Analysis of xx-top500-026-base.sdk
Contents
Original Sudoku
level: medium
position: 35.....2....41....9...........7..1.482.............6....16..2.......9.5.......... initial
Autosolve
position: 354..672167241...89182.746.539762184826.41.7.1475..6.27.16..24.4631298572.5.74.16 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E6: 3 => CTR => E6: 8,9 * PRF # G2: 3,5 => SOL * DIS # G2: 9 => CTR => G2: 3,5 * DIS # F7: 8 => CTR => F7: 3,5 * DIS # E7: 8 => CTR => E7: 3,5 * PRF # G2: 5 => SOL * PRF # G2: 3,5 => SOL * DIS # G2: 9 => CTR => G2: 3,5 * PRF # I5: 3,5 => SOL * DIS # I5: 9 => CTR => I5: 3,5 * DIS # E6: 8 => CTR => E6: 3,9 * PRF # G5: 3,9 => SOL * DIS # E6: 3,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F7: 5 => SOL * PRF # G5: 3,9 => SOL * DIS # E6: 8 => CTR => E6: 3,9 * PRF # E7: 3,8 => SOL * PRF # I5: 5 => SOL * PRF # G5: 3,9 => SOL * CNT 20 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E6: 3 => CTR => E6: 8,9 * PRF E6: 8,9 # G2: 3,5 => SOL * STA E6: 8,9 + G2: 3,5 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 35.....2....41....9...........7..1.482.............6....16..2.......9.5.......... | initial |
| 354..672167241...89182.746.539762184826.41.7.1475..6.27.16..24.4631298572.5.74.16 | autosolve |
| 354986721672413598918257463539762184826341975147598632781635249463129857295874316 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) D1: 8,9 E1: 8,9 F2: 3,5 E3: 3,5 H2: 3,9 I3: 3,5 D5: 3,9 F6: 3,8 H6: 3,9 B7: 8,9 B9: 8,9 D9: 3,8 I7: 3,9 G9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F2,E3: 3.. / F2 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) I7,G9: 3.. / I7 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) E3,I3: 3.. / E3 = 3 => 15 pairs (_) / I3 = 3 => 0 pairs (*) D9,G9: 3.. / D9 = 3 => 0 pairs (X) / G9 = 3 => 0 pairs (_) D5,D9: 3.. / D5 = 3 => 0 pairs (*) / D9 = 3 => 0 pairs (X) H2,H6: 3.. / H2 = 3 => 0 pairs (X) / H6 = 3 => 0 pairs (_) F2,E3: 5.. / F2 = 5 => 15 pairs (_) / E3 = 5 => 0 pairs (*) G2,I3: 5.. / G2 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) G5,I5: 5.. / G5 = 5 => 15 pairs (_) / I5 = 5 => 0 pairs (*) E7,F7: 5.. / E7 = 5 => 15 pairs (_) / F7 = 5 => 0 pairs (*) F2,G2: 5.. / F2 = 5 => 15 pairs (_) / G2 = 5 => 0 pairs (*) E3,I3: 5.. / E3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) E3,E7: 5.. / E3 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) F2,F7: 5.. / F2 = 5 => 15 pairs (_) / F7 = 5 => 0 pairs (*) G2,G5: 5.. / G2 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) I3,I5: 5.. / I3 = 5 => 15 pairs (_) / I5 = 5 => 0 pairs (*) D1,E1: 8.. / D1 = 8 => 0 pairs (X) / E1 = 8 => 0 pairs (_) E6,F6: 8.. / E6 = 8 => 0 pairs (X) / F6 = 8 => 15 pairs (_) B7,B9: 8.. / B7 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) B9,D9: 8.. / B9 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) D1,D9: 8.. / D1 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) F6,F7: 8.. / F6 = 8 => 15 pairs (_) / F7 = 8 => 0 pairs (X) D1,E1: 9.. / D1 = 9 => 0 pairs (*) / E1 = 9 => 0 pairs (X) G2,H2: 9.. / G2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) D5,E6: 9.. / D5 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) B7,B9: 9.. / B7 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) I7,G9: 9.. / I7 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) E6,H6: 9.. / E6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) B7,I7: 9.. / B7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) B9,G9: 9.. / B9 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) D1,D5: 9.. / D1 = 9 => 0 pairs (*) / D5 = 9 => 0 pairs (X) E1,E6: 9.. / E1 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) H2,H6: 9.. / H2 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) I5,I7: 9.. / I5 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) * DURATION: 0:01:13.076118 START: 03:29:34.520035 END: 03:30:47.596153 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,D1,D5,D9,E1,E3,F2,F6,G9,H2,H6,I3,I7) * 354..672167241...89182.746.539762184826.41.7.1475..6.27.16..24.4631298572.5.74.16 * PAIR E1: 8,9 COL E E6: 8,9,3 # reduction candidate for 8,9 E6: 3 => CTR * 354.9672167241...89182.746.539762184826941.7.1475386927.168524.4631298572.5.74.16 E6: 8,9 # 16 pairs * PAIR F2: 3,5 ROW 2 G2: 3,5,9 # reduction candidate for 3,5 G2: 3,5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 G2: 9 => CTR * 354..6721672415938918237465539762184826.415731475.36927.16582494631298572.5.74.16 * PAIR F2: 3,5 COL F F7: 3,5,8 # reduction candidate for 3,5 F7: 8 => CTR * 354..6721672415..8918237465539762184826.4157.1475.36927.165.24.4631298572.5.74.16 F7: 3,5 # 15 pairs * PAIR E3: 3,5 COL E E7: 3,5,8 # reduction candidate for 3,5 E7: 8 => CTR * 354..672167241...8918257463539762184826.41.751475386.27.16..24.4631298572.5.74.16 E7: 3,5 # 16 pairs * PAIR H2: 3,9 BLK 3 G2: 3,9,5 # reduction candidate for 3,9 G2: 5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 G2: 3,9 # 15 pairs * PAIR I3: 3,5 BLK 3 G2: 3,5,9 # reduction candidate for 3,5 G2: 3,5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 G2: 9 => CTR * 354..6721672415938918237465539762184826.415731475.36927.16582494631298572.5.74.16 * PAIR I3: 3,5 COL I I5: 3,5,9 # reduction candidate for 3,5 I5: 3,5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 I5: 9 => CTR * 354..672167241...89182.7465539762184826.415791475986327916..24.4631298572.5.74.16 * PAIR D5: 3,9 BLK 5 E6: 3,9,8 # reduction candidate for 3,9 E6: 8 => CTR * 354.9672167241...89182.746.539762184826941.7.1475836927.16.82494631298572.5.74.16 E6: 3,9 # 15 pairs * PAIR D5: 3,9 ROW 5 G5: 3,9,5 # reduction candidate for 3,9 G5: 3,9 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 G5: 5 # 15 pairs I5: 3,9,5 # reduction candidate for 3,9 I5: 3,9 # 15 pairs * PAIR F6: 3,8 BLK 5 E6: 3,8,9 # reduction candidate for 3,8 E6: 3,8 => CTR * 354.9672167241...89182.746.539762184826941.7.1475..6927.16..249463129857295.74.16 E6: 9 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 * PAIR F6: 3,8 COL F F7: 3,8,5 # reduction candidate for 3,8 F7: 5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 F7: 3,8 # 15 pairs * PAIR H6: 3,9 BLK 6 G5: 3,9,5 # reduction candidate for 3,9 G5: 3,9 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 G5: 5 # 15 pairs I5: 3,9,5 # reduction candidate for 3,9 I5: 3,9 # 15 pairs * PAIR H6: 3,9 ROW 6 E6: 3,9,8 # reduction candidate for 3,9 E6: 8 => CTR * 354.9672167241...89182.746.539762184826941.7.1475836927.16.82494631298572.5.74.16 E6: 3,9 # 15 pairs * PAIR D9: 3,8 BLK 8 E7: 3,8,5 # reduction candidate for 3,8 E7: 3,8 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 E7: 5 # 15 pairs F7: 3,8,5 # reduction candidate for 3,8 F7: 3,8 # 15 pairs * PAIR I7: 3,9 COL I I5: 3,9,5 # reduction candidate for 3,9 I5: 5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 I5: 3,9 # 15 pairs * PAIR G9: 3,9 COL G G2: 3,9,5 # reduction candidate for 3,9 G2: 3,9 # 15 pairs G5: 3,9,5 # reduction candidate for 3,9 G5: 3,9 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 G5: 5 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-026-base-pr-000.dot * REASONING * DIS # E6: 3 => CTR => E6: 8,9 * PRF # G2: 3,5 => SOL * DIS # G2: 9 => CTR => G2: 3,5 * DIS # F7: 8 => CTR => F7: 3,5 * DIS # E7: 8 => CTR => E7: 3,5 * PRF # G2: 5 => SOL * PRF # G2: 3,5 => SOL * DIS # G2: 9 => CTR => G2: 3,5 * PRF # I5: 3,5 => SOL * DIS # I5: 9 => CTR => I5: 3,5 * DIS # E6: 8 => CTR => E6: 3,9 * PRF # G5: 3,9 => SOL * DIS # E6: 3,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # F7: 5 => SOL * PRF # G5: 3,9 => SOL * DIS # E6: 8 => CTR => E6: 3,9 * PRF # E7: 3,8 => SOL * PRF # I5: 5 => SOL * PRF # G5: 3,9 => SOL * CNT 20 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,D1,D5,D9,E1,E3,F2,F6,G9,H2,H6,I3,I7) * 354..672167241...89182.746.539762184826.41.7.1475..6.27.16..24.4631298572.5.74.16 * PAIR E1: 8,9 COL E E6: 8,9,3 # reduction candidate for 8,9 E6: 3 => CTR * 354.9672167241...89182.746.539762184826941.7.1475386927.168524.4631298572.5.74.16 * PAIR RESTART * PAIR F2: 3,5 ROW 2 G2: 3,5,9 # reduction candidate for 3,5 G2: 3,5 => SOLVED * 354986721672413598918257463539762184826341975147598632781635249463129857295874316 * DURATION: 0:00:04.721507 START: 03:31:35.744980 END: 03:31:40.466487 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-026-base-pr-001.dot * REASONING * DIS # E6: 3 => CTR => E6: 8,9 * PRF E6: 8,9 # G2: 3,5 => SOL * STA E6: 8,9 + G2: 3,5 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 026 solution: 354986721672413598918257463539762184826341975147598632781635249463129857295874316 info: 1323 FNBTWXY S8.f 30025 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 354986721672413598918257463539762184826341975147598632781635249463129857295874316 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 # E6: 8,9 => UNS * DIS # E6: 3 => CTR => E6: 8,9 * PRF # G2: 3,5 => SOL * DIS # G2: 9 => CTR => G2: 3,5 * INC # F7: 3,5 => UNS * DIS # F7: 8 => CTR => F7: 3,5 * INC # E7: 3,5 => UNS * DIS # E7: 8 => CTR => E7: 3,5 * INC # G2: 3,9 => UNS * PRF # G2: 5 => SOL * PRF # G2: 3,5 => SOL * DIS # G2: 9 => CTR => G2: 3,5 * PRF # I5: 3,5 => SOL * DIS # I5: 9 => CTR => I5: 3,5 * INC # E6: 3,9 => UNS * DIS # E6: 8 => CTR => E6: 3,9 * PRF # G5: 3,9 => SOL * INC # G5: 5 => UNS * INC # I5: 3,9 => UNS * DIS # E6: 3,8 => CTR => E6: 9 * PRF # E6: 9 => SOL * INC # F7: 3,8 => UNS * PRF # F7: 5 => SOL * PRF # G5: 3,9 => SOL * INC # G5: 5 => UNS * INC # I5: 3,9 => UNS * INC # E6: 3,9 => UNS * DIS # E6: 8 => CTR => E6: 3,9 * PRF # E7: 3,8 => SOL * INC # E7: 5 => UNS * INC # F7: 3,8 => UNS * INC # I5: 3,9 => UNS * PRF # I5: 5 => SOL * INC # G2: 3,9 => UNS * PRF # G5: 3,9 => SOL * INC # G5: 5 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E6: 8,9 => UNS * DIS # E6: 3 => CTR => E6: 8,9 * PRF E6: 8,9 # G2: 3,5 => SOL * STA E6: 8,9 + G2: 3,5 * CNT 3 HDP CHAINS / 3 HYP OPENED