Analysis of xx-top500-302-base.sdk
Contents
Original Sudoku
level: medium
position: .8.....1.4...7........3.....1.2....5....6.7........3.....1.5...3.....9..7..8..... initial
Autosolve
position: .87.52.13435.718.21...3857..13287..55.836.72127.51.3..8..1.52373.17.69..7..8.31.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D1: 6,9 => SOL * DIS # D1: 4 => CTR => D1: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 4 => CTR => D1: 6,9 * DIS # D3: 6,9 => CTR => D3: 4 * PRF # D3: 4 => SOL * PRF # I3: 4,6 => SOL * DIS # I3: 9 => CTR => I3: 4,6 * DIS # D1: 4,6 => CTR => D1: 9 * PRF # D1: 9 => SOL * PRF # I3: 6,9 => SOL * DIS # I3: 4 => CTR => I3: 6,9 * DIS # H4: 6,9 => CTR => H4: 4 * PRF # H4: 4 => SOL * DIS # H6: 6,9 => CTR => H6: 8 * DIS # C6: 4 => CTR => C6: 6,9 * DIS # H4: 6,9 => CTR => H4: 4 * PRF # H4: 4 => SOL * DIS # C6: 4,9 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # B7: 4,9 => CTR => B7: 6 * DIS # C6: 4,9 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H4: 4,6 => SOL * DIS # H4: 9 => CTR => H4: 4,6 * DIS # B7: 4,9 => CTR => B7: 6 * PRF # I3: 4,6 => SOL * DIS # I3: 9 => CTR => I3: 4,6 * CNT 28 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D1: 6,9 => SOL * STA D1: 6,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8.....1.4...7........3.....1.2....5....6.7........3.....1.5...3.....9..7..8..... | initial |
| .87.52.13435.718.21...3857..13287..55.836.72127.51.3..8..1.52373.17.69..7..8.31.. | autosolve |
| 687952413435671892192438576913287645548369721276514389864195237321746958759823164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 6,9 D2: 6,9 G1: 4,6 H2: 6,9 A4: 6,9 B5: 4,9 F5: 4,9 F6: 4,9 G4: 4,6 E7: 4,9 E8: 2,4 I8: 4,8 I9: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B3,C3: 2.. / B3 = 2 => 16 pairs (_) / C3 = 2 => 17 pairs (_) E8,E9: 2.. / E8 = 2 => 14 pairs (_) / E9 = 2 => 16 pairs (_) B8,E8: 2.. / B8 = 2 => 16 pairs (_) / E8 = 2 => 14 pairs (_) C3,C9: 2.. / C3 = 2 => 17 pairs (_) / C9 = 2 => 16 pairs (_) D1,D3: 4.. / D1 = 4 => 0 pairs (X) / D3 = 4 => 0 pairs (_) G1,I3: 4.. / G1 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) B5,C6: 4.. / B5 = 4 => 13 pairs (_) / C6 = 4 => 0 pairs (X) F5,F6: 4.. / F5 = 4 => 0 pairs (X) / F6 = 4 => 13 pairs (_) G4,H4: 4.. / G4 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) D1,G1: 4.. / D1 = 4 => 0 pairs (X) / G1 = 4 => 0 pairs (_) D3,I3: 4.. / D3 = 4 => 0 pairs (*) / I3 = 4 => 0 pairs (X) B5,F5: 4.. / B5 = 4 => 13 pairs (_) / F5 = 4 => 0 pairs (X) C6,F6: 4.. / C6 = 4 => 0 pairs (X) / F6 = 4 => 13 pairs (_) G1,G4: 4.. / G1 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) B8,B9: 5.. / B8 = 5 => 15 pairs (_) / B9 = 5 => 17 pairs (_) H8,H9: 5.. / H8 = 5 => 17 pairs (_) / H9 = 5 => 15 pairs (_) B8,H8: 5.. / B8 = 5 => 15 pairs (_) / H8 = 5 => 17 pairs (_) B9,H9: 5.. / B9 = 5 => 17 pairs (_) / H9 = 5 => 15 pairs (_) A4,C6: 6.. / A4 = 6 => 0 pairs (X) / C6 = 6 => 0 pairs (_) B7,C7: 6.. / B7 = 6 => 15 pairs (_) / C7 = 6 => 0 pairs (X) H9,I9: 6.. / H9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) D2,H2: 6.. / D2 = 6 => 0 pairs (*) / H2 = 6 => 0 pairs (X) A1,A4: 6.. / A1 = 6 => 0 pairs (*) / A4 = 6 => 0 pairs (X) B3,B7: 6.. / B3 = 6 => 0 pairs (X) / B7 = 6 => 15 pairs (_) G1,G4: 6.. / G1 = 6 => 0 pairs (X) / G4 = 6 => 0 pairs (_) H6,I6: 8.. / H6 = 8 => 14 pairs (_) / I6 = 8 => 0 pairs (X) H8,I8: 8.. / H8 = 8 => 0 pairs (X) / I8 = 8 => 14 pairs (_) H6,H8: 8.. / H6 = 8 => 14 pairs (_) / H8 = 8 => 0 pairs (X) I6,I8: 8.. / I6 = 8 => 0 pairs (X) / I8 = 8 => 14 pairs (_) H2,I3: 9.. / H2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) F5,F6: 9.. / F5 = 9 => 13 pairs (_) / F6 = 9 => 0 pairs (X) E7,E9: 9.. / E7 = 9 => 17 pairs (_) / E9 = 9 => 15 pairs (_) A1,D1: 9.. / A1 = 9 => 0 pairs (X) / D1 = 9 => 0 pairs (_) D2,H2: 9.. / D2 = 9 => 0 pairs (X) / H2 = 9 => 0 pairs (_) A4,H4: 9.. / A4 = 9 => 0 pairs (*) / H4 = 9 => 0 pairs (X) B5,F5: 9.. / B5 = 9 => 0 pairs (X) / F5 = 9 => 13 pairs (_) A1,A4: 9.. / A1 = 9 => 0 pairs (X) / A4 = 9 => 0 pairs (_) I3,I6: 9.. / I3 = 9 => 0 pairs (X) / I6 = 9 => 0 pairs (_) * DURATION: 0:01:05.641100 START: 13:16:52.637268 END: 13:17:58.278368 2017-05-04 * CP COUNT: (38) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B5,D2,E7,E8,F5,F6,G1,G4,H2,I8,I9) * .87.52.13435.718.21...3857..13287..55.836.72127.51.3..8..1.52373.17.69..7..8.31.. * PAIR A1: 6,9 BLK 1 B3: 6,9,2 # reduction candidate for 6,9 B3: 6,9 # 17 pairs C3: 6,9,2 # reduction candidate for 6,9 C3: 6,9 # 16 pairs * PAIR A1: 6,9 ROW 1 D1: 6,9,4 # reduction candidate for 6,9 D1: 6,9 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 D1: 4 => CTR * 9874526134356718921..9385746132874.55.836.72127.51.3..8..1.52373.17.69..7..8.31.. * PAIR D2: 6,9 BLK 2 D1: 6,9,4 # reduction candidate for 6,9 D1: 6,9 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 D1: 4 => CTR * 9874526134356718921..9385746132874.55.836.72127.51.3..8..1.52373.17.69..7..8.31.. D3: 6,9,4 # reduction candidate for 6,9 D3: 6,9 => CTR * .874526134356718921..938574.13287..55.836.72127.51.3..8..1.52373.17.69..7..8.31.. D3: 4 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 * PAIR G1: 4,6 BLK 3 I3: 4,6,9 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 I3: 9 => CTR * .87.52413435.718621..438579.132876455.836.72127651439886.1.52373.17.69847..8.3156 * PAIR G1: 4,6 ROW 1 D1: 4,6,9 # reduction candidate for 4,6 D1: 4,6 => CTR * 987.52.13435.718.21...3857.6132874955.836.72127.51.3..8..1.52373.17.69..7..8.31.. D1: 9 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 * PAIR H2: 6,9 BLK 3 I3: 6,9,4 # reduction candidate for 6,9 I3: 6,9 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 I3: 4 => CTR * .87.52.13435.718921...3857491328746554836972127651438986.1.52373.17.69.87..8.31.6 * PAIR H2: 6,9 COL H H4: 6,9,4 # reduction candidate for 6,9 H4: 6,9 => CTR * .874526134356718921..938574.132874.55.836.72127.51.3..8..1.52373.17.69..7..8.31.. H4: 4 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 H6: 6,9,8 # reduction candidate for 6,9 H6: 6,9 => CTR * .87.52413435.718621..438579.132876455.836.72127651439886.1.52373517269847..8.3156 H6: 8 # 14 pairs * PAIR A4: 6,9 BLK 4 C6: 6,9,4 # reduction candidate for 6,9 C6: 4 => CTR * .87.52.13435.718.21...3857.6132874955983647212745193..8..1.52373.17.69..7..8.31.. C6: 6,9 # 13 pairs * PAIR A4: 6,9 ROW 4 H4: 6,9,4 # reduction candidate for 6,9 H4: 6,9 => CTR * .874526134356718921..938574.132874.55.836.72127.51.3..8..1.52373.17.69..7..8.31.. H4: 4 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 * PAIR B5: 4,9 BLK 4 C6: 4,9,6 # reduction candidate for 4,9 C6: 4,9 => CTR * .87.52.13435.718.21...3857.6132874955.836.72127.51.3..8..1.52373.17.69..7..8.31.. C6: 6 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 * PAIR B5: 4,9 COL B B7: 4,9,6 # reduction candidate for 4,9 B7: 4,9 => CTR * .87.52.13435.718.2162.3857.6132874955.836.72127.51.3..8.61.52373.17.69..7..8.31.. B7: 6 # 15 pairs B9: 4,9,2,5 # reduction candidate for 4,9 B9: 4,9 # 18 pairs * PAIR F6: 4,9 ROW 6 C6: 4,9,6 # reduction candidate for 4,9 C6: 4,9 => CTR * .87.52.13435.718.21...3857.6132874955.836.72127.51.3..8..1.52373.17.69..7..8.31.. C6: 6 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 * PAIR G4: 4,6 BLK 6 H4: 4,6,9 # reduction candidate for 4,6 H4: 4,6 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 H4: 9 => CTR * .87.52.13435.718.21...3857..132874955.836.72127.51.3..8..1.52373.17.69..7..8.31.. * PAIR E7: 4,9 BLK 8 E9: 4,9,2 # reduction candidate for 4,9 E9: 2 # 16 pairs E9: 4,9 # 14 pairs * PAIR E7: 4,9 ROW 7 B7: 4,9,6 # reduction candidate for 4,9 B7: 4,9 => CTR * .87.52.13435.718.2162.3857.6132874955.836.72127.51.3..8.61.52373.17.69..7..8.31.. B7: 6 # 15 pairs C7: 4,9,6 # reduction candidate for 4,9 C7: 4,9 # 15 pairs * PAIR E8: 2,4 BLK 8 E9: 2,4,9 # reduction candidate for 2,4 E9: 2,4 # 17 pairs E9: 9 # 15 pairs * PAIR E8: 2,4 ROW 8 B8: 2,4,5 # reduction candidate for 2,4 B8: 2,4 # 17 pairs B8: 5 # 15 pairs * PAIR I8: 4,8 BLK 9 H8: 4,8,5 # reduction candidate for 4,8 H8: 5 # 17 pairs H8: 4,8 # 15 pairs * PAIR I9: 4,6 BLK 9 H9: 4,6,5 # reduction candidate for 4,6 H9: 4,6 # 17 pairs H9: 5 # 15 pairs * PAIR I9: 4,6 COL I I3: 4,6,9 # reduction candidate for 4,6 I3: 4,6 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 I3: 9 => CTR * .87.52413435.718621..438579.132876455.836.72127651439886.1.52373.17.69847..8.3156 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-302-base-pr-000.dot * REASONING * PRF # D1: 6,9 => SOL * DIS # D1: 4 => CTR => D1: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 4 => CTR => D1: 6,9 * DIS # D3: 6,9 => CTR => D3: 4 * PRF # D3: 4 => SOL * PRF # I3: 4,6 => SOL * DIS # I3: 9 => CTR => I3: 4,6 * DIS # D1: 4,6 => CTR => D1: 9 * PRF # D1: 9 => SOL * PRF # I3: 6,9 => SOL * DIS # I3: 4 => CTR => I3: 6,9 * DIS # H4: 6,9 => CTR => H4: 4 * PRF # H4: 4 => SOL * DIS # H6: 6,9 => CTR => H6: 8 * DIS # C6: 4 => CTR => C6: 6,9 * DIS # H4: 6,9 => CTR => H4: 4 * PRF # H4: 4 => SOL * DIS # C6: 4,9 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # B7: 4,9 => CTR => B7: 6 * DIS # C6: 4,9 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H4: 4,6 => SOL * DIS # H4: 9 => CTR => H4: 4,6 * DIS # B7: 4,9 => CTR => B7: 6 * PRF # I3: 4,6 => SOL * DIS # I3: 9 => CTR => I3: 4,6 * CNT 28 HDP CHAINS / 46 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B5,D2,E7,E8,F5,F6,G1,G4,H2,I8,I9) * .87.52.13435.718.21...3857..13287..55.836.72127.51.3..8..1.52373.17.69..7..8.31.. * PAIR A1: 6,9 BLK 1 B3: 6,9,2 # reduction candidate for 6,9 B3: 6,9 # 17 pairs C3: 6,9,2 # reduction candidate for 6,9 C3: 6,9 # 16 pairs * PAIR A1: 6,9 ROW 1 D1: 6,9,4 # reduction candidate for 6,9 D1: 6,9 => SOLVED * 687952413435671892192438576913287645548369721276514389864195237321746958759823164 * DURATION: 0:00:03.874930 START: 13:18:45.602573 END: 13:18:49.477503 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-302-base-pr-001.dot * REASONING * PRF # D1: 6,9 => SOL * STA D1: 6,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 302 solution: 687952413435671892192438576913287645548369721276514389864195237321746958759823164 info: 2585 FNBWY S8.f 23272 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 687952413435671892192438576913287645548369721276514389864195237321746958759823164 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 # B3: 6,9 => UNS * INC # C3: 6,9 => UNS * PRF # D1: 6,9 => SOL * DIS # D1: 4 => CTR => D1: 6,9 * PRF # D1: 6,9 => SOL * DIS # D1: 4 => CTR => D1: 6,9 * DIS # D3: 6,9 => CTR => D3: 4 * PRF # D3: 4 => SOL * PRF # I3: 4,6 => SOL * DIS # I3: 9 => CTR => I3: 4,6 * DIS # D1: 4,6 => CTR => D1: 9 * PRF # D1: 9 => SOL * PRF # I3: 6,9 => SOL * DIS # I3: 4 => CTR => I3: 6,9 * DIS # H4: 6,9 => CTR => H4: 4 * PRF # H4: 4 => SOL * DIS # H6: 6,9 => CTR => H6: 8 * INC # H6: 8 => UNS * INC # C6: 6,9 => UNS * DIS # C6: 4 => CTR => C6: 6,9 * DIS # H4: 6,9 => CTR => H4: 4 * PRF # H4: 4 => SOL * DIS # C6: 4,9 => CTR => C6: 6 * PRF # C6: 6 => SOL * DIS # B7: 4,9 => CTR => B7: 6 * INC # B7: 6 => UNS * INC # B9: 4,9 => UNS * DIS # C6: 4,9 => CTR => C6: 6 * PRF # C6: 6 => SOL * PRF # H4: 4,6 => SOL * DIS # H4: 9 => CTR => H4: 4,6 * INC # E9: 4,9 => UNS * INC # E9: 2 => UNS * DIS # B7: 4,9 => CTR => B7: 6 * INC # B7: 6 => UNS * INC # C7: 4,9 => UNS * INC # E9: 2,4 => UNS * INC # E9: 9 => UNS * INC # B8: 2,4 => UNS * INC # B8: 5 => UNS * INC # H8: 4,8 => UNS * INC # H8: 5 => UNS * INC # H9: 4,6 => UNS * INC # H9: 5 => UNS * PRF # I3: 4,6 => SOL * DIS # I3: 9 => CTR => I3: 4,6 * CNT 46 HDP CHAINS / 46 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B3: 6,9 => UNS * INC # C3: 6,9 => UNS * PRF # D1: 6,9 => SOL * STA D1: 6,9 * CNT 3 HDP CHAINS / 3 HYP OPENED