Analysis of xx-top500-267-base.sdk
Contents
Original Sudoku
level: medium
position: ..36..2......9.8...7.......2..5..1......7..4......3...6..2......4.....7....1..... initial
Autosolve
position: 4.36182.7126795834.7.432.1.2.75..1.336..71.42.14.2376.6.12.7....423...717..1...2. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B7: 5,9 => CTR => B7: 3,8 * DIS # B9: 5,9 => CTR => B9: 3,8 * PRF # H7: 5,9 => SOL * DIS # H7: 8 => CTR => H7: 5,9 * DIS # C5: 8,9 => CTR => C5: 5 * PRF # C5: 5 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 5 => CTR => A6: 8,9 * PRF # B7: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 3,5 * DIS # C5: 8,9 => CTR => C5: 5 * PRF # C5: 5 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 5 => CTR => A6: 8,9 * DIS # I6: 8,9 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # I6: 8,9 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # H7: 8,9 => CTR => H7: 5 * PRF # H7: 5 => SOL * PRF # I6: 5,9 => SOL * DIS # I6: 8 => CTR => I6: 5,9 * DIS # C5: 8 => CTR => C5: 5,9 * DIS # G8: 5 => CTR => G8: 6,9 * CNT 24 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B7: 5,9 => CTR => B7: 3,8 * DIS B7: 3,8 # B9: 5,9 => CTR => B9: 3,8 * PRF B7: 3,8 + B9: 3,8 => SOL * STA B7: 3,8 + B9: 3,8 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..36..2......9.8...7.......2..5..1......7..4......3...6..2......4.....7....1..... | initial |
| 4.36182.7126795834.7.432.1.2.75..1.336..71.42.14.2376.6.12.7....423...717..1...2. | autosolve |
| 453618297126795834978432516297564183365871942814923765681247359542389671739156428 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B1: 5,9 H1: 5,9 B4: 8,9 E4: 4,6 F4: 4,6 D5: 8,9 D6: 8,9 H4: 8,9 G5: 5,9 F8: 6,9 G7: 3,4 G9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B7,B9: 3.. / B7 = 3 => 12 pairs (_) / B9 = 3 => 11 pairs (_) G7,G9: 3.. / G7 = 3 => 11 pairs (_) / G9 = 3 => 12 pairs (_) B7,G7: 3.. / B7 = 3 => 12 pairs (_) / G7 = 3 => 11 pairs (_) B9,G9: 3.. / B9 = 3 => 11 pairs (_) / G9 = 3 => 12 pairs (_) E4,F4: 4.. / E4 = 4 => 10 pairs (_) / F4 = 4 => 12 pairs (_) G7,G9: 4.. / G7 = 4 => 12 pairs (_) / G9 = 4 => 11 pairs (_) E7,G7: 4.. / E7 = 4 => 11 pairs (_) / G7 = 4 => 12 pairs (_) F4,F9: 4.. / F4 = 4 => 12 pairs (_) / F9 = 4 => 10 pairs (_) C5,A6: 5.. / C5 = 5 => 0 pairs (*) / A6 = 5 => 0 pairs (X) G5,I6: 5.. / G5 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) B1,H1: 5.. / B1 = 5 => 0 pairs (*) / H1 = 5 => 0 pairs (X) C5,G5: 5.. / C5 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) A6,I6: 5.. / A6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) H1,H7: 5.. / H1 = 5 => 0 pairs (X) / H7 = 5 => 0 pairs (_) G3,I3: 6.. / G3 = 6 => 16 pairs (_) / I3 = 6 => 15 pairs (_) E4,F4: 6.. / E4 = 6 => 12 pairs (_) / F4 = 6 => 10 pairs (_) G8,I9: 6.. / G8 = 6 => 15 pairs (_) / I9 = 6 => 16 pairs (_) G3,G8: 6.. / G3 = 6 => 16 pairs (_) / G8 = 6 => 15 pairs (_) I3,I9: 6.. / I3 = 6 => 15 pairs (_) / I9 = 6 => 16 pairs (_) A3,C3: 8.. / A3 = 8 => 16 pairs (_) / C3 = 8 => 15 pairs (_) D5,D6: 8.. / D5 = 8 => 13 pairs (_) / D6 = 8 => 0 pairs (X) H4,I6: 8.. / H4 = 8 => 0 pairs (*) / I6 = 8 => 0 pairs (X) B4,H4: 8.. / B4 = 8 => 0 pairs (X) / H4 = 8 => 0 pairs (_) C5,D5: 8.. / C5 = 8 => 0 pairs (X) / D5 = 8 => 13 pairs (_) A8,E8: 8.. / A8 = 8 => 0 pairs (X) / E8 = 8 => 14 pairs (_) H4,H7: 8.. / H4 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) D5,D6: 9.. / D5 = 9 => 0 pairs (X) / D6 = 9 => 13 pairs (_) F8,F9: 9.. / F8 = 9 => 14 pairs (_) / F9 = 9 => 14 pairs (_) B1,H1: 9.. / B1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) B4,H4: 9.. / B4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) * DURATION: 0:00:59.217525 START: 12:00:12.032731 END: 12:01:11.250256 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,D5,D6,E4,F4,F8,G5,G7,G9,H1,H4) * 4.36182.7126795834.7.432.1.2.75..1.336..71.42.14.2376.6.12.7....423...717..1...2. * PAIR B1: 5,9 BLK 1 A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 # 15 pairs C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 # 16 pairs * PAIR B1: 5,9 COL B B7: 5,9,3,8 # reduction candidate for 5,9 B7: 5,9 => CTR * 49361825712679583487.432.1.2875.419336.8715425149237686.124738..4235..7173.18.42. B7: 3,8 # 14 pairs B9: 5,9,3,8 # reduction candidate for 5,9 B9: 5,9 => CTR * 4.36182.7126795834.7.432.1.2875..19336.8715425149237686312.7489.4235..717..1..32. B9: 3,8 # 13 pairs * PAIR H1: 5,9 BLK 3 G3: 5,9,6 # reduction candidate for 5,9 G3: 5,9 # 15 pairs I3: 5,9,6 # reduction candidate for 5,9 I3: 5,9 # 16 pairs * PAIR H1: 5,9 COL H H7: 5,9,8 # reduction candidate for 5,9 H7: 5,9 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 H7: 8 => CTR * 49361825712679583487.432.1.2.75..19336..715425149237686.12.7.8..4235..717..18..2. * PAIR B4: 8,9 BLK 4 C5: 8,9,5 # reduction candidate for 8,9 C5: 8,9 => CTR * 4.36182.71267958349784326152875..19336..71542514.2376.6.12.7...84235..717..1...2. C5: 5 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 A6: 8,9,5 # reduction candidate for 8,9 A6: 8,9 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 A6: 5 => CTR * 4.36182.71267958349784326152875..19336..71542514.2376.6.12.7...84235..717..1...2. * PAIR B4: 8,9 COL B B7: 8,9,3,5 # reduction candidate for 8,9 B7: 8,9 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 B7: 3,5 # 14 pairs B9: 8,9,3,5 # reduction candidate for 8,9 B9: 8,9 => CTR * 453618297126795834.7.432.1.2975..18336..71.42.14.2376.6312.7459.423..67178.1..32. B9: 3,5 # 13 pairs * PAIR E4: 4,6 COL E E9: 4,6,5,8 # reduction candidate for 4,6 E9: 4,6 # 14 pairs E9: 5,8 # 13 pairs * PAIR F4: 4,6 COL F F9: 4,6,9 # reduction candidate for 4,6 F9: 9 # 14 pairs F9: 4,6 # 14 pairs * PAIR D5: 8,9 ROW 5 C5: 8,9,5 # reduction candidate for 8,9 C5: 8,9 => CTR * 4.36182.71267958349784326152875..19336..71542514.2376.6.12.7...84235..717..1...2. C5: 5 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 * PAIR D6: 8,9 ROW 6 A6: 8,9,5 # reduction candidate for 8,9 A6: 8,9 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 A6: 5 => CTR * 4.36182.71267958349784326152875..19336..71542514.2376.6.12.7...84235..717..1...2. I6: 8,9,5 # reduction candidate for 8,9 I6: 8,9 => CTR * 4.36182.71267958349784326152875..19336..71542514.2376.6.12.7...84235..717..1...2. I6: 5 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 * PAIR H4: 8,9 BLK 6 I6: 8,9,5 # reduction candidate for 8,9 I6: 8,9 => CTR * 4.36182.71267958349784326152875..19336..71542514.2376.6.12.7...84235..717..1...2. I6: 5 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 * PAIR H4: 8,9 COL H H7: 8,9,5 # reduction candidate for 8,9 H7: 8,9 => CTR * 493618257126795834.7.432.1.2875..19336.8715425149237686.12.7.899423...717..1...2. H7: 5 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 * PAIR G5: 5,9 BLK 6 I6: 5,9,8 # reduction candidate for 5,9 I6: 5,9 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 I6: 8 => CTR * 4.3618257126795834.75432.1.2875..1.336..715425149237686.12.7.8..4235..717..18..2. * PAIR G5: 5,9 ROW 5 C5: 5,9,8 # reduction candidate for 5,9 C5: 8 => CTR * 4.36182.712679583487.432.1.2975..1833689715425148237696.12.7.9.942356.717..1...2. C5: 5,9 # 13 pairs * PAIR G5: 5,9 COL G G3: 5,9,6 # reduction candidate for 5,9 G3: 5,9 # 15 pairs G8: 5,9,6 # reduction candidate for 5,9 G8: 5,9 # 16 pairs * PAIR F8: 6,9 BLK 8 F9: 6,9,4 # reduction candidate for 6,9 F9: 6,9 # 12 pairs F9: 4 # 10 pairs * PAIR F8: 6,9 ROW 8 G8: 6,9,5 # reduction candidate for 6,9 G8: 5 => CTR * 4.36182571267958345784326192975..1.336..71942.149237656.12.7....423..5717..1...26 G8: 6,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-267-base-pr-000.dot * REASONING * DIS # B7: 5,9 => CTR => B7: 3,8 * DIS # B9: 5,9 => CTR => B9: 3,8 * PRF # H7: 5,9 => SOL * DIS # H7: 8 => CTR => H7: 5,9 * DIS # C5: 8,9 => CTR => C5: 5 * PRF # C5: 5 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 5 => CTR => A6: 8,9 * PRF # B7: 8,9 => SOL * DIS # B9: 8,9 => CTR => B9: 3,5 * DIS # C5: 8,9 => CTR => C5: 5 * PRF # C5: 5 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 5 => CTR => A6: 8,9 * DIS # I6: 8,9 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # I6: 8,9 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # H7: 8,9 => CTR => H7: 5 * PRF # H7: 5 => SOL * PRF # I6: 5,9 => SOL * DIS # I6: 8 => CTR => I6: 5,9 * DIS # C5: 8 => CTR => C5: 5,9 * DIS # G8: 5 => CTR => G8: 6,9 * CNT 24 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B1,B4,D5,D6,E4,F4,F8,G5,G7,G9,H1,H4) * 4.36182.7126795834.7.432.1.2.75..1.336..71.42.14.2376.6.12.7....423...717..1...2. * PAIR B1: 5,9 BLK 1 A3: 5,9,8 # reduction candidate for 5,9 A3: 5,9 # 15 pairs C3: 5,9,8 # reduction candidate for 5,9 C3: 5,9 # 16 pairs * PAIR B1: 5,9 COL B B7: 5,9,3,8 # reduction candidate for 5,9 B7: 5,9 => CTR * 49361825712679583487.432.1.2875.419336.8715425149237686.124738..4235..7173.18.42. B9: 5,9,3,8 # reduction candidate for 5,9 B9: 5,9 => CTR * 4.36182.7126795834.7.432.1.2875..19336.8715425149237686312.7489.4235..717..1..32. B9: 3,8 => SOLVED * 453618297126795834978432516297564183365871942814923765681247359542389671739156428 * DURATION: 0:00:05.207242 START: 12:01:59.890644 END: 12:02:05.097886 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-267-base-pr-001.dot * REASONING * DIS # B7: 5,9 => CTR => B7: 3,8 * DIS B7: 3,8 # B9: 5,9 => CTR => B9: 3,8 * PRF B7: 3,8 + B9: 3,8 => SOL * STA B7: 3,8 + B9: 3,8 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 267 solution: 453618297126795834978432516297564183365871942814923765681247359542389671739156428 info: 2139 FNBHWXY S8.f 13530 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 453618297126795834978432516297564183365871942814923765681247359542389671739156428 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 # A3: 5,9 => UNS * INC # C3: 5,9 => UNS * DIS # B7: 5,9 => CTR => B7: 3,8 * INC # B7: 3,8 => UNS * DIS # B9: 5,9 => CTR => B9: 3,8 * INC # B9: 3,8 => UNS * INC # G3: 5,9 => UNS * INC # I3: 5,9 => UNS * PRF # H7: 5,9 => SOL * DIS # H7: 8 => CTR => H7: 5,9 * DIS # C5: 8,9 => CTR => C5: 5 * PRF # C5: 5 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 5 => CTR => A6: 8,9 * PRF # B7: 8,9 => SOL * INC # B7: 3,5 => UNS * DIS # B9: 8,9 => CTR => B9: 3,5 * INC # B9: 3,5 => UNS * INC # E9: 4,6 => UNS * INC # E9: 5,8 => UNS * INC # F9: 4,6 => UNS * INC # F9: 9 => UNS * DIS # C5: 8,9 => CTR => C5: 5 * PRF # C5: 5 => SOL * PRF # A6: 8,9 => SOL * DIS # A6: 5 => CTR => A6: 8,9 * DIS # I6: 8,9 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # I6: 8,9 => CTR => I6: 5 * PRF # I6: 5 => SOL * DIS # H7: 8,9 => CTR => H7: 5 * PRF # H7: 5 => SOL * PRF # I6: 5,9 => SOL * DIS # I6: 8 => CTR => I6: 5,9 * INC # C5: 5,9 => UNS * DIS # C5: 8 => CTR => C5: 5,9 * INC # G3: 5,9 => UNS * INC # G8: 5,9 => UNS * INC # F9: 6,9 => UNS * INC # F9: 4 => UNS * INC # G8: 6,9 => UNS * DIS # G8: 5 => CTR => G8: 6,9 * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 5,9 => UNS * INC # C3: 5,9 => UNS * DIS # B7: 5,9 => CTR => B7: 3,8 * DIS B7: 3,8 # B9: 5,9 => CTR => B9: 3,8 * PRF B7: 3,8 + B9: 3,8 => SOL * STA B7: 3,8 + B9: 3,8 * CNT 5 HDP CHAINS / 4 HYP OPENED