Analysis of xx-top500-130-base.sdk
Contents
Original Sudoku
level: medium
position: .6.3.2.....8...41........9..3.5..6......1..2.............7..3..9...2....1........ initial
Autosolve
position: 461392...2986..4133..1..296.325.96.1....13.2..1.2...3..2.7.13.99.3.2.1..1..93...2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 5,7 => CTR => B9: 4,8 * DIS # E6: 4,8 => CTR => E6: 6,7 * DIS # E7: 4,8 => CTR => E7: 5,6 * DIS # F6: 4,8 => CTR => F6: 6,7 * PRF # F8: 4,8 => SOL * PRF # A5: 7,8 => SOL * DIS # E4: 7,8 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H4: 7,8 => SOL * DIS # H4: 4 => CTR => H4: 7,8 * DIS # E6: 4,8 => CTR => E6: 6,7 * DIS # F6: 4,8 => CTR => F6: 6,7 * DIS # I5: 4,8 => CTR => I5: 5,7 * DIS # E7: 4,8 => CTR => E7: 5,6 * PRF # F8: 4,8 => SOL * DIS # B8: 4,8 => CTR => B8: 5,7 * DIS # H8: 4,8 => CTR => H8: 5,6,7 * CNT 17 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 5,7 => CTR => B9: 4,8 * DIS B9: 4,8 # B8: 4,8 => CTR => B8: 5,7 * DIS B9: 4,8 + B8: 5,7 # E6: 4,8 => CTR => E6: 6,7 * DIS B9: 4,8 + B8: 5,7 + E6: 6,7 # E7: 4,8 => CTR => E7: 5,6 * PRF B9: 4,8 + B8: 5,7 + E6: 6,7 + E7: 5,6 # F8: 4,8 => SOL * STA B9: 4,8 + B8: 5,7 + E6: 6,7 + E7: 5,6 + F8: 4,8 * CNT 5 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.3.2.....8...41........9..3.5..6......1..2.............7..3..9...2....1........ | initial |
| 461392...2986..4133..1..296.325.96.1....13.2..1.2...3..2.7.13.99.3.2.1..1..93...2 | autosolve |
| 461392758298675413375184296832549671746813925519267834624751389953428167187936542 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B3: 5,7 C3: 5,7 E2: 5,7 F2: 5,7 E3: 4,8 F3: 4,8 A4: 7,8 D5: 4,8 D8: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 4.. / E3 = 4 => 0 pairs (X) / F3 = 4 => 8 pairs (_) E4,H4: 4.. / E4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) D5,D8: 4.. / D5 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) B3,C3: 5.. / B3 = 5 => 9 pairs (_) / C3 = 5 => 10 pairs (_) E2,F2: 5.. / E2 = 5 => 7 pairs (_) / F2 = 5 => 17 pairs (_) E2,E7: 5.. / E2 = 5 => 7 pairs (_) / E7 = 5 => 17 pairs (_) A5,C5: 6.. / A5 = 6 => 11 pairs (_) / C5 = 6 => 0 pairs (*) E6,F6: 6.. / E6 = 6 => 9 pairs (_) / F6 = 6 => 14 pairs (_) F8,H8: 6.. / F8 = 6 => 9 pairs (_) / H8 = 6 => 9 pairs (_) A5,A7: 6.. / A5 = 6 => 11 pairs (_) / A7 = 6 => 0 pairs (*) E6,E7: 6.. / E6 = 6 => 9 pairs (_) / E7 = 6 => 14 pairs (_) B3,C3: 7.. / B3 = 7 => 10 pairs (_) / C3 = 7 => 9 pairs (_) E2,F2: 7.. / E2 = 7 => 17 pairs (_) / F2 = 7 => 7 pairs (_) C3,C9: 7.. / C3 = 7 => 9 pairs (_) / C9 = 7 => 10 pairs (_) F2,F6: 7.. / F2 = 7 => 7 pairs (_) / F6 = 7 => 17 pairs (_) E3,F3: 8.. / E3 = 8 => 8 pairs (_) / F3 = 8 => 0 pairs (X) D5,D8: 8.. / D5 = 8 => 0 pairs (*) / D8 = 8 => 0 pairs (X) C5,C6: 9.. / C5 = 9 => 12 pairs (_) / C6 = 9 => 0 pairs (*) G5,G6: 9.. / G5 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) C5,G5: 9.. / C5 = 9 => 12 pairs (_) / G5 = 9 => 0 pairs (*) C6,G6: 9.. / C6 = 9 => 0 pairs (*) / G6 = 9 => 0 pairs (X) * DURATION: 0:00:36.260069 START: 07:12:43.484598 END: 07:13:19.744667 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,C3,D5,D8,E2,E3,F2,F3) * 461392...2986..4133..1..296.325.96.1....13.2..1.2...3..2.7.13.99.3.2.1..1..93...2 * PAIR B3: 5,7 COL B B8: 5,7,4,8 # reduction candidate for 5,7 B8: 5,7 # 13 pairs B9: 5,7,4,8 # reduction candidate for 5,7 B9: 5,7 => CTR * 4613927582986..413357184296832549671746813.2..1.2...34.2.7.138998342.1..1..938542 B9: 4,8 # 10 pairs * PAIR C3: 5,7 COL C C9: 5,7,4,6 # reduction candidate for 5,7 C9: 5,7 # 12 pairs C9: 4,6 # 8 pairs * PAIR E3: 4,8 COL E E4: 4,8,7 # reduction candidate for 4,8 E4: 4,8 # 14 pairs E6: 4,8,6,7 # reduction candidate for 4,8 E6: 4,8 => CTR * 461392...29865741335714829683257964164.813.2.71.2.6.3.5247613899.3.2.1641.6934..2 E6: 6,7 # 10 pairs E7: 4,8,5,6 # reduction candidate for 4,8 E7: 4,8 => CTR * 461392...2986574133..1..296832579641...413.2..1426893..2.7413899.382.1.41..93...2 E7: 5,6 # 10 pairs * PAIR F3: 4,8 COL F F6: 4,8,6,7 # reduction candidate for 4,8 F6: 4,8 => CTR * 461392...2986574133..1..296832579641...413.2..1426893..2.7413899.382.1.41..93...2 F6: 6,7 # 10 pairs F8: 4,8,5,6 # reduction candidate for 4,8 F8: 4,8 => SOLVED * 461392758298675413375184296832549671746813925519267834624751389953428167187936542 F8: 5,6 # 10 pairs F9: 4,8,5,6 # reduction candidate for 4,8 F9: 4,8 # 13 pairs * PAIR A4: 7,8 BLK 4 A5: 7,8,5,6 # reduction candidate for 7,8 A5: 7,8 => SOLVED * 461392758298675413375184296832549671746813925519267834624751389953428167187936542 A5: 5,6 # 11 pairs A6: 7,8,5 # reduction candidate for 7,8 A6: 7,8 # 14 pairs * PAIR A4: 7,8 ROW 4 E4: 7,8,4 # reduction candidate for 7,8 E4: 7,8 => CTR * 461392...2986574133..184296832579641.59413.2.71426893552674138997382.1.414.93...2 E4: 4 => SOLVED * 461392758298675413375184296832549671746813925519267834624751389953428167187936542 H4: 7,8,4 # reduction candidate for 7,8 H4: 7,8 => SOLVED * 461392758298675413375184296832549671746813925519267834624751389953428167187936542 H4: 4 => CTR * 461392...2986574133..184296832579641.59413.2.71426893552674138997382.1.414.93...2 * PAIR D5: 4,8 BLK 5 E4: 4,8,7 # reduction candidate for 4,8 E4: 4,8 # 14 pairs E6: 4,8,6,7 # reduction candidate for 4,8 E6: 4,8 => CTR * 461392...29865741335714829683257964164.813.2.71.2.6.3.5247613899.3.2.1641.6934..2 E6: 6,7 # 10 pairs F6: 4,8,6,7 # reduction candidate for 4,8 F6: 4,8 => CTR * 461392...2986574133..1..296832579641...413.2..1426893..2.7413899.382.1.41..93...2 F6: 6,7 # 10 pairs * PAIR D5: 4,8 ROW 5 B5: 4,8,5 # reduction candidate for 4,8 B5: 4,8 # 11 pairs I5: 4,8,5,7 # reduction candidate for 4,8 I5: 4,8 => CTR * 46139285729865741337518429683257964165941372871426893552674138994382.1..18793.5.2 I5: 5,7 # 10 pairs * PAIR D8: 4,8 BLK 8 E7: 4,8,5,6 # reduction candidate for 4,8 E7: 4,8 => CTR * 461392...2986574133..1..296832579641...413.2..1426893..2.7413899.382.1.41..93...2 E7: 5,6 # 10 pairs F8: 4,8,5,6 # reduction candidate for 4,8 F8: 4,8 => SOLVED * 461392758298675413375184296832549671746813925519267834624751389953428167187936542 F8: 5,6 # 10 pairs F9: 4,8,5,6 # reduction candidate for 4,8 F9: 4,8 # 13 pairs * PAIR D8: 4,8 ROW 8 B8: 4,8,5,7 # reduction candidate for 4,8 B8: 4,8 => CTR * 461392.5.2986..4133..1842968325496717468139255192...3..2.7.138998342.1..1..938542 B8: 5,7 # 13 pairs H8: 4,8,5,6,7 # reduction candidate for 4,8 H8: 4,8 => CTR * 461392...2986..4133..1..296.325496.1...813.2..1.267.3..2.7.13.99.342618.18.935..2 H8: 5,6,7 # 9 pairs I8: 4,8,5,7 # reduction candidate for 4,8 I8: 4,8 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-130-base-pr-000.dot * REASONING * DIS # B9: 5,7 => CTR => B9: 4,8 * DIS # E6: 4,8 => CTR => E6: 6,7 * DIS # E7: 4,8 => CTR => E7: 5,6 * DIS # F6: 4,8 => CTR => F6: 6,7 * PRF # F8: 4,8 => SOL * PRF # A5: 7,8 => SOL * DIS # E4: 7,8 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H4: 7,8 => SOL * DIS # H4: 4 => CTR => H4: 7,8 * DIS # E6: 4,8 => CTR => E6: 6,7 * DIS # F6: 4,8 => CTR => F6: 6,7 * DIS # I5: 4,8 => CTR => I5: 5,7 * DIS # E7: 4,8 => CTR => E7: 5,6 * PRF # F8: 4,8 => SOL * DIS # B8: 4,8 => CTR => B8: 5,7 * DIS # H8: 4,8 => CTR => H8: 5,6,7 * CNT 17 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,C3,D5,D8,E2,E3,F2,F3) * 461392...2986..4133..1..296.325.96.1....13.2..1.2...3..2.7.13.99.3.2.1..1..93...2 * PAIR B3: 5,7 COL B B8: 5,7,4,8 # reduction candidate for 5,7 B8: 5,7 # 13 pairs B9: 5,7,4,8 # reduction candidate for 5,7 B9: 5,7 => CTR * 4613927582986..413357184296832549671746813.2..1.2...34.2.7.138998342.1..1..938542 * RESTART * PAIR B3: 5,7 COL B B8: 5,7,4,8 # reduction candidate for 5,7 B8: 4,8 => CTR * 461392...2986574133751..296.3257964165..13.2.71.26..3.5267413899.382.1.41.793...2 * PAIR RESTART * PAIR C3: 5,7 COL C C9: 5,7,4,6 # reduction candidate for 5,7 C9: 5,7 # 18 pairs C9: 4,6 # 9 pairs * PAIR E3: 4,8 COL E E4: 4,8,7 # reduction candidate for 4,8 E4: 4,8 # 18 pairs E6: 4,8,6,7 # reduction candidate for 4,8 E6: 4,8 => CTR * 461392...2986574133.71..296.325796416...13.2.71.2.6.3.524761389973.2.164186934..2 E7: 4,8,5,6 # reduction candidate for 4,8 E7: 4,8 => CTR * 461392...2986574133..1..296832579641.4..13.2..1.26..3..2.7.13.99.3.2.1.41..93...2 * RESTART * PAIR RESTART * PAIR F3: 4,8 COL F F8: 4,8,5,6 # reduction candidate for 4,8 F8: 4,8 => SOLVED * 461392758298675413375184296832549671746813925519267834624751389953428167187936542 * DURATION: 0:00:12.203700 START: 07:13:58.271779 END: 07:14:10.475479 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-130-base-pr-001.dot * REASONING * DIS # B9: 5,7 => CTR => B9: 4,8 * DIS B9: 4,8 # B8: 4,8 => CTR => B8: 5,7 * DIS B9: 4,8 + B8: 5,7 # E6: 4,8 => CTR => E6: 6,7 * DIS B9: 4,8 + B8: 5,7 + E6: 6,7 # E7: 4,8 => CTR => E7: 5,6 * PRF B9: 4,8 + B8: 5,7 + E6: 6,7 + E7: 5,6 # F8: 4,8 => SOL * STA B9: 4,8 + B8: 5,7 + E6: 6,7 + E7: 5,6 + F8: 4,8 * CNT 5 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 130 solution: 461392758298675413375184296832549671746813925519267834624751389953428167187936542 info: 1811 FNBWXY S8.f 21420 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 461392758298675413375184296832549671746813925519267834624751389953428167187936542 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 # B8: 5,7 => UNS * DIS # B9: 5,7 => CTR => B9: 4,8 * INC # B9: 4,8 => UNS * INC # C9: 5,7 => UNS * INC # C9: 4,6 => UNS * INC # E4: 4,8 => UNS * DIS # E6: 4,8 => CTR => E6: 6,7 * INC # E6: 6,7 => UNS * DIS # E7: 4,8 => CTR => E7: 5,6 * INC # E7: 5,6 => UNS * DIS # F6: 4,8 => CTR => F6: 6,7 * INC # F6: 6,7 => UNS * PRF # F8: 4,8 => SOL * INC # F8: 5,6 => UNS * INC # F9: 4,8 => UNS * PRF # A5: 7,8 => SOL * INC # A5: 5,6 => UNS * INC # A6: 7,8 => UNS * DIS # E4: 7,8 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H4: 7,8 => SOL * DIS # H4: 4 => CTR => H4: 7,8 * INC # E4: 4,8 => UNS * DIS # E6: 4,8 => CTR => E6: 6,7 * INC # E6: 6,7 => UNS * DIS # F6: 4,8 => CTR => F6: 6,7 * INC # F6: 6,7 => UNS * INC # B5: 4,8 => UNS * DIS # I5: 4,8 => CTR => I5: 5,7 * INC # I5: 5,7 => UNS * DIS # E7: 4,8 => CTR => E7: 5,6 * INC # E7: 5,6 => UNS * PRF # F8: 4,8 => SOL * INC # F8: 5,6 => UNS * INC # F9: 4,8 => UNS * DIS # B8: 4,8 => CTR => B8: 5,7 * INC # B8: 5,7 => UNS * DIS # H8: 4,8 => CTR => H8: 5,6,7 * INC # H8: 5,6,7 => UNS * INC # I8: 4,8 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B8: 5,7 => UNS * DIS # B9: 5,7 => CTR => B9: 4,8 * INC B9: 4,8 # B8: 5,7 => UNS * DIS B9: 4,8 # B8: 4,8 => CTR => B8: 5,7 * INC B9: 4,8 + B8: 5,7 # C9: 5,7 => UNS * INC B9: 4,8 + B8: 5,7 # C9: 4,6 => UNS * INC B9: 4,8 + B8: 5,7 # E4: 4,8 => UNS * DIS B9: 4,8 + B8: 5,7 # E6: 4,8 => CTR => E6: 6,7 * DIS B9: 4,8 + B8: 5,7 + E6: 6,7 # E7: 4,8 => CTR => E7: 5,6 * PRF B9: 4,8 + B8: 5,7 + E6: 6,7 + E7: 5,6 # F8: 4,8 => SOL * STA B9: 4,8 + B8: 5,7 + E6: 6,7 + E7: 5,6 + F8: 4,8 * CNT 10 HDP CHAINS / 10 HYP OPENED