Analysis of xx-top500-090-base.sdk
Contents
Original Sudoku
level: medium
position: 7..4.86..........13.........5..21...4......7............235.......7..4...1....... initial
Autosolve
position: 7914386..24..753.13.51.27.4.57.21.4342...317.1...472...72354.1.5..71.4...1428.537 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 6,8 => CTR => C6: 3,9 * PRF # C8: 6,8 => SOL * DIS # D5: 6,9 => CTR => D5: 5,8 * DIS # D6: 6,9 => CTR => D6: 5,8 * DIS # D5: 6,9 => CTR => D5: 5,8 * DIS # D6: 6,9 => CTR => D6: 5,8 * DIS # I5: 6,9 => CTR => I5: 5,8 * DIS # A4: 8,9 => CTR => A4: 6 * PRF # A4: 6 => SOL * PRF # D4: 8,9 => SOL * DIS # D4: 6 => CTR => D4: 8,9 * DIS # A7: 6,9 => CTR => A7: 8 * PRF # C8: 6,9 => SOL * DIS # A4: 8 => CTR => A4: 6,9 * PRF # C8: 6,9 => SOL * DIS # I8: 6,9 => CTR => I8: 2,8 * DIS # I7: 8,9 => CTR => I7: 6 * DIS # A7: 6 => CTR => A7: 8,9 * DIS # I8: 2,6 => CTR => I8: 8,9 * CNT 19 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 6,8 => CTR => C6: 3,9 * PRF C6: 3,9 # C8: 6,8 => SOL * STA C6: 3,9 + C8: 6,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..4.86..........13.........5..21...4......7............235.......7..4...1....... | initial |
| 7914386..24..753.13.51.27.4.57.21.4342...317.1...472...72354.1.5..71.4...1428.537 | autosolve |
| 791438652248675391365192784657921843429863175183547269872354916536719428914286537 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) C2: 6,8 B3: 6,8 D2: 6,9 E3: 6,9 H1: 2,5 I1: 2,5 H2: 8,9 H3: 8,9 E5: 6,9 G4: 8,9 H6: 5,6 A9: 6,9 F8: 6,9 F9: 6,9 G7: 8,9 H8: 2,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,I1: 2.. / H1 = 2 => 0 pairs (X) / I1 = 2 => 13 pairs (_) H8,I8: 2.. / H8 = 2 => 13 pairs (_) / I8 = 2 => 0 pairs (X) H1,H8: 2.. / H1 = 2 => 0 pairs (X) / H8 = 2 => 13 pairs (_) I1,I8: 2.. / I1 = 2 => 13 pairs (_) / I8 = 2 => 0 pairs (X) B6,C6: 3.. / B6 = 3 => 18 pairs (_) / C6 = 3 => 17 pairs (_) B8,C8: 3.. / B8 = 3 => 17 pairs (_) / C8 = 3 => 18 pairs (_) B6,B8: 3.. / B6 = 3 => 18 pairs (_) / B8 = 3 => 17 pairs (_) C6,C8: 3.. / C6 = 3 => 17 pairs (_) / C8 = 3 => 18 pairs (_) H1,I1: 5.. / H1 = 5 => 13 pairs (_) / I1 = 5 => 0 pairs (X) D5,D6: 5.. / D5 = 5 => 16 pairs (_) / D6 = 5 => 14 pairs (_) D5,I5: 5.. / D5 = 5 => 16 pairs (_) / I5 = 5 => 14 pairs (_) H1,H6: 5.. / H1 = 5 => 13 pairs (_) / H6 = 5 => 0 pairs (X) C2,B3: 6.. / C2 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) D2,E3: 6.. / D2 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) F8,F9: 6.. / F8 = 6 => 0 pairs (X) / F9 = 6 => 15 pairs (_) C2,D2: 6.. / C2 = 6 => 0 pairs (X) / D2 = 6 => 0 pairs (_) B3,E3: 6.. / B3 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) A4,D4: 6.. / A4 = 6 => 0 pairs (*) / D4 = 6 => 0 pairs (X) A7,I7: 6.. / A7 = 6 => 0 pairs (X) / I7 = 6 => 15 pairs (_) A9,F9: 6.. / A9 = 6 => 0 pairs (X) / F9 = 6 => 15 pairs (_) E3,E5: 6.. / E3 = 6 => 0 pairs (X) / E5 = 6 => 0 pairs (_) H6,H8: 6.. / H6 = 6 => 13 pairs (_) / H8 = 6 => 0 pairs (X) C2,B3: 8.. / C2 = 8 => 0 pairs (*) / B3 = 8 => 0 pairs (X) H2,H3: 8.. / H2 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) C2,H2: 8.. / C2 = 8 => 0 pairs (*) / H2 = 8 => 0 pairs (X) B3,H3: 8.. / B3 = 8 => 0 pairs (X) / H3 = 8 => 0 pairs (_) A4,A7: 8.. / A4 = 8 => 0 pairs (X) / A7 = 8 => 18 pairs (_) G4,G7: 8.. / G4 = 8 => 18 pairs (_) / G7 = 8 => 0 pairs (X) D2,E3: 9.. / D2 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) H2,H3: 9.. / H2 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) F8,F9: 9.. / F8 = 9 => 15 pairs (_) / F9 = 9 => 0 pairs (X) D2,H2: 9.. / D2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) E3,H3: 9.. / E3 = 9 => 0 pairs (*) / H3 = 9 => 0 pairs (X) A9,F9: 9.. / A9 = 9 => 15 pairs (_) / F9 = 9 => 0 pairs (X) E3,E5: 9.. / E3 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) G4,G7: 9.. / G4 = 9 => 0 pairs (X) / G7 = 9 => 18 pairs (_) * DURATION: 0:01:01.597440 START: 05:51:22.620136 END: 05:52:24.217576 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,C2,D2,E3,E5,F8,F9,G4,G7,H1,H2,H3,H6,H8,I1) * 7914386..24..753.13.51.27.4.57.21.4342...317.1...472...72354.1.5..71.4...1428.537 * PAIR C2: 6,8 COL C C5: 6,8,9 # reduction candidate for 6,8 C5: 6,8 # 19 pairs C6: 6,8,3,9 # reduction candidate for 6,8 C6: 6,8 => CTR * 7914386..24.675391365192784657.21.43429.6317.138.472...72354.1.5.371.4...1428.537 C6: 3,9 # 17 pairs C8: 6,8,3,9 # reduction candidate for 6,8 C8: 6,8 => SOLVED * 791438652248675391365192784657921843429863175183547269872354916536719428914286537 C8: 3,9 # 17 pairs * PAIR B3: 6,8 COL B B6: 6,8,3 # reduction candidate for 6,8 B6: 6,8 # 17 pairs B8: 6,8,3 # reduction candidate for 6,8 B8: 6,8 # 18 pairs * PAIR D2: 6,9 COL D D4: 6,9,8 # reduction candidate for 6,9 D4: 6,9 # 19 pairs D5: 6,9,5,8 # reduction candidate for 6,9 D5: 6,9 => CTR * 79143865224..753.13.51.27.4.57821943428..3175139547268872354.1.5..71.42..1428.537 D5: 5,8 # 17 pairs D6: 6,9,5,8 # reduction candidate for 6,9 D6: 6,9 => CTR * 7914386..24..753.13.51.27.4.5782194342.5.317.1...472..872354.1.5..71.4...1428.537 D6: 5,8 # 17 pairs * PAIR E5: 6,9 BLK 5 D4: 6,9,8 # reduction candidate for 6,9 D4: 6,9 # 19 pairs D5: 6,9,5,8 # reduction candidate for 6,9 D5: 6,9 => CTR * 79143865224..753.13.51.27.4.57821943428..3175139547268872354.1.5..71.42..1428.537 D5: 5,8 # 17 pairs D6: 6,9,5,8 # reduction candidate for 6,9 D6: 6,9 => CTR * 7914386..24..753.13.51.27.4.5782194342.5.317.1...472..872354.1.5..71.4...1428.537 D6: 5,8 # 17 pairs * PAIR E5: 6,9 ROW 5 C5: 6,9,8 # reduction candidate for 6,9 C5: 6,9 # 20 pairs I5: 6,9,5,8 # reduction candidate for 6,9 I5: 6,9 => CTR * 7914386522469753813851627.4.57.21.434285.317.1...472..8723549165..71.428.1428.537 I5: 5,8 # 18 pairs * PAIR G4: 8,9 BLK 6 I5: 8,9,5,6 # reduction candidate for 8,9 I5: 8,9 # 20 pairs I6: 8,9,5,6 # reduction candidate for 8,9 I6: 8,9 # 18 pairs * PAIR G4: 8,9 ROW 4 A4: 8,9,6 # reduction candidate for 8,9 A4: 8,9 => CTR * 7914386..246975381385162794.57621.43428593176163847259.72354.1.5..71.4...1428.537 A4: 6 => SOLVED * 791438652248675391365192784657921843429863175183547269872354916536719428914286537 D4: 8,9,6 # reduction candidate for 8,9 D4: 8,9 => SOLVED * 791438652248675391365192784657921843429863175183547269872354916536719428914286537 D4: 6 => CTR * 7914386..246975381385162794.57621.43428593176163847259.72354.1.5..71.4...1428.537 * PAIR H6: 5,6 BLK 6 I5: 5,6,8,9 # reduction candidate for 5,6 I5: 5,6 # 18 pairs I6: 5,6,8,9 # reduction candidate for 5,6 I6: 5,6 # 20 pairs * PAIR H6: 5,6 ROW 6 D6: 5,6,8,9 # reduction candidate for 5,6 D6: 5,6 # 20 pairs D6: 8,9 # 17 pairs * PAIR A9: 6,9 BLK 7 A7: 6,9,8 # reduction candidate for 6,9 A7: 6,9 => CTR * 7914386..24..753.13.51.27.485762194342..9317.1.9.472...7235481.5.371.4...1428.537 A7: 8 # 18 pairs C8: 6,9,3,8 # reduction candidate for 6,9 C8: 6,9 => SOLVED * 791438652248675391365192784657921843429863175183547269872354916536719428914286537 C8: 3,8 # 18 pairs * PAIR A9: 6,9 COL A A4: 6,9,8 # reduction candidate for 6,9 A4: 8 => CTR * 7914386..24..753.13.51.27.485762194342..9317.1.9.472...7235481.5.371.4...1428.537 A4: 6,9 # 18 pairs * PAIR F8: 6,9 ROW 8 C8: 6,9,3,8 # reduction candidate for 6,9 C8: 6,9 => SOLVED * 791438652248675391365192784657921843429863175183547269872354916536719428914286537 C8: 3,8 # 18 pairs I8: 6,9,2,8 # reduction candidate for 6,9 I8: 6,9 => CTR * 79143865224..753.13.51.27.4857621943426.9317.139.4726..7235481.5.371.42..1428.537 I8: 2,8 # 18 pairs * PAIR G7: 8,9 BLK 9 I7: 8,9,6 # reduction candidate for 8,9 I7: 8,9 => CTR * 7914386..24..753.13.51.27.485762194342..9317.1.9.472..6723548195.37194..914286537 I7: 6 # 15 pairs I8: 8,9,2,6 # reduction candidate for 8,9 I8: 8,9 # 15 pairs * PAIR G7: 8,9 ROW 7 A7: 8,9,6 # reduction candidate for 8,9 A7: 6 => CTR * 7914386..24..753.13.51.27.485762194342..9317.1.9.472..6723548195.37194..914286537 A7: 8,9 # 15 pairs * PAIR H8: 2,6 BLK 9 I8: 2,6,8,9 # reduction candidate for 2,6 I8: 2,6 => CTR * 7914386..24..753.13.51.27.485762194342..9317.1.9.472..6723548195.37194..914286537 I8: 8,9 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-090-base-pr-000.dot * REASONING * DIS # C6: 6,8 => CTR => C6: 3,9 * PRF # C8: 6,8 => SOL * DIS # D5: 6,9 => CTR => D5: 5,8 * DIS # D6: 6,9 => CTR => D6: 5,8 * DIS # D5: 6,9 => CTR => D5: 5,8 * DIS # D6: 6,9 => CTR => D6: 5,8 * DIS # I5: 6,9 => CTR => I5: 5,8 * DIS # A4: 8,9 => CTR => A4: 6 * PRF # A4: 6 => SOL * PRF # D4: 8,9 => SOL * DIS # D4: 6 => CTR => D4: 8,9 * DIS # A7: 6,9 => CTR => A7: 8 * PRF # C8: 6,9 => SOL * DIS # A4: 8 => CTR => A4: 6,9 * PRF # C8: 6,9 => SOL * DIS # I8: 6,9 => CTR => I8: 2,8 * DIS # I7: 8,9 => CTR => I7: 6 * DIS # A7: 6 => CTR => A7: 8,9 * DIS # I8: 2,6 => CTR => I8: 8,9 * CNT 19 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B3,C2,D2,E3,E5,F8,F9,G4,G7,H1,H2,H3,H6,H8,I1) * 7914386..24..753.13.51.27.4.57.21.4342...317.1...472...72354.1.5..71.4...1428.537 * PAIR C2: 6,8 COL C C5: 6,8,9 # reduction candidate for 6,8 C5: 6,8 # 19 pairs C6: 6,8,3,9 # reduction candidate for 6,8 C6: 6,8 => CTR * 7914386..24.675391365192784657.21.43429.6317.138.472...72354.1.5.371.4...1428.537 C8: 6,8,3,9 # reduction candidate for 6,8 C8: 6,8 => SOLVED * 791438652248675391365192784657921843429863175183547269872354916536719428914286537 * DURATION: 0:00:03.967656 START: 05:53:07.388717 END: 05:53:11.356373 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-090-base-pr-001.dot * REASONING * DIS # C6: 6,8 => CTR => C6: 3,9 * PRF C6: 3,9 # C8: 6,8 => SOL * STA C6: 3,9 + C8: 6,8 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 090 solution: 791438652248675391365192784657921843429863175183547269872354916536719428914286537 info: 1566 FNBTWXY S8.f 36984 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 791438652248675391365192784657921843429863175183547269872354916536719428914286537 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 # C5: 6,8 => UNS * DIS # C6: 6,8 => CTR => C6: 3,9 * INC # C6: 3,9 => UNS * PRF # C8: 6,8 => SOL * INC # C8: 3,9 => UNS * INC # B6: 6,8 => UNS * INC # B8: 6,8 => UNS * INC # D4: 6,9 => UNS * DIS # D5: 6,9 => CTR => D5: 5,8 * INC # D5: 5,8 => UNS * DIS # D6: 6,9 => CTR => D6: 5,8 * INC # D6: 5,8 => UNS * INC # D4: 6,9 => UNS * DIS # D5: 6,9 => CTR => D5: 5,8 * INC # D5: 5,8 => UNS * DIS # D6: 6,9 => CTR => D6: 5,8 * INC # D6: 5,8 => UNS * INC # C5: 6,9 => UNS * DIS # I5: 6,9 => CTR => I5: 5,8 * INC # I5: 5,8 => UNS * INC # I5: 8,9 => UNS * INC # I6: 8,9 => UNS * DIS # A4: 8,9 => CTR => A4: 6 * PRF # A4: 6 => SOL * PRF # D4: 8,9 => SOL * DIS # D4: 6 => CTR => D4: 8,9 * INC # I5: 5,6 => UNS * INC # I6: 5,6 => UNS * INC # D6: 5,6 => UNS * INC # D6: 8,9 => UNS * DIS # A7: 6,9 => CTR => A7: 8 * INC # A7: 8 => UNS * PRF # C8: 6,9 => SOL * INC # C8: 3,8 => UNS * INC # A4: 6,9 => UNS * DIS # A4: 8 => CTR => A4: 6,9 * PRF # C8: 6,9 => SOL * INC # C8: 3,8 => UNS * DIS # I8: 6,9 => CTR => I8: 2,8 * INC # I8: 2,8 => UNS * DIS # I7: 8,9 => CTR => I7: 6 * INC # I7: 6 => UNS * INC # I8: 8,9 => UNS * INC # A7: 8,9 => UNS * DIS # A7: 6 => CTR => A7: 8,9 * DIS # I8: 2,6 => CTR => I8: 8,9 * INC # I8: 8,9 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C5: 6,8 => UNS * DIS # C6: 6,8 => CTR => C6: 3,9 * PRF C6: 3,9 # C8: 6,8 => SOL * STA C6: 3,9 + C8: 6,8 * CNT 3 HDP CHAINS / 3 HYP OPENED