Analysis of xx-top500-499-base.sdk
Contents
Original Sudoku
level: medium
position: 6.71............48.............4..2.....85...1...........3.87...45...6...2....... initial
Autosolve
position: 6871.42.5...567.48...8.2.......41.2.....85...1...73...9..328754.457196.272.456... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A5: 2,3 => SOL * DIS # A5: 4 => CTR => A5: 2,3 * DIS # B3: 3,9 => CTR => B3: 1,5 * DIS # C3: 3,9 => CTR => C3: 1,4 * DIS # H5: 3,9 => CTR => H5: 1,6,7 * DIS # H9: 3,9 => CTR => H9: 1,8 * DIS # H5: 1,3,9 => CTR => H5: 6,7 * DIS # I5: 6,7 => CTR => I5: 1,3,9 * DIS # D6: 6,9 => CTR => D6: 2 * DIS # B4: 6,9 => CTR => B4: 3,5,7 * DIS # I4: 6,9 => CTR => I4: 3,7 * DIS # I4: 6,9 => CTR => I4: 3,7 * DIS # H5: 6,9 => CTR => H5: 1,3,7 * DIS # I5: 6,9 => CTR => I5: 1,3,7 * DIS # H6: 6,9 => CTR => H6: 8 * PRF # H6: 8 => SOL * PRF # B6: 6,9 => SOL * DIS # B6: 5 => CTR => B6: 6,9 * DIS # C6: 6,9 => CTR => C6: 2,4,8 * DIS # D6: 6,9 => CTR => D6: 2 * DIS # A4: 3,8 => CTR => A4: 5 * PRF # A4: 5 => SOL * DIS # H9: 3,8 => CTR => H9: 1,9 * DIS # H9: 3,8 => CTR => H9: 1,9 * CNT 24 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A5: 2,3 => SOL * STA A5: 2,3 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6.71............48.............4..2.....85...1...........3.87...45...6...2....... | initial |
| 6871.42.5...567.48...8.2.......41.2.....85...1...73...9..328754.457196.272.456... | autosolve |
| 687134295239567148451892367578641923362985471194273586916328754845719632723456819 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A2: 2,3 E1: 3,9 E3: 3,9 H1: 3,9 H3: 6,7 I3: 6,7 D4: 6,9 I6: 6,9 B7: 1,6 C7: 1,6 A8: 3,8 C9: 3,8 H8: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 1.. / G2 = 1 => 18 pairs (_) / G3 = 1 => 14 pairs (_) H5,I5: 1.. / H5 = 1 => 0 pairs (X) / I5 = 1 => 14 pairs (_) B7,C7: 1.. / B7 = 1 => 12 pairs (_) / C7 = 1 => 12 pairs (_) H9,I9: 1.. / H9 = 1 => 14 pairs (_) / I9 = 1 => 0 pairs (X) H5,H9: 1.. / H5 = 1 => 0 pairs (X) / H9 = 1 => 14 pairs (_) I5,I9: 1.. / I5 = 1 => 14 pairs (_) / I9 = 1 => 0 pairs (X) A2,C2: 2.. / A2 = 2 => 13 pairs (_) / C2 = 2 => 0 pairs (X) D5,D6: 2.. / D5 = 2 => 0 pairs (X) / D6 = 2 => 14 pairs (_) C6,D6: 2.. / C6 = 2 => 0 pairs (X) / D6 = 2 => 14 pairs (_) A2,A5: 2.. / A2 = 2 => 13 pairs (_) / A5 = 2 => 0 pairs (X) E1,E3: 3.. / E1 = 3 => 18 pairs (_) / E3 = 3 => 0 pairs (X) A8,C9: 3.. / A8 = 3 => 0 pairs (X) / C9 = 3 => 20 pairs (_) E1,H1: 3.. / E1 = 3 => 18 pairs (_) / H1 = 3 => 0 pairs (X) A8,H8: 3.. / A8 = 3 => 0 pairs (X) / H8 = 3 => 20 pairs (_) A3,C3: 4.. / A3 = 4 => 0 pairs (*) / C3 = 4 => 0 pairs (X) G5,G6: 4.. / G5 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) C6,G6: 4.. / C6 = 4 => 0 pairs (*) / G6 = 4 => 0 pairs (X) A3,A5: 4.. / A3 = 4 => 0 pairs (*) / A5 = 4 => 0 pairs (X) A3,B3: 5.. / A3 = 5 => 0 pairs (X) / B3 = 5 => 0 pairs (_) G4,G6: 5.. / G4 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) B6,G6: 5.. / B6 = 5 => 0 pairs (X) / G6 = 5 => 0 pairs (_) A3,A4: 5.. / A3 = 5 => 0 pairs (X) / A4 = 5 => 0 pairs (_) H3,I3: 6.. / H3 = 6 => 13 pairs (_) / I3 = 6 => 16 pairs (_) B7,C7: 6.. / B7 = 6 => 12 pairs (_) / C7 = 6 => 12 pairs (_) H3,I3: 7.. / H3 = 7 => 16 pairs (_) / I3 = 7 => 13 pairs (_) B4,B5: 7.. / B4 = 7 => 15 pairs (_) / B5 = 7 => 16 pairs (_) B4,I4: 7.. / B4 = 7 => 15 pairs (_) / I4 = 7 => 16 pairs (_) H3,H5: 7.. / H3 = 7 => 16 pairs (_) / H5 = 7 => 13 pairs (_) A8,C9: 8.. / A8 = 8 => 20 pairs (_) / C9 = 8 => 0 pairs (X) A8,H8: 8.. / A8 = 8 => 20 pairs (_) / H8 = 8 => 0 pairs (X) A4,A8: 8.. / A4 = 8 => 0 pairs (X) / A8 = 8 => 20 pairs (_) E1,E3: 9.. / E1 = 9 => 0 pairs (X) / E3 = 9 => 18 pairs (_) E1,H1: 9.. / E1 = 9 => 0 pairs (X) / H1 = 9 => 18 pairs (_) * DURATION: 0:00:53.615590 START: 19:45:18.515986 END: 19:46:12.131576 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B7,C7,C9,D4,E1,E3,H1,H3,H8,I3,I6) * 6871.42.5...567.48...8.2.......41.2.....85...1...73...9..328754.457196.272.456... * PAIR A2: 2,3 BLK 1 C2: 2,3,1,9 # reduction candidate for 2,3 C2: 2,3 # 21 pairs C2: 1,9 # 14 pairs * PAIR A2: 2,3 COL A A5: 2,3,4 # reduction candidate for 2,3 A5: 2,3 => SOLVED * 687134295239567148451892367578641923362985471194273586916328754845719632723456819 A5: 4 => CTR * 6871342952..567.485.4892...3.8.4152.4...859.315..734869..3287548457196327234568.. * PAIR E3: 3,9 ROW 3 B3: 3,9,1,5 # reduction candidate for 3,9 B3: 3,9 => CTR * 6871342952..5673485348921..3.8.4152.4...859.315..734869..3287548457196327234568.. B3: 1,5 # 14 pairs C3: 3,9,1,4 # reduction candidate for 3,9 C3: 3,9 => CTR * 687134295...5673484598.21..5...41.2.....85...1...735..9..328754845719632723456... C3: 1,4 # 14 pairs G3: 3,9,1 # reduction candidate for 3,9 G3: 3,9 # 18 pairs * PAIR H1: 3,9 BLK 3 G2: 3,9,1 # reduction candidate for 3,9 G2: 3,9 # 14 pairs G3: 3,9,1 # reduction candidate for 3,9 G3: 3,9 # 18 pairs * PAIR H1: 3,9 COL H H5: 3,9,1,6,7 # reduction candidate for 3,9 H5: 3,9 => CTR * 6871342952..567.485.4892.76....41.27.7..85.3115.273.699..328754345719682728456913 H5: 1,6,7 # 13 pairs H9: 3,9,1,8 # reduction candidate for 3,9 H9: 3,9 => CTR * 6871.42.52..567.485.48.2.768...41.2.....85.1.15.2738699..328754345719682728456..1 H9: 1,8 # 14 pairs * PAIR H3: 6,7 COL H H5: 6,7,1,3,9 # reduction candidate for 6,7 H5: 1,3,9 => CTR * 6871.42.5...567.485.48.2.76....4152.4.2.853..15.273.699..328754.457196.272.456... H5: 6,7 # 16 pairs * PAIR I3: 6,7 COL I I4: 6,7,3,9 # reduction candidate for 6,7 I4: 6,7 # 19 pairs I5: 6,7,1,3,9 # reduction candidate for 6,7 I5: 6,7 => CTR * 6871.42.5...567.48...8.2.76.7..41.23....854171542738699..328754.457196.272.456..1 I5: 1,3,9 # 13 pairs * PAIR D4: 6,9 BLK 5 D5: 6,9,2 # reduction candidate for 6,9 D5: 6,9 # 14 pairs D6: 6,9,2 # reduction candidate for 6,9 D6: 6,9 => CTR * 6871342952.9567.485.4892.673.8.4152....2859..1529734869..328754845719632723456819 D6: 2 # 14 pairs * PAIR D4: 6,9 ROW 4 B4: 6,9,3,5,7 # reduction candidate for 6,9 B4: 6,9 => CTR * 6871.42.52..567.48...8.2.76....41.27.7..85.611...73.899..32875484571963272.456... B4: 3,5,7 # 13 pairs C4: 6,9,3,8 # reduction candidate for 6,9 C4: 6,9 # 15 pairs I4: 6,9,3,7 # reduction candidate for 6,9 I4: 6,9 => CTR * 6871.42.5...567.48...8.2.67.7..41.2.....85.711...73.8.9..32875484571963272.456... I4: 3,7 # 14 pairs * PAIR I6: 6,9 BLK 6 I4: 6,9,3,7 # reduction candidate for 6,9 I4: 6,9 => CTR * 6871.42.5...567.48...8.2.67.7..41.2.....85.711...73.8.9..32875484571963272.456... I4: 3,7 # 14 pairs H5: 6,9,1,3,7 # reduction candidate for 6,9 H5: 6,9 => CTR * 6871.42.5...567.48...8.2.76....41.2.....85..11...73..99..328754.457196.272.456.13 H5: 1,3,7 # 13 pairs I5: 6,9,1,3,7 # reduction candidate for 6,9 I5: 6,9 => CTR * 6871.42.5...567.48...8.2.......41.2.....85.1.1...73...9..328754.457196.272.456..1 I5: 1,3,7 # 13 pairs H6: 6,9,8 # reduction candidate for 6,9 H6: 6,9 => CTR * 6871.42.5...567.48...8.2.......41.2.....854..1542738..9..328754.457196.272.456... H6: 8 => SOLVED * 687134295239567148451892367578641923362985471194273586916328754845719632723456819 * PAIR I6: 6,9 ROW 6 B6: 6,9,5 # reduction candidate for 6,9 B6: 6,9 => SOLVED * 687134295239567148451892367578641923362985471194273586916328754845719632723456819 B6: 5 => CTR * 6871342952..567.485.4892...3.8.4152.4...859.315..734869..3287548457196327234568.. C6: 6,9,2,4,8 # reduction candidate for 6,9 C6: 6,9 => CTR * 687134295.9.567.485.4892.673.8.4152.....859..1592734869..328754845719632723456819 C6: 2,4,8 # 13 pairs D6: 6,9,2 # reduction candidate for 6,9 D6: 6,9 => CTR * 6871342952.9567.485.4892.673.8.4152....2859..1529734869..328754845719632723456819 D6: 2 # 14 pairs * PAIR A8: 3,8 COL A A4: 3,8,5 # reduction candidate for 3,8 A4: 3,8 => CTR * 6871342952..567.485.4892...3.8.4152.4...859.315..734869..3287548457196327234568.. A4: 5 => SOLVED * 687134295239567148451892367578641923362985471194273586916328754845719632723456819 * PAIR C9: 3,8 ROW 9 G9: 3,8,9 # reduction candidate for 3,8 G9: 3,8 # 21 pairs H9: 3,8,1,9 # reduction candidate for 3,8 H9: 3,8 => CTR * 687134295...567.485.4892.76....4152.4.2.8531.15.273.699..328754.457196.272.4569.1 H9: 1,9 # 14 pairs * PAIR C9: 3,8 COL C C4: 3,8,6,9 # reduction candidate for 3,8 C4: 6,9 # 15 pairs C4: 3,8 # 14 pairs * PAIR H8: 3,8 BLK 9 G9: 3,8,9 # reduction candidate for 3,8 G9: 3,8 # 21 pairs H9: 3,8,1,9 # reduction candidate for 3,8 H9: 3,8 => CTR * 687134295...567.485.4892.76....4152.4.2.8531.15.273.699..328754.457196.272.4569.1 H9: 1,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-499-base-pr-000.dot * REASONING * PRF # A5: 2,3 => SOL * DIS # A5: 4 => CTR => A5: 2,3 * DIS # B3: 3,9 => CTR => B3: 1,5 * DIS # C3: 3,9 => CTR => C3: 1,4 * DIS # H5: 3,9 => CTR => H5: 1,6,7 * DIS # H9: 3,9 => CTR => H9: 1,8 * DIS # H5: 1,3,9 => CTR => H5: 6,7 * DIS # I5: 6,7 => CTR => I5: 1,3,9 * DIS # D6: 6,9 => CTR => D6: 2 * DIS # B4: 6,9 => CTR => B4: 3,5,7 * DIS # I4: 6,9 => CTR => I4: 3,7 * DIS # I4: 6,9 => CTR => I4: 3,7 * DIS # H5: 6,9 => CTR => H5: 1,3,7 * DIS # I5: 6,9 => CTR => I5: 1,3,7 * DIS # H6: 6,9 => CTR => H6: 8 * PRF # H6: 8 => SOL * PRF # B6: 6,9 => SOL * DIS # B6: 5 => CTR => B6: 6,9 * DIS # C6: 6,9 => CTR => C6: 2,4,8 * DIS # D6: 6,9 => CTR => D6: 2 * DIS # A4: 3,8 => CTR => A4: 5 * PRF # A4: 5 => SOL * DIS # H9: 3,8 => CTR => H9: 1,9 * DIS # H9: 3,8 => CTR => H9: 1,9 * CNT 24 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A8,B7,C7,C9,D4,E1,E3,H1,H3,H8,I3,I6) * 6871.42.5...567.48...8.2.......41.2.....85...1...73...9..328754.457196.272.456... * PAIR A2: 2,3 BLK 1 C2: 2,3,1,9 # reduction candidate for 2,3 C2: 2,3 # 21 pairs C2: 1,9 # 14 pairs * PAIR A2: 2,3 COL A A5: 2,3,4 # reduction candidate for 2,3 A5: 2,3 => SOLVED * 687134295239567148451892367578641923362985471194273586916328754845719632723456819 * DURATION: 0:00:03.861395 START: 19:46:58.110901 END: 19:47:01.972296 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-499-base-pr-001.dot * REASONING * PRF # A5: 2,3 => SOL * STA A5: 2,3 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 499 solution: 687134295239567148451892367578641923362985471194273586916328754845719632723456819 info: 96705 FNBHYK S8.f 35575 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 687134295239567148451892367578641923362985471194273586916328754845719632723456819 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 # C2: 2,3 => UNS * INC # C2: 1,9 => UNS * PRF # A5: 2,3 => SOL * DIS # A5: 4 => CTR => A5: 2,3 * DIS # B3: 3,9 => CTR => B3: 1,5 * INC # B3: 1,5 => UNS * DIS # C3: 3,9 => CTR => C3: 1,4 * INC # C3: 1,4 => UNS * INC # G3: 3,9 => UNS * INC # G2: 3,9 => UNS * INC # G3: 3,9 => UNS * DIS # H5: 3,9 => CTR => H5: 1,6,7 * INC # H5: 1,6,7 => UNS * DIS # H9: 3,9 => CTR => H9: 1,8 * INC # H9: 1,8 => UNS * INC # H5: 6,7 => UNS * DIS # H5: 1,3,9 => CTR => H5: 6,7 * INC # I4: 6,7 => UNS * DIS # I5: 6,7 => CTR => I5: 1,3,9 * INC # I5: 1,3,9 => UNS * INC # D5: 6,9 => UNS * DIS # D6: 6,9 => CTR => D6: 2 * INC # D6: 2 => UNS * DIS # B4: 6,9 => CTR => B4: 3,5,7 * INC # B4: 3,5,7 => UNS * INC # C4: 6,9 => UNS * DIS # I4: 6,9 => CTR => I4: 3,7 * INC # I4: 3,7 => UNS * DIS # I4: 6,9 => CTR => I4: 3,7 * INC # I4: 3,7 => UNS * DIS # H5: 6,9 => CTR => H5: 1,3,7 * INC # H5: 1,3,7 => UNS * DIS # I5: 6,9 => CTR => I5: 1,3,7 * INC # I5: 1,3,7 => UNS * DIS # H6: 6,9 => CTR => H6: 8 * PRF # H6: 8 => SOL * PRF # B6: 6,9 => SOL * DIS # B6: 5 => CTR => B6: 6,9 * DIS # C6: 6,9 => CTR => C6: 2,4,8 * INC # C6: 2,4,8 => UNS * DIS # D6: 6,9 => CTR => D6: 2 * INC # D6: 2 => UNS * DIS # A4: 3,8 => CTR => A4: 5 * PRF # A4: 5 => SOL * INC # G9: 3,8 => UNS * DIS # H9: 3,8 => CTR => H9: 1,9 * INC # H9: 1,9 => UNS * INC # C4: 3,8 => UNS * INC # C4: 6,9 => UNS * INC # G9: 3,8 => UNS * DIS # H9: 3,8 => CTR => H9: 1,9 * INC # H9: 1,9 => UNS * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 2,3 => UNS * INC # C2: 1,9 => UNS * PRF # A5: 2,3 => SOL * STA A5: 2,3 * CNT 3 HDP CHAINS / 3 HYP OPENED