 => UNS * DIS # H4: 5 => CTR => H4: 7,8 * INC # E6: 7,8 => UNS * DIS # E6: 4,6 => CTR => E6: 7,8 * DIS # I2: 7,8 => CTR => I2: 9 * PRF # I2: 9 => SOL * PRF # I2: 7,9 => SOL * DIS # I2: 8 => CTR => I2: 7,9 * PRF # H2: 8,9 => SOL * DIS # H2: 7 => CTR => H2: 8,9 * CNT 35 HDP CHAINS / 35 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H2: 7,8 => SOL * STA H2: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED