Analysis of xx-top500-171-base.sdk
Contents
Original Sudoku
level: medium
position: .9.5............1.........4...82.9..7.....3....1......4....1.6....6...7..2....5.. initial
Autosolve
position: .9451673..6.4...15.1....6946438279517..1..3.6..1.6.4.747...1.6..3.6..17.126...54. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I7: 2,8 => CTR => I7: 3,9 * DIS # F6: 3,9 => CTR => F6: 5 * PRF # D7: 3,9 => SOL * DIS # D7: 2 => CTR => D7: 3,9 * DIS # D9: 3,9 => CTR => D9: 7 * DIS # I7: 2,8 => CTR => I7: 3,9 * CNT 6 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I7: 2,8 => CTR => I7: 3,9 * DIS I7: 3,9 # I8: 9 => CTR => I8: 2,8 * PRF I7: 3,9 + I8: 2,8 # A2: 2,8 => SOL * STA I7: 3,9 + I8: 2,8 + A2: 2,8 * CNT 3 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9.5............1.........4...82.9..7.....3....1......4....1.6....6...7..2....5.. | initial |
| .9451673..6.4...15.1....6946438279517..1..3.6..1.6.4.747...1.6..3.6..17.126...54. | autosolve |
| 894516732267439815315278694643827951752194386981365427478951263539642178126783549 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) A1: 2,8 I1: 2,8 G2: 2,8 B5: 5,8 C5: 2,9 A6: 2,9 B6: 5,8 D6: 3,9 H5: 2,8 H6: 2,8 G7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,G2: 2.. / I1 = 2 => 0 pairs (*) / G2 = 2 => 0 pairs (X) C5,A6: 2.. / C5 = 2 => 12 pairs (_) / A6 = 2 => 0 pairs (X) H5,H6: 2.. / H5 = 2 => 0 pairs (X) / H6 = 2 => 12 pairs (_) D7,F8: 2.. / D7 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) A1,I1: 2.. / A1 = 2 => 15 pairs (_) / I1 = 2 => 0 pairs (*) C5,H5: 2.. / C5 = 2 => 12 pairs (_) / H5 = 2 => 0 pairs (X) A6,H6: 2.. / A6 = 2 => 0 pairs (X) / H6 = 2 => 12 pairs (_) F8,I8: 2.. / F8 = 2 => 0 pairs (*) / I8 = 2 => 0 pairs (X) D3,D7: 2.. / D3 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) G2,G7: 2.. / G2 = 2 => 15 pairs (_) / G7 = 2 => 0 pairs (*) A2,A3: 3.. / A2 = 3 => 11 pairs (_) / A3 = 3 => 19 pairs (_) D6,F6: 3.. / D6 = 3 => 15 pairs (_) / F6 = 3 => 0 pairs (X) I7,I9: 3.. / I7 = 3 => 13 pairs (_) / I9 = 3 => 16 pairs (_) E5,F5: 4.. / E5 = 4 => 0 pairs (X) / F5 = 4 => 12 pairs (_) E8,F8: 4.. / E8 = 4 => 12 pairs (_) / F8 = 4 => 0 pairs (X) E5,E8: 4.. / E5 = 4 => 0 pairs (X) / E8 = 4 => 12 pairs (_) F5,F8: 4.. / F5 = 4 => 12 pairs (_) / F8 = 4 => 0 pairs (X) A3,C3: 5.. / A3 = 5 => 12 pairs (_) / C3 = 5 => 14 pairs (_) B5,B6: 5.. / B5 = 5 => 12 pairs (_) / B6 = 5 => 0 pairs (X) B6,F6: 5.. / B6 = 5 => 0 pairs (X) / F6 = 5 => 12 pairs (_) C7,E7: 5.. / C7 = 5 => 0 pairs (X) / E7 = 5 => 13 pairs (_) A3,A8: 5.. / A3 = 5 => 12 pairs (_) / A8 = 5 => 14 pairs (_) C2,C3: 7.. / C2 = 7 => 11 pairs (_) / C3 = 7 => 18 pairs (_) D9,E9: 7.. / D9 = 7 => 12 pairs (_) / E9 = 7 => 0 pairs (X) C2,E2: 7.. / C2 = 7 => 11 pairs (_) / E2 = 7 => 18 pairs (_) D3,D9: 7.. / D3 = 7 => 0 pairs (X) / D9 = 7 => 12 pairs (_) I1,G2: 8.. / I1 = 8 => 15 pairs (_) / G2 = 8 => 0 pairs (*) B5,B6: 8.. / B5 = 8 => 0 pairs (X) / B6 = 8 => 12 pairs (_) H5,H6: 8.. / H5 = 8 => 12 pairs (_) / H6 = 8 => 0 pairs (X) A1,I1: 8.. / A1 = 8 => 0 pairs (*) / I1 = 8 => 0 pairs (X) B5,H5: 8.. / B5 = 8 => 0 pairs (X) / H5 = 8 => 12 pairs (_) B6,H6: 8.. / B6 = 8 => 12 pairs (_) / H6 = 8 => 0 pairs (X) G2,G7: 8.. / G2 = 8 => 0 pairs (*) / G7 = 8 => 0 pairs (X) E2,F2: 9.. / E2 = 9 => 12 pairs (_) / F2 = 9 => 14 pairs (_) C5,A6: 9.. / C5 = 9 => 0 pairs (X) / A6 = 9 => 12 pairs (_) A6,A8: 9.. / A6 = 9 => 12 pairs (_) / A8 = 9 => 0 pairs (X) * DURATION: 0:00:57.867257 START: 08:34:42.208270 END: 08:35:40.075527 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B5,B6,C5,D6,G2,G7,H5,H6,I1) * .9451673..6.4...15.1....6946438279517..1..3.6..1.6.4.747...1.6..3.6..17.126...54. * PAIR A1: 2,8 BLK 1 A2: 2,8,3 # reduction candidate for 2,8 A2: 2,8 # 19 pairs C2: 2,8,7 # reduction candidate for 2,8 C2: 2,8 # 18 pairs A3: 2,8,3,5 # reduction candidate for 2,8 A3: 2,8 # 18 pairs C3: 2,8,5,7 # reduction candidate for 2,8 C3: 2,8 # 14 pairs * PAIR I1: 2,8 COL I I7: 2,8,3,9 # reduction candidate for 2,8 I7: 2,8 => CTR * .9451673..6.4...15.1....6946438279517..1..3.69.13654274792.1.6..3.6..179126...543 I7: 3,9 # 12 pairs I8: 2,8,9 # reduction candidate for 2,8 I8: 2,8 # 14 pairs * PAIR G2: 2,8 ROW 2 A2: 2,8,3 # reduction candidate for 2,8 A2: 2,8 # 19 pairs C2: 2,8,7 # reduction candidate for 2,8 C2: 2,8 # 18 pairs F2: 2,8,3,9 # reduction candidate for 2,8 F2: 2,8 # 13 pairs * PAIR D6: 3,9 BLK 5 F6: 3,9,5 # reduction candidate for 3,9 F6: 3,9 => CTR * 89451673236.4..81551....6946438279517891..326251.6.48747...126.93.6.2178126...54. F6: 5 # 12 pairs * PAIR D6: 3,9 COL D D7: 3,9,2 # reduction candidate for 3,9 D7: 3,9 => SOLVED * 894516732267439815315278694643827951752194386981365427478951263539642178126783549 D7: 2 => CTR * 294516738.674.32153157826946438279517.21..38698136542747.2.186..3.6..172126978543 D9: 3,9,7 # reduction candidate for 3,9 D9: 3,9 => CTR * 294516738.674..215.1.7.26946438279517.21..38698136542747.231869.39654172126978543 D9: 7 # 12 pairs * PAIR G7: 2,8 BLK 9 I7: 2,8,3,9 # reduction candidate for 2,8 I7: 2,8 => CTR * .9451673..6.4...15.1....6946438279517..1..3.69.13654274792.1.6..3.6..179126...543 I7: 3,9 # 12 pairs I8: 2,8,9 # reduction candidate for 2,8 I8: 2,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-171-base-pr-000.dot * REASONING * DIS # I7: 2,8 => CTR => I7: 3,9 * DIS # F6: 3,9 => CTR => F6: 5 * PRF # D7: 3,9 => SOL * DIS # D7: 2 => CTR => D7: 3,9 * DIS # D9: 3,9 => CTR => D9: 7 * DIS # I7: 2,8 => CTR => I7: 3,9 * CNT 6 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B5,B6,C5,D6,G2,G7,H5,H6,I1) * .9451673..6.4...15.1....6946438279517..1..3.6..1.6.4.747...1.6..3.6..17.126...54. * PAIR A1: 2,8 BLK 1 A2: 2,8,3 # reduction candidate for 2,8 A2: 2,8 # 19 pairs C2: 2,8,7 # reduction candidate for 2,8 C2: 2,8 # 18 pairs A3: 2,8,3,5 # reduction candidate for 2,8 A3: 2,8 # 18 pairs C3: 2,8,5,7 # reduction candidate for 2,8 C3: 2,8 # 14 pairs * PAIR I1: 2,8 COL I I7: 2,8,3,9 # reduction candidate for 2,8 I7: 2,8 => CTR * .9451673..6.4...15.1....6946438279517..1..3.69.13654274792.1.6..3.6..179126...543 I8: 2,8,9 # reduction candidate for 2,8 I8: 2,8 # 14 pairs * RESTART * PAIR I1: 2,8 COL I I8: 2,8,9 # reduction candidate for 2,8 I8: 9 => CTR * 894516732.6.4..815.1.2.86946438279517..1.43.69.1365427479..126..3.6.2179126...548 * PAIR RESTART * PAIR G2: 2,8 ROW 2 A2: 2,8,3 # reduction candidate for 2,8 A2: 2,8 => SOLVED * 894516732267439815315278694643827951752194386981365427478951263539642178126783549 * DURATION: 0:00:09.343236 START: 08:35:57.752258 END: 08:36:07.095494 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-171-base-pr-001.dot * REASONING * DIS # I7: 2,8 => CTR => I7: 3,9 * DIS I7: 3,9 # I8: 9 => CTR => I8: 2,8 * PRF I7: 3,9 + I8: 2,8 # A2: 2,8 => SOL * STA I7: 3,9 + I8: 2,8 + A2: 2,8 * CNT 3 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 171 solution: 894516732267439815315278694643827951752194386981365427478951263539642178126783549 info: 1826 FNBTWXY S8.f 24550 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 894516732267439815315278694643827951752194386981365427478951263539642178126783549 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 # A2: 2,8 => UNS * INC # C2: 2,8 => UNS * INC # A3: 2,8 => UNS * INC # C3: 2,8 => UNS * DIS # I7: 2,8 => CTR => I7: 3,9 * INC # I7: 3,9 => UNS * INC # I8: 2,8 => UNS * INC # A2: 2,8 => UNS * INC # C2: 2,8 => UNS * INC # F2: 2,8 => UNS * DIS # F6: 3,9 => CTR => F6: 5 * INC # F6: 5 => UNS * PRF # D7: 3,9 => SOL * DIS # D7: 2 => CTR => D7: 3,9 * DIS # D9: 3,9 => CTR => D9: 7 * INC # D9: 7 => UNS * DIS # I7: 2,8 => CTR => I7: 3,9 * INC # I7: 3,9 => UNS * INC # I8: 2,8 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 2,8 => UNS * INC # C2: 2,8 => UNS * INC # A3: 2,8 => UNS * INC # C3: 2,8 => UNS * DIS # I7: 2,8 => CTR => I7: 3,9 * INC I7: 3,9 # I8: 2,8 => UNS * INC I7: 3,9 # I8: 2,8 => UNS * DIS I7: 3,9 # I8: 9 => CTR => I8: 2,8 * PRF I7: 3,9 + I8: 2,8 # A2: 2,8 => SOL * STA I7: 3,9 + I8: 2,8 + A2: 2,8 * CNT 9 HDP CHAINS / 9 HYP OPENED