Analysis of xx-top500-227-base.sdk
Contents
Original Sudoku
level: medium
position: .3.89....1......6............6....79....3.5..2.........5...13....46...........9.. initial
Autosolve
position: 63789.1..1.93...6.5.816..93386.1.4794917365..2754896318529713469146.3...763.4891. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F2: 2,4 => SOL * DIS # I2: 2,4 => CTR => I2: 5,7,8 * PRF # F3: 7 => SOL * DIS # F2: 2,5 => CTR => F2: 4,7 * DIS # I2: 2,5 => CTR => I2: 4,7,8 * DIS # I1: 2,5 => CTR => I1: 4 * DIS # I2: 2,5 => CTR => I2: 4,7,8 * DIS # F1: 4 => CTR => F1: 2,5 * DIS # H8: 2,5 => CTR => H8: 8 * DIS # G2: 2,7 => CTR => G2: 8 * PRF # I2: 2,7 => SOL * PRF # F3: 2,7 => SOL * DIS # G8: 8 => CTR => G8: 2,7 * DIS # F2: 2,5 => CTR => F2: 4,7 * DIS # H8: 5 => CTR => H8: 2,8 * DIS # I2: 2,8 => CTR => I2: 4,5,7 * DIS # I8: 2,8 => CTR => I8: 5,7 * DIS # H8: 2,5 => CTR => H8: 8 * PRF # I8: 2,5 => SOL * DIS # H8: 2,5 => CTR => H8: 8 * PRF # I8: 2,5 => SOL * DIS # I1: 2,5 => CTR => I1: 4 * DIS # I2: 2,5 => CTR => I2: 4,7,8 * CNT 23 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F2: 2,4 => SOL * STA F2: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3.89....1......6............6....79....3.5..2.........5...13....46...........9.. | initial |
| 63789.1..1.93...6.5.816..93386.1.4794917365..2754896318529713469146.3...763.4891. | autosolve |
| 637892154129354867548167293386215479491736528275489631852971346914623785763548912 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B2: 2,4 B3: 2,4 E2: 2,5 H1: 2,5 G3: 2,7 D4: 2,5 F4: 2,5 H5: 2,8 I5: 2,8 E8: 2,5 D9: 2,5 I9: 2,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 2.. / B2 = 2 => 0 pairs (*) / B3 = 2 => 0 pairs (X) D4,F4: 2.. / D4 = 2 => 0 pairs (*) / F4 = 2 => 0 pairs (X) H5,I5: 2.. / H5 = 2 => 12 pairs (_) / I5 = 2 => 0 pairs (X) E8,D9: 2.. / E8 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) D9,I9: 2.. / D9 = 2 => 0 pairs (X) / I9 = 2 => 0 pairs (_) D4,D9: 2.. / D4 = 2 => 0 pairs (*) / D9 = 2 => 0 pairs (X) E2,E8: 2.. / E2 = 2 => 0 pairs (X) / E8 = 2 => 0 pairs (_) B2,B3: 4.. / B2 = 4 => 12 pairs (_) / B3 = 4 => 0 pairs (*) I1,I2: 4.. / I1 = 4 => 15 pairs (_) / I2 = 4 => 0 pairs (X) F1,I1: 4.. / F1 = 4 => 0 pairs (X) / I1 = 4 => 15 pairs (_) B3,F3: 4.. / B3 = 4 => 0 pairs (*) / F3 = 4 => 0 pairs (X) D4,F4: 5.. / D4 = 5 => 0 pairs (X) / F4 = 5 => 0 pairs (_) E8,D9: 5.. / E8 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) D9,I9: 5.. / D9 = 5 => 0 pairs (*) / I9 = 5 => 0 pairs (X) D4,D9: 5.. / D4 = 5 => 0 pairs (X) / D9 = 5 => 0 pairs (_) E2,E8: 5.. / E2 = 5 => 0 pairs (*) / E8 = 5 => 0 pairs (X) H1,H8: 5.. / H1 = 5 => 14 pairs (_) / H8 = 5 => 0 pairs (X) F2,F3: 7.. / F2 = 7 => 14 pairs (_) / F3 = 7 => 0 pairs (*) G8,I8: 7.. / G8 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) F3,G3: 7.. / F3 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) I2,I8: 7.. / I2 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) G2,I2: 8.. / G2 = 8 => 13 pairs (_) / I2 = 8 => 0 pairs (X) H5,I5: 8.. / H5 = 8 => 0 pairs (X) / I5 = 8 => 12 pairs (_) G2,G8: 8.. / G2 = 8 => 13 pairs (_) / G8 = 8 => 0 pairs (X) H5,H8: 8.. / H5 = 8 => 0 pairs (X) / H8 = 8 => 12 pairs (_) * DURATION: 0:00:40.512021 START: 10:36:45.650837 END: 10:37:26.162858 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,D4,D9,E2,E8,F4,G3,H1,H5,I5,I9) * 63789.1..1.93...6.5.816..93386.1.4794917365..2754896318529713469146.3...763.4891. * PAIR B2: 2,4 ROW 2 F2: 2,4,5,7 # reduction candidate for 2,4 F2: 2,4 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 F2: 5,7 # 13 pairs I2: 2,4,5,7,8 # reduction candidate for 2,4 I2: 2,4 => CTR * 63789.15.1.932.86.5.816.793386.1.4794917365..2754896318529713469146.32.7763248915 I2: 5,7,8 # 15 pairs * PAIR B3: 2,4 ROW 3 F3: 2,4,7 # reduction candidate for 2,4 F3: 7 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 F3: 2,4 # 14 pairs * PAIR E2: 2,5 BLK 2 F1: 2,5,4 # reduction candidate for 2,5 F1: 2,5 # 15 pairs F2: 2,5,4,7 # reduction candidate for 2,5 F2: 2,5 => CTR * 63789.1..1.93...6.5.8167293386.1.4794917365..2754896318529713469146.3...763.4891. F2: 4,7 # 13 pairs * PAIR E2: 2,5 ROW 2 I2: 2,5,4,7,8 # reduction candidate for 2,5 I2: 2,5 => CTR * 63789.1541.932.86.5.816.793386.1.4794917365..2754896318529713469146.32.7763248915 I2: 4,7,8 # 13 pairs * PAIR H1: 2,5 BLK 3 I1: 2,5,4 # reduction candidate for 2,5 I1: 2,5 => CTR * 6378941..1293578645481627933862154794917365.8275489631852971346914623..7763.4891. I1: 4 # 15 pairs I2: 2,5,4,7,8 # reduction candidate for 2,5 I2: 2,5 => CTR * 63789.1541.932.86.5.816.793386.1.4794917365..2754896318529713469146.32.7763248915 I2: 4,7,8 # 13 pairs * PAIR H1: 2,5 ROW 1 F1: 2,5,4 # reduction candidate for 2,5 F1: 4 => CTR * 6378941..1293578645481627933862154794917365.8275489631852971346914623..7763.4891. F1: 2,5 # 15 pairs * PAIR H1: 2,5 COL H H8: 2,5,8 # reduction candidate for 2,5 H8: 2,5 => CTR * 63789.1541.932..6.5.816..93386.1.4794917365822754896318529713469146.3...763248915 H8: 8 # 12 pairs * PAIR G3: 2,7 BLK 3 G2: 2,7,8 # reduction candidate for 2,7 G2: 2,7 => CTR * 6378921541.935..685.816..93386.1.4794917365822754896318529713469146.3827763248915 G2: 8 # 13 pairs I2: 2,7,4,5,8 # reduction candidate for 2,7 I2: 2,7 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 I2: 4,5,8 # 13 pairs * PAIR G3: 2,7 ROW 3 F3: 2,7,4 # reduction candidate for 2,7 F3: 2,7 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 F3: 4 # 12 pairs * PAIR G3: 2,7 COL G G8: 2,7,8 # reduction candidate for 2,7 G8: 8 => CTR * 6378921541.935..685.816..93386.1.4794917365822754896318529713469146.3827763248915 G8: 2,7 # 13 pairs * PAIR F4: 2,5 COL F F1: 2,5,4 # reduction candidate for 2,5 F1: 2,5 # 15 pairs F2: 2,5,4,7 # reduction candidate for 2,5 F2: 2,5 => CTR * 63789.1..1.93...6.5.8167293386.1.4794917365..2754896318529713469146.3...763.4891. F2: 4,7 # 13 pairs * PAIR H5: 2,8 COL H H8: 2,8,5 # reduction candidate for 2,8 H8: 5 => CTR * 63789.1..1.93...6.5.816..93386.1.4794917365822754896318529713469146.325.763.4891. H8: 2,8 # 14 pairs * PAIR I5: 2,8 COL I I2: 2,8,4,5,7 # reduction candidate for 2,8 I2: 2,8 => CTR * 63789.1541.93...6.5.816..933865124794917365..2754896318529713469146.3..7763.48915 I2: 4,5,7 # 13 pairs I8: 2,8,5,7 # reduction candidate for 2,8 I8: 2,8 => CTR * 63789215412935..675.8167293386.1.4794917365..2754896318529713469146.37..763.4891. I8: 5,7 # 13 pairs * PAIR E8: 2,5 ROW 8 H8: 2,5,8 # reduction candidate for 2,5 H8: 2,5 => CTR * 63789.1541.932..6.5.816..93386.1.4794917365822754896318529713469146.3...763248915 H8: 8 # 12 pairs I8: 2,5,7,8 # reduction candidate for 2,5 I8: 2,5 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 I8: 7,8 # 13 pairs * PAIR I9: 2,5 BLK 9 H8: 2,5,8 # reduction candidate for 2,5 H8: 2,5 => CTR * 63789.1541.932..6.5.816..93386.1.4794917365822754896318529713469146.3...763248915 H8: 8 # 12 pairs I8: 2,5,7,8 # reduction candidate for 2,5 I8: 2,5 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 I8: 7,8 # 13 pairs * PAIR I9: 2,5 COL I I1: 2,5,4 # reduction candidate for 2,5 I1: 2,5 => CTR * 6378941..1293578645481627933862154794917365.8275489631852971346914623..7763.4891. I1: 4 # 15 pairs I2: 2,5,4,7,8 # reduction candidate for 2,5 I2: 2,5 => CTR * 63789.1541.932.86.5.816.793386.1.4794917365..2754896318529713469146.32.7763248915 I2: 4,7,8 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-227-base-pr-000.dot * REASONING * PRF # F2: 2,4 => SOL * DIS # I2: 2,4 => CTR => I2: 5,7,8 * PRF # F3: 7 => SOL * DIS # F2: 2,5 => CTR => F2: 4,7 * DIS # I2: 2,5 => CTR => I2: 4,7,8 * DIS # I1: 2,5 => CTR => I1: 4 * DIS # I2: 2,5 => CTR => I2: 4,7,8 * DIS # F1: 4 => CTR => F1: 2,5 * DIS # H8: 2,5 => CTR => H8: 8 * DIS # G2: 2,7 => CTR => G2: 8 * PRF # I2: 2,7 => SOL * PRF # F3: 2,7 => SOL * DIS # G8: 8 => CTR => G8: 2,7 * DIS # F2: 2,5 => CTR => F2: 4,7 * DIS # H8: 5 => CTR => H8: 2,8 * DIS # I2: 2,8 => CTR => I2: 4,5,7 * DIS # I8: 2,8 => CTR => I8: 5,7 * DIS # H8: 2,5 => CTR => H8: 8 * PRF # I8: 2,5 => SOL * DIS # H8: 2,5 => CTR => H8: 8 * PRF # I8: 2,5 => SOL * DIS # I1: 2,5 => CTR => I1: 4 * DIS # I2: 2,5 => CTR => I2: 4,7,8 * CNT 23 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,D4,D9,E2,E8,F4,G3,H1,H5,I5,I9) * 63789.1..1.93...6.5.816..93386.1.4794917365..2754896318529713469146.3...763.4891. * PAIR B2: 2,4 ROW 2 F2: 2,4,5,7 # reduction candidate for 2,4 F2: 2,4 => SOLVED * 637892154129354867548167293386215479491736528275489631852971346914623785763548912 * DURATION: 0:00:01.883764 START: 10:38:13.757563 END: 10:38:15.641327 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-227-base-pr-001.dot * REASONING * PRF # F2: 2,4 => SOL * STA F2: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 227 solution: 637892154129354867548167293386215479491736528275489631852971346914623785763548912 info: 2064 FNWXY S8.f 18110 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 637892154129354867548167293386215479491736528275489631852971346914623785763548912 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 # F2: 2,4 => SOL * INC # F2: 5,7 => UNS * DIS # I2: 2,4 => CTR => I2: 5,7,8 * INC # I2: 5,7,8 => UNS * INC # F3: 2,4 => UNS * PRF # F3: 7 => SOL * INC # F1: 2,5 => UNS * DIS # F2: 2,5 => CTR => F2: 4,7 * INC # F2: 4,7 => UNS * DIS # I2: 2,5 => CTR => I2: 4,7,8 * INC # I2: 4,7,8 => UNS * DIS # I1: 2,5 => CTR => I1: 4 * INC # I1: 4 => UNS * DIS # I2: 2,5 => CTR => I2: 4,7,8 * INC # I2: 4,7,8 => UNS * INC # F1: 2,5 => UNS * DIS # F1: 4 => CTR => F1: 2,5 * DIS # H8: 2,5 => CTR => H8: 8 * INC # H8: 8 => UNS * DIS # G2: 2,7 => CTR => G2: 8 * INC # G2: 8 => UNS * PRF # I2: 2,7 => SOL * INC # I2: 4,5,8 => UNS * PRF # F3: 2,7 => SOL * INC # F3: 4 => UNS * INC # G8: 2,7 => UNS * DIS # G8: 8 => CTR => G8: 2,7 * INC # F1: 2,5 => UNS * DIS # F2: 2,5 => CTR => F2: 4,7 * INC # F2: 4,7 => UNS * INC # H8: 2,8 => UNS * DIS # H8: 5 => CTR => H8: 2,8 * DIS # I2: 2,8 => CTR => I2: 4,5,7 * INC # I2: 4,5,7 => UNS * DIS # I8: 2,8 => CTR => I8: 5,7 * INC # I8: 5,7 => UNS * DIS # H8: 2,5 => CTR => H8: 8 * INC # H8: 8 => UNS * PRF # I8: 2,5 => SOL * INC # I8: 7,8 => UNS * DIS # H8: 2,5 => CTR => H8: 8 * INC # H8: 8 => UNS * PRF # I8: 2,5 => SOL * INC # I8: 7,8 => UNS * DIS # I1: 2,5 => CTR => I1: 4 * INC # I1: 4 => UNS * DIS # I2: 2,5 => CTR => I2: 4,7,8 * INC # I2: 4,7,8 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F2: 2,4 => SOL * STA F2: 2,4 * CNT 1 HDP CHAINS / 1 HYP OPENED