Analysis of xx-top500-485-base.sdk
Contents
Original Sudoku
level: medium
position: .2.97........8..1.......3.....5..2..7.1......84.......9.......71......8....3..... initial
Autosolve
position: .2.971.......83.12.1....3.....5..2..751......842......9......271......832..3..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 4,6 => CTR => A1: 3,5 * PRF # A2: 4,6 => SOL * PRF # A2: 4,6 => SOL * DIS # G2: 4,6 => CTR => G2: 5,7,9 * DIS # D5: 4,6 => CTR => D5: 2,8 * DIS # D7: 4,6 => CTR => D7: 1,8 * DIS # D8: 4,6 => CTR => D8: 2,7 * DIS # G2: 7,9 => CTR => G2: 4,5,6 * PRF # G2: 4,5,6 => SOL * DIS # C3: 7,9 => CTR => C3: 8 * PRF # C3: 8 => SOL * DIS # H6: 7,9 => CTR => H6: 3,5,6 * PRF # C3: 8,9 => SOL * DIS # C3: 7 => CTR => C3: 8,9 * DIS # I5: 8,9 => CTR => I5: 4,6 * PRF # A1: 4,5 => SOL * DIS # I4: 1,4 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # F4: 4,7 => SOL * DIS # F4: 8 => CTR => F4: 4,7 * DIS # C8: 6,7 => CTR => C8: 4,5 * DIS # B9: 6,7 => CTR => B9: 8 * DIS # F8: 6,7 => CTR => F8: 2,4,5,9 * CNT 23 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 4,6 => CTR => A1: 3,5 * PRF A1: 3,5 # A2: 4,6 => SOL * STA A1: 3,5 + A2: 4,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .2.97........8..1.......3.....5..2..7.1......84.......9.......71......8....3..... | initial |
| .2.971.......83.12.1....3.....5..2..751......842......9......271......832..3..... | autosolve |
| 523971864679483512418265379396517248751824936842639751934158627165792483287346195 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A3: 4,6 D2: 4,6 H3: 7,9 I3: 8,9 A4: 3,6 E4: 1,4 H4: 4,7 B8: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E4,I4: 1.. / E4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) D6,D7: 1.. / D6 = 1 => 0 pairs (X) / D7 = 1 => 0 pairs (_) A1,C1: 3.. / A1 = 3 => 9 pairs (_) / C1 = 3 => 0 pairs (*) E5,E6: 3.. / E5 = 3 => 8 pairs (_) / E6 = 3 => 8 pairs (_) H5,H6: 3.. / H5 = 3 => 8 pairs (_) / H6 = 3 => 8 pairs (_) B7,C7: 3.. / B7 = 3 => 9 pairs (_) / C7 = 3 => 15 pairs (_) E5,H5: 3.. / E5 = 3 => 8 pairs (_) / H5 = 3 => 8 pairs (_) E6,H6: 3.. / E6 = 3 => 8 pairs (_) / H6 = 3 => 8 pairs (_) A1,A4: 3.. / A1 = 3 => 9 pairs (_) / A4 = 3 => 0 pairs (*) B4,B7: 3.. / B4 = 3 => 15 pairs (_) / B7 = 3 => 9 pairs (_) A1,A2: 5.. / A1 = 5 => 0 pairs (*) / A2 = 5 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 8 pairs (_) / F3 = 5 => 8 pairs (_) A2,G2: 5.. / A2 = 5 => 8 pairs (_) / G2 = 5 => 0 pairs (*) G2,H3: 7.. / G2 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) C3,H3: 7.. / C3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) F4,H4: 7.. / F4 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) D6,D8: 7.. / D6 = 7 => 0 pairs (X) / D8 = 7 => 13 pairs (_) G2,G6: 7.. / G2 = 7 => 0 pairs (X) / G6 = 7 => 0 pairs (_) C1,C3: 8.. / C1 = 8 => 0 pairs (X) / C3 = 8 => 0 pairs (_) B7,B9: 8.. / B7 = 8 => 0 pairs (X) / B9 = 8 => 9 pairs (_) C3,I3: 8.. / C3 = 8 => 0 pairs (*) / I3 = 8 => 0 pairs (X) F4,I4: 8.. / F4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) B9,F9: 8.. / B9 = 8 => 9 pairs (_) / F9 = 8 => 0 pairs (X) D5,D7: 8.. / D5 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) G1,G5: 8.. / G1 = 8 => 0 pairs (*) / G5 = 8 => 0 pairs (X) B4,C4: 9.. / B4 = 9 => 10 pairs (_) / C4 = 9 => 13 pairs (_) B2,B4: 9.. / B2 = 9 => 13 pairs (_) / B4 = 9 => 10 pairs (_) * DURATION: 0:00:50.082082 START: 19:12:35.830520 END: 19:13:25.912602 2017-05-04 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B8,D2,E4,H3,H4,I3) * .2.971.......83.12.1....3.....5..2..751......842......9......271......832..3..... * PAIR A3: 4,6 BLK 1 A1: 4,6,3,5 # reduction candidate for 4,6 A1: 4,6 => CTR * .23971865579483.12.18...3793965172487518..93684263975193.1.8.2716.792.832873..19. A1: 3,5 # 9 pairs A2: 4,6,5 # reduction candidate for 4,6 A2: 4,6 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 A2: 5 # 8 pairs * PAIR A3: 4,6 ROW 3 D3: 4,6,2 # reduction candidate for 4,6 D3: 4,6 # 15 pairs E3: 4,6,2,5 # reduction candidate for 4,6 E3: 4,6 # 9 pairs F3: 4,6,2,5 # reduction candidate for 4,6 F3: 4,6 # 9 pairs * PAIR D2: 4,6 BLK 2 D3: 4,6,2 # reduction candidate for 4,6 D3: 4,6 # 15 pairs E3: 4,6,2,5 # reduction candidate for 4,6 E3: 4,6 # 9 pairs F3: 4,6,2,5 # reduction candidate for 4,6 F3: 4,6 # 9 pairs * PAIR D2: 4,6 ROW 2 A2: 4,6,5 # reduction candidate for 4,6 A2: 4,6 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 A2: 5 # 8 pairs G2: 4,6,5,7,9 # reduction candidate for 4,6 G2: 4,6 => CTR * .2.9718655.6483.12.18...379...5172487518..9368426397519..1...2716.792.832..3..19. G2: 5,7,9 # 10 pairs * PAIR D2: 4,6 COL D D5: 4,6,2,8 # reduction candidate for 4,6 D5: 4,6 => CTR * .2.971....7..83.12.1.2..37..9.54.2..751......8421.....9..8...271..7...832873..... D5: 2,8 # 9 pairs D7: 4,6,1,8 # reduction candidate for 4,6 D7: 4,6 => CTR * .2.971.......83.12.1....3.....5..2..7518.....8421.....9......271..7...832..3..... D7: 1,8 # 9 pairs D8: 4,6,2,7 # reduction candidate for 4,6 D8: 4,6 => CTR * .2.971.......83712.17...398...5.827.751...8..8427.....9831...271......832..3..... D8: 2,7 # 9 pairs * PAIR H3: 7,9 BLK 3 G2: 7,9,4,5,6 # reduction candidate for 7,9 G2: 7,9 => CTR * 328971...5..483712417...3986..5.827.751...8..8421.7...9..8...2717.....8328.3..... G2: 4,5,6 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 * PAIR H3: 7,9 ROW 3 C3: 7,9,8 # reduction candidate for 7,9 C3: 7,9 => CTR * 328971...5...83712417...3986..5.827.751...8..8421.7...9..8...2717.....8328.3..... C3: 8 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 * PAIR H3: 7,9 COL H H6: 7,9,3,5,6 # reduction candidate for 7,9 H6: 7,9 => CTR * .2.9718......83.12.18...379...517248751....36842639...9......271..7...832..3..... H6: 3,5,6 # 8 pairs * PAIR I3: 8,9 ROW 3 C3: 8,9,7 # reduction candidate for 8,9 C3: 8,9 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 C3: 7 => CTR * .28971.......83.12.17...398...5.827.751...8..842......9..8...271......8328.3.7... * PAIR I3: 8,9 COL I I5: 8,9,4,6 # reduction candidate for 8,9 I5: 8,9 => CTR * .2.971.......83712.17...398...5.827.751...8.98421.7...9..8...2717.....8328.3..... I5: 4,6 # 9 pairs * PAIR A4: 3,6 BLK 4 B4: 3,6,9 # reduction candidate for 3,6 B4: 3,6 # 13 pairs C4: 3,6,9 # reduction candidate for 3,6 C4: 3,6 # 10 pairs * PAIR A4: 3,6 COL A A1: 3,6,4,5 # reduction candidate for 3,6 A1: 4,5 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 A1: 3,6 # 8 pairs * PAIR E4: 1,4 ROW 4 I4: 1,4,8 # reduction candidate for 1,4 I4: 1,4 => CTR * .2.971.......83712.17...398...5.827.751...8..8421.7...9..8...2717.....8328.3..... I4: 8 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 * PAIR E4: 1,4 COL E E7: 1,4,5,6 # reduction candidate for 1,4 E7: 1,4 # 9 pairs E9: 1,4,5,6,9 # reduction candidate for 1,4 E9: 1,4 # 10 pairs * PAIR H4: 4,7 ROW 4 F4: 4,7,8 # reduction candidate for 4,7 F4: 4,7 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 F4: 8 => CTR * .2.971.......83712.17...398...5.827.751...8..8421.7...9..8...2717.....8328.3..... * PAIR B8: 6,7 BLK 7 C8: 6,7,4,5 # reduction candidate for 6,7 C8: 6,7 => CTR * .2.971.......83712.17...398...5.4271751......8427.....93.1.8.271......8328.3.7... C8: 4,5 # 9 pairs B9: 6,7,8 # reduction candidate for 6,7 B9: 6,7 => CTR * 3269718545974836124182..3796395172487518..9368426.97.19831...271..7...8327.3.81.. B9: 8 # 9 pairs C9: 6,7,4,5 # reduction candidate for 6,7 C9: 6,7 # 12 pairs * PAIR B8: 6,7 ROW 8 D8: 6,7,2,4 # reduction candidate for 6,7 D8: 6,7 # 10 pairs F8: 6,7,2,4,5,9 # reduction candidate for 6,7 F8: 6,7 => CTR * .2.971.......83712.17...398...5.827.751...8..8427.....9831...271......832..3..... F8: 2,4,5,9 # 8 pairs * PAIR B8: 6,7 COL B B2: 6,7,9 # reduction candidate for 6,7 B2: 9 # 13 pairs B2: 6,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-485-base-pr-000.dot * REASONING * DIS # A1: 4,6 => CTR => A1: 3,5 * PRF # A2: 4,6 => SOL * PRF # A2: 4,6 => SOL * DIS # G2: 4,6 => CTR => G2: 5,7,9 * DIS # D5: 4,6 => CTR => D5: 2,8 * DIS # D7: 4,6 => CTR => D7: 1,8 * DIS # D8: 4,6 => CTR => D8: 2,7 * DIS # G2: 7,9 => CTR => G2: 4,5,6 * PRF # G2: 4,5,6 => SOL * DIS # C3: 7,9 => CTR => C3: 8 * PRF # C3: 8 => SOL * DIS # H6: 7,9 => CTR => H6: 3,5,6 * PRF # C3: 8,9 => SOL * DIS # C3: 7 => CTR => C3: 8,9 * DIS # I5: 8,9 => CTR => I5: 4,6 * PRF # A1: 4,5 => SOL * DIS # I4: 1,4 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # F4: 4,7 => SOL * DIS # F4: 8 => CTR => F4: 4,7 * DIS # C8: 6,7 => CTR => C8: 4,5 * DIS # B9: 6,7 => CTR => B9: 8 * DIS # F8: 6,7 => CTR => F8: 2,4,5,9 * CNT 23 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A4,B8,D2,E4,H3,H4,I3) * .2.971.......83.12.1....3.....5..2..751......842......9......271......832..3..... * PAIR A3: 4,6 BLK 1 A1: 4,6,3,5 # reduction candidate for 4,6 A1: 4,6 => CTR * .23971865579483.12.18...3793965172487518..93684263975193.1.8.2716.792.832873..19. A2: 4,6,5 # reduction candidate for 4,6 A2: 4,6 => SOLVED * 523971864679483512418265379396517248751824936842639751934158627165792483287346195 * DURATION: 0:00:04.027474 START: 19:14:15.062055 END: 19:14:19.089529 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-485-base-pr-001.dot * REASONING * DIS # A1: 4,6 => CTR => A1: 3,5 * PRF A1: 3,5 # A2: 4,6 => SOL * STA A1: 3,5 + A2: 4,6 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 485 solution: 523971864679483512418265379396517248751824936842639751934158627165792483287346195 info: 95984 FNBHWXYK S8.f 41704 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 523971864679483512418265379396517248751824936842639751934158627165792483287346195 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:
* DIS # A1: 4,6 => CTR => A1: 3,5 * INC # A1: 3,5 => UNS * PRF # A2: 4,6 => SOL * INC # A2: 5 => UNS * INC # D3: 4,6 => UNS * INC # E3: 4,6 => UNS * INC # F3: 4,6 => UNS * INC # D3: 4,6 => UNS * INC # E3: 4,6 => UNS * INC # F3: 4,6 => UNS * PRF # A2: 4,6 => SOL * INC # A2: 5 => UNS * DIS # G2: 4,6 => CTR => G2: 5,7,9 * INC # G2: 5,7,9 => UNS * DIS # D5: 4,6 => CTR => D5: 2,8 * INC # D5: 2,8 => UNS * DIS # D7: 4,6 => CTR => D7: 1,8 * INC # D7: 1,8 => UNS * DIS # D8: 4,6 => CTR => D8: 2,7 * INC # D8: 2,7 => UNS * DIS # G2: 7,9 => CTR => G2: 4,5,6 * PRF # G2: 4,5,6 => SOL * DIS # C3: 7,9 => CTR => C3: 8 * PRF # C3: 8 => SOL * DIS # H6: 7,9 => CTR => H6: 3,5,6 * INC # H6: 3,5,6 => UNS * PRF # C3: 8,9 => SOL * DIS # C3: 7 => CTR => C3: 8,9 * DIS # I5: 8,9 => CTR => I5: 4,6 * INC # I5: 4,6 => UNS * INC # B4: 3,6 => UNS * INC # C4: 3,6 => UNS * INC # A1: 3,6 => UNS * PRF # A1: 4,5 => SOL * DIS # I4: 1,4 => CTR => I4: 8 * PRF # I4: 8 => SOL * INC # E7: 1,4 => UNS * INC # E9: 1,4 => UNS * PRF # F4: 4,7 => SOL * DIS # F4: 8 => CTR => F4: 4,7 * DIS # C8: 6,7 => CTR => C8: 4,5 * INC # C8: 4,5 => UNS * DIS # B9: 6,7 => CTR => B9: 8 * INC # B9: 8 => UNS * INC # C9: 6,7 => UNS * INC # D8: 6,7 => UNS * DIS # F8: 6,7 => CTR => F8: 2,4,5,9 * INC # F8: 2,4,5,9 => UNS * INC # B2: 6,7 => UNS * INC # B2: 9 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 4,6 => CTR => A1: 3,5 * PRF A1: 3,5 # A2: 4,6 => SOL * STA A1: 3,5 + A2: 4,6 * CNT 2 HDP CHAINS / 2 HYP OPENED