Analysis of xx-top500-310-base.sdk
Contents
Original Sudoku
level: medium
position: .7..2.....1....5.....3...4....6.71..2......6..8.......4..2.....3.......8......7.. initial
Autosolve
position: .74.2.38..138..5728.237..4..4.6871232314..8677861324..4.7218.3.36.7..218128.637.4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 6,9 => SOL * DIS # A1: 5 => CTR => A1: 6,9 * DIS # F2: 4 => CTR => F2: 6,9 * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * PRF # F1: 5,9 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # F2: 4,9 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # E8: 5 => CTR => E8: 4,9 * PRF # I3: 6,9 => SOL * DIS # F3: 6,9 => CTR => F3: 1,5 * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # E8: 4 => CTR => E8: 5,9 * PRF # F1: 5,9 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * DIS # F8: 5,9 => CTR => F8: 4 * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * DIS # F8: 5,9 => CTR => F8: 4 * DIS # F8: 5,9 => CTR => F8: 4 * DIS # I7: 6,9 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * CNT 34 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 6,9 => SOL * STA A1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7..2.....1....5.....3...4....6.71..2......6..8.......4..2.....3.......8......7.. | initial |
| .74.2.38..138..5728.237..4..4.6871232314..8677861324..4.7218.3.36.7..218128.637.4 | autosolve |
| 674925381913846572852371946549687123231459867786132459497218635365794218128563794 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 6,9 B3: 5,9 D1: 5,9 E2: 4,9 G3: 6,9 A4: 5,9 C4: 5,9 E5: 5,9 F5: 5,9 H6: 5,9 I6: 5,9 B7: 5,9 C8: 5,9 D9: 5,9 G7: 6,9 H9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 1.. / F1 = 1 => 17 pairs (_) / F3 = 1 => 0 pairs (*) I1,I3: 1.. / I1 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) F1,I1: 1.. / F1 = 1 => 17 pairs (_) / I1 = 1 => 0 pairs (*) F3,I3: 1.. / F3 = 1 => 0 pairs (*) / I3 = 1 => 0 pairs (X) E2,F2: 4.. / E2 = 4 => 17 pairs (_) / F2 = 4 => 0 pairs (X) E8,F8: 4.. / E8 = 4 => 0 pairs (X) / F8 = 4 => 17 pairs (_) E2,E8: 4.. / E2 = 4 => 17 pairs (_) / E8 = 4 => 0 pairs (X) F2,F8: 4.. / F2 = 4 => 0 pairs (X) / F8 = 4 => 17 pairs (_) A1,B3: 5.. / A1 = 5 => 0 pairs (X) / B3 = 5 => 0 pairs (_) A4,C4: 5.. / A4 = 5 => 0 pairs (*) / C4 = 5 => 0 pairs (X) E5,F5: 5.. / E5 = 5 => 17 pairs (_) / F5 = 5 => 0 pairs (X) H6,I6: 5.. / H6 = 5 => 0 pairs (*) / I6 = 5 => 0 pairs (X) B7,C8: 5.. / B7 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) I7,H9: 5.. / I7 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) B3,F3: 5.. / B3 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) B7,I7: 5.. / B7 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) D9,H9: 5.. / D9 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) A1,A4: 5.. / A1 = 5 => 0 pairs (X) / A4 = 5 => 0 pairs (_) B3,B7: 5.. / B3 = 5 => 0 pairs (*) / B7 = 5 => 0 pairs (X) C4,C8: 5.. / C4 = 5 => 0 pairs (X) / C8 = 5 => 0 pairs (_) D1,D9: 5.. / D1 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) E5,E8: 5.. / E5 = 5 => 17 pairs (_) / E8 = 5 => 0 pairs (X) H6,H9: 5.. / H6 = 5 => 0 pairs (*) / H9 = 5 => 0 pairs (X) I6,I7: 5.. / I6 = 5 => 0 pairs (X) / I7 = 5 => 0 pairs (_) A1,A2: 6.. / A1 = 6 => 0 pairs (*) / A2 = 6 => 0 pairs (X) G7,I7: 6.. / G7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) A2,F2: 6.. / A2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) G3,G7: 6.. / G3 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) A4,C4: 9.. / A4 = 9 => 0 pairs (X) / C4 = 9 => 0 pairs (_) E5,F5: 9.. / E5 = 9 => 0 pairs (X) / F5 = 9 => 17 pairs (_) H6,I6: 9.. / H6 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) B7,C8: 9.. / B7 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) D9,H9: 9.. / D9 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) B3,B7: 9.. / B3 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) C4,C8: 9.. / C4 = 9 => 0 pairs (*) / C8 = 9 => 0 pairs (X) D1,D9: 9.. / D1 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) G3,G7: 9.. / G3 = 9 => 0 pairs (*) / G7 = 9 => 0 pairs (X) H6,H9: 9.. / H6 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) * DURATION: 0:01:14.329520 START: 13:34:52.844131 END: 13:36:07.173651 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B3,B7,C4,C8,D1,D9,E2,E5,F5,G3,G7,H6,H9,I6) * .74.2.38..138..5728.237..4..4.6871232314..8677861324..4.7218.3.36.7..218128.637.4 * PAIR A2: 6,9 BLK 1 A1: 6,9,5 # reduction candidate for 6,9 A1: 6,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 A1: 5 => CTR * 57492.38..138..5728.237..4..4.6871232314..8677861324..4.7218.3.36.7..218128.637.4 * PAIR A2: 6,9 ROW 2 F2: 6,9,4 # reduction candidate for 6,9 F2: 4 => CTR * .74.2.38.6138945728.237..4..4.6871232314598677861324..4.7218.3.369745218128963754 F2: 6,9 # 17 pairs * PAIR B3: 5,9 BLK 1 A1: 5,9,6 # reduction candidate for 5,9 A1: 5,9 => CTR * .7452.38.6138..57285237..4.5496871232314..8677861324..4.7218.3.36.7..218128.637.4 A1: 6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR B3: 5,9 ROW 3 F3: 5,9,1,6 # reduction candidate for 5,9 F3: 5,9 => CTR * 67452138991384657285237964154968712323149.8677861324..4.7218.3.36.7.4218128.637.4 F3: 1,6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR D1: 5,9 BLK 2 F1: 5,9,1,6 # reduction candidate for 5,9 F1: 5,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 F1: 1,6 # 17 pairs F3: 5,9,1,6 # reduction candidate for 5,9 F3: 5,9 => CTR * 67452138991384657285237964154968712323149.8677861324..4.7218.3.36.7.4218128.637.4 F3: 1,6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR D1: 5,9 ROW 1 A1: 5,9,6 # reduction candidate for 5,9 A1: 5,9 => CTR * .7452.38.6138..57285237..4.5496871232314..8677861324..4.7218.3.36.7..218128.637.4 A1: 6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR E2: 4,9 BLK 2 F2: 4,9,6 # reduction candidate for 4,9 F2: 4,9 => CTR * .7452.38.6138..57285237..4.5496871232314..8677861324..4.7218.3.36.7..218128.637.4 F2: 6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR E2: 4,9 COL E E8: 4,9,5 # reduction candidate for 4,9 E8: 5 => CTR * .7452.38..1384.57285237..4.5496871232314958677861324..4.7218.3.36.754218128963754 E8: 4,9 # 17 pairs * PAIR G3: 6,9 BLK 3 I1: 6,9,1 # reduction candidate for 6,9 I1: 6,9 # 17 pairs I3: 6,9,1 # reduction candidate for 6,9 I3: 6,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 I3: 1 # 17 pairs * PAIR G3: 6,9 ROW 3 F3: 6,9,1,5 # reduction candidate for 6,9 F3: 6,9 => CTR * .74.2138..138..57285237..415496871232314..8677861324..4972186353657..218128563794 F3: 1,5 # 18 pairs * PAIR A4: 5,9 COL A A1: 5,9,6 # reduction candidate for 5,9 A1: 5,9 => CTR * .7452.38.6138..57285237..4.5496871232314..8677861324..4.7218.3.36.7..218128.637.4 A1: 6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR E5: 5,9 COL E E8: 5,9,4 # reduction candidate for 5,9 E8: 4 => CTR * .74.2.38..138..5728.237..4..4.6871232314598677861324..4.7218.3.369745218128963754 E8: 5,9 # 17 pairs * PAIR F5: 5,9 COL F F1: 5,9,1,6 # reduction candidate for 5,9 F1: 5,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 F1: 1,6 # 17 pairs F3: 5,9,1,6 # reduction candidate for 5,9 F3: 5,9 => CTR * 67452138991384657285237964154968712323149.8677861324..4.7218.3.36.7.4218128.637.4 F3: 1,6 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 F8: 5,9,4 # reduction candidate for 5,9 F8: 5,9 => CTR * .74.2.38.6138945728.237..4..4.6871232314598677861324..4.7218.3.369745218128963754 F8: 4 # 17 pairs * PAIR I6: 5,9 COL I I7: 5,9,6 # reduction candidate for 5,9 I7: 5,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 I7: 6 => CTR * 574.2.38..138..5728.237..4..4.6871232314..8677861324.54572189363697..218128963754 * PAIR B7: 5,9 ROW 7 I7: 5,9,6 # reduction candidate for 5,9 I7: 5,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 I7: 6 => CTR * 574.2.38..138..5728.237..4..4.6871232314..8677861324.54572189363697..218128963754 * PAIR C8: 5,9 ROW 8 E8: 5,9,4 # reduction candidate for 5,9 E8: 5,9 # 17 pairs F8: 5,9,4 # reduction candidate for 5,9 F8: 5,9 => CTR * .74.2.38.6138945728.237..4..4.6871232314598677861324..4.7218.3.369745218128963754 F8: 4 # 17 pairs * PAIR D9: 5,9 BLK 8 E8: 5,9,4 # reduction candidate for 5,9 E8: 5,9 # 17 pairs F8: 5,9,4 # reduction candidate for 5,9 F8: 5,9 => CTR * .74.2.38.6138945728.237..4..4.6871232314598677861324..4.7218.3.369745218128963754 F8: 4 # 17 pairs * PAIR G7: 6,9 BLK 9 I7: 6,9,5 # reduction candidate for 6,9 I7: 6,9 => CTR * 574.2.38..138..5728.237..4..4.6871232314..8677861324.5457218.3.3697..218128963754 I7: 5 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * PAIR H9: 5,9 BLK 9 I7: 5,9,6 # reduction candidate for 5,9 I7: 5,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 I7: 6 => CTR * 574.2.38..138..5728.237..4..4.6871232314..8677861324.54572189363697..218128963754 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-310-base-pr-000.dot * REASONING * PRF # A1: 6,9 => SOL * DIS # A1: 5 => CTR => A1: 6,9 * DIS # F2: 4 => CTR => F2: 6,9 * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * PRF # F1: 5,9 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # F2: 4,9 => CTR => F2: 6 * PRF # F2: 6 => SOL * DIS # E8: 5 => CTR => E8: 4,9 * PRF # I3: 6,9 => SOL * DIS # F3: 6,9 => CTR => F3: 1,5 * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # E8: 4 => CTR => E8: 5,9 * PRF # F1: 5,9 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * DIS # F8: 5,9 => CTR => F8: 4 * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * DIS # F8: 5,9 => CTR => F8: 4 * DIS # F8: 5,9 => CTR => F8: 4 * DIS # I7: 6,9 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * CNT 34 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,B3,B7,C4,C8,D1,D9,E2,E5,F5,G3,G7,H6,H9,I6) * .74.2.38..138..5728.237..4..4.6871232314..8677861324..4.7218.3.36.7..218128.637.4 * PAIR A2: 6,9 BLK 1 A1: 6,9,5 # reduction candidate for 6,9 A1: 6,9 => SOLVED * 674925381913846572852371946549687123231459867786132459497218635365794218128563794 * DURATION: 0:00:02.188476 START: 13:37:04.896251 END: 13:37:07.084727 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-310-base-pr-001.dot * REASONING * PRF # A1: 6,9 => SOL * STA A1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 310 solution: 674925381913846572852371946549687123231459867786132459497218635365794218128563794 info: 2729 FNBTHWX S8.f 22394 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 674925381913846572852371946549687123231459867786132459497218635365794218128563794 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 # A1: 6,9 => SOL * DIS # A1: 5 => CTR => A1: 6,9 * INC # F2: 6,9 => UNS * DIS # F2: 4 => CTR => F2: 6,9 * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * PRF # F1: 5,9 => SOL * INC # F1: 1,6 => UNS * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * DIS # F2: 4,9 => CTR => F2: 6 * PRF # F2: 6 => SOL * INC # E8: 4,9 => UNS * DIS # E8: 5 => CTR => E8: 4,9 * INC # I1: 6,9 => UNS * PRF # I3: 6,9 => SOL * INC # I3: 1 => UNS * DIS # F3: 6,9 => CTR => F3: 1,5 * INC # F3: 1,5 => UNS * DIS # A1: 5,9 => CTR => A1: 6 * PRF # A1: 6 => SOL * INC # E8: 5,9 => UNS * DIS # E8: 4 => CTR => E8: 5,9 * PRF # F1: 5,9 => SOL * INC # F1: 1,6 => UNS * DIS # F3: 5,9 => CTR => F3: 1,6 * PRF # F3: 1,6 => SOL * DIS # F8: 5,9 => CTR => F8: 4 * INC # F8: 4 => UNS * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * INC # E8: 5,9 => UNS * DIS # F8: 5,9 => CTR => F8: 4 * INC # F8: 4 => UNS * INC # E8: 5,9 => UNS * DIS # F8: 5,9 => CTR => F8: 4 * INC # F8: 4 => UNS * DIS # I7: 6,9 => CTR => I7: 5 * PRF # I7: 5 => SOL * PRF # I7: 5,9 => SOL * DIS # I7: 6 => CTR => I7: 5,9 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 6,9 => SOL * STA A1: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED