Analysis of xx-top500-160-base.sdk
Contents
Original Sudoku
level: medium
position: ....68.1..25...............1..5........2..7....6....4.6...1...2.7....3.....4..... initial
Autosolve
position: ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 4,7 * DIS # B1: 3,9 => CTR => B1: 4 * DIS # A2: 3,9 => CTR => A2: 7,8 * PRF # A2: 7,8 => SOL * PRF # A3: 3,9 => SOL * DIS # D1: 7 => CTR => D1: 3,9 * PRF # D1: 3,7 => SOL * DIS # D1: 9 => CTR => D1: 3,7 * DIS # D3: 3,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # A2: 3,7 => CTR => A2: 8,9 * PRF # H2: 3,7 => SOL * DIS # H2: 9 => CTR => H2: 3,7 * DIS # E6: 3,7 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # I2: 8,9 => SOL * DIS # I2: 7 => CTR => I2: 8,9 * DIS # A3: 8,9 => CTR => A3: 3,7 * PRF # A3: 3,7 => SOL * DIS # E6: 3,7 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 3 => CTR => I4: 8,9 * DIS # I4: 3,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # E6: 3,9 => SOL * DIS # E6: 7 => CTR => E6: 3,9 * DIS # A1: 3,9 => CTR => A1: 4,7 * DIS # A2: 3,9 => CTR => A2: 7,8 * PRF # A2: 7,8 => SOL * PRF # A3: 3,9 => SOL * DIS # A5: 3,9 => CTR => A5: 4 * PRF # D1: 3,7 => SOL * DIS # D1: 9 => CTR => D1: 3,7 * DIS # D3: 3,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # H2: 7,9 => CTR => H2: 3 * PRF # H2: 3 => SOL * PRF # H3: 7,9 => SOL * DIS # H3: 3 => CTR => H3: 7,9 * PRF # I2: 7,9 => SOL * DIS # I2: 8 => CTR => I2: 7,9 * CNT 42 HDP CHAINS / 54 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A1: 3,9 => CTR => A1: 4,7 * DIS A1: 4,7 # B1: 3,9 => CTR => B1: 4 * DIS A1: 4,7 + B1: 4 # A2: 3,9 => CTR => A2: 8 * PRF A1: 4,7 + B1: 4 + A2: 8 => SOL * STA A1: 4,7 + B1: 4 + A2: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....68.1..25...............1..5........2..7....6....4.6...1...2.7....3.....4..... | initial |
| ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56. | autosolve |
| 749368215825174639361952874137546928498231756256897143683715492574629381912483567 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) C1: 3,9 E2: 3,7 G3: 8,9 F6: 3,7 G4: 8,9 I6: 3,9 A9: 3,9 D7: 3,7 F9: 3,7 H7: 7,9 I9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 3.. / H2 = 3 => 0 pairs (*) / H3 = 3 => 0 pairs (X) I4,I6: 3.. / I4 = 3 => 0 pairs (X) / I6 = 3 => 0 pairs (_) D7,F9: 3.. / D7 = 3 => 0 pairs (X) / F9 = 3 => 0 pairs (_) A9,F9: 3.. / A9 = 3 => 0 pairs (X) / F9 = 3 => 0 pairs (_) F6,F9: 3.. / F6 = 3 => 0 pairs (X) / F9 = 3 => 0 pairs (_) A1,B1: 4.. / A1 = 4 => 0 pairs (X) / B1 = 4 => 13 pairs (_) E4,E5: 4.. / E4 = 4 => 13 pairs (_) / E5 = 4 => 0 pairs (X) B4,E4: 4.. / B4 = 4 => 0 pairs (X) / E4 = 4 => 13 pairs (_) A1,A5: 4.. / A1 = 4 => 0 pairs (X) / A5 = 4 => 13 pairs (_) E6,F6: 7.. / E6 = 7 => 0 pairs (X) / F6 = 7 => 0 pairs (_) D7,F9: 7.. / D7 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) H7,I9: 7.. / H7 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) A1,D1: 7.. / A1 = 7 => 14 pairs (_) / D1 = 7 => 0 pairs (X) D7,H7: 7.. / D7 = 7 => 0 pairs (*) / H7 = 7 => 0 pairs (X) F9,I9: 7.. / F9 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) E2,E6: 7.. / E2 = 7 => 0 pairs (*) / E6 = 7 => 0 pairs (X) F6,F9: 7.. / F6 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) I2,I9: 7.. / I2 = 7 => 0 pairs (X) / I9 = 7 => 0 pairs (_) A2,A3: 8.. / A2 = 8 => 0 pairs (*) / A3 = 8 => 0 pairs (X) I2,G3: 8.. / I2 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) B5,C5: 8.. / B5 = 8 => 13 pairs (_) / C5 = 8 => 12 pairs (_) G4,I4: 8.. / G4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) B7,C7: 8.. / B7 = 8 => 12 pairs (_) / C7 = 8 => 13 pairs (_) A2,I2: 8.. / A2 = 8 => 0 pairs (*) / I2 = 8 => 0 pairs (X) A3,G3: 8.. / A3 = 8 => 0 pairs (X) / G3 = 8 => 0 pairs (_) B5,B7: 8.. / B5 = 8 => 13 pairs (_) / B7 = 8 => 12 pairs (_) C5,C7: 8.. / C5 = 8 => 12 pairs (_) / C7 = 8 => 13 pairs (_) G3,G4: 8.. / G3 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) I2,I4: 8.. / I2 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) D1,D3: 9.. / D1 = 9 => 0 pairs (X) / D3 = 9 => 0 pairs (_) H7,I9: 9.. / H7 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) E6,I6: 9.. / E6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) A9,I9: 9.. / A9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) G3,G4: 9.. / G3 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) * DURATION: 0:00:56.869682 START: 08:12:56.856763 END: 08:13:53.726445 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C1,D7,E2,F6,F9,G3,G4,H7,I6,I9) * ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56. * PAIR C1: 3,9 BLK 1 A1: 3,9,4,7 # reduction candidate for 3,9 A1: 3,9 => CTR * .4.768215.251346...619528341.75469284..2917562568..14.6...154.2574629381.1248.56. A1: 4,7 # 12 pairs B1: 3,9,4 # reduction candidate for 3,9 B1: 3,9 => CTR * 4..768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56. B1: 4 # 13 pairs A2: 3,9,7,8 # reduction candidate for 3,9 A2: 3,9 => CTR * ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567 A2: 7,8 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 A3: 3,9,7,8 # reduction candidate for 3,9 A3: 3,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 A3: 7,8 # 12 pairs * PAIR C1: 3,9 ROW 1 D1: 3,9,7 # reduction candidate for 3,9 D1: 7 => CTR * ...768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56. D1: 3,9 # 14 pairs * PAIR C1: 3,9 COL C C5: 3,9,8 # reduction candidate for 3,9 C5: 3,9 # 13 pairs C7: 3,9,8 # reduction candidate for 3,9 C7: 3,9 # 12 pairs * PAIR E2: 3,7 BLK 2 D1: 3,7,9 # reduction candidate for 3,7 D1: 3,7 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 D1: 9 => CTR * 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569 D3: 3,7,9 # reduction candidate for 3,7 D3: 3,7 => CTR * 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569 D3: 9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * PAIR E2: 3,7 ROW 2 A2: 3,7,8,9 # reduction candidate for 3,7 A2: 3,7 => CTR * ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567 A2: 8,9 # 12 pairs H2: 3,7,9 # reduction candidate for 3,7 H2: 3,7 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 H2: 9 => CTR * ....68215.251.469..61.528341.75.6928...2.17562568971436...154.2574629381.1248.56. * PAIR E2: 3,7 COL E E6: 3,7,9 # reduction candidate for 3,7 E6: 3,7 => CTR * ....68215.251.46...61.52..41.75.6.2....2.17562568..1496...15492574629381912483567 E6: 9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * PAIR G3: 8,9 BLK 3 I2: 8,9,7 # reduction candidate for 8,9 I2: 8,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 I2: 7 => CTR * ....682158251.4697.61.528341.75.6928...2.17562568..14.6...154.2574629381.1248.56. * PAIR G3: 8,9 ROW 3 A3: 8,9,3,7 # reduction candidate for 8,9 A3: 8,9 => CTR * 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569 A3: 3,7 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * PAIR F6: 3,7 BLK 5 E6: 3,7,9 # reduction candidate for 3,7 E6: 3,7 => CTR * ....68215.251.46...61.52..41.75.6.2....2.17562568..1496...15492574629381912483567 E6: 9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * PAIR G4: 8,9 BLK 6 I4: 8,9,3 # reduction candidate for 8,9 I4: 8,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 I4: 3 => CTR * ....68215.251.46.8861.529.41.75.6823...2.17562568..1496...15492574629381912483567 * PAIR I6: 3,9 BLK 6 I4: 3,9,8 # reduction candidate for 3,9 I4: 3,9 => CTR * ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567 I4: 8 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * PAIR I6: 3,9 ROW 6 E6: 3,9,7 # reduction candidate for 3,9 E6: 3,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 E6: 7 => CTR * ....68215.251.46...61.52..41.75.6.2....2.17562568731496..3154.2574629381.1248.56. * PAIR A9: 3,9 BLK 7 B7: 3,9,8 # reduction candidate for 3,9 B7: 3,9 # 13 pairs C7: 3,9,8 # reduction candidate for 3,9 C7: 3,9 # 12 pairs * PAIR A9: 3,9 COL A A1: 3,9,4,7 # reduction candidate for 3,9 A1: 3,9 => CTR * .4.768215.251346...619528341.75469284..2917562568..14.6...154.2574629381.1248.56. A1: 4,7 # 12 pairs A2: 3,9,7,8 # reduction candidate for 3,9 A2: 3,9 => CTR * ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567 A2: 7,8 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 A3: 3,9,7,8 # reduction candidate for 3,9 A3: 3,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 A3: 7,8 # 12 pairs A5: 3,9,4 # reduction candidate for 3,9 A5: 3,9 => CTR * 4..768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56. A5: 4 # 13 pairs * PAIR D7: 3,7 COL D D1: 3,7,9 # reduction candidate for 3,7 D1: 3,7 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 D1: 9 => CTR * 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569 D3: 3,7,9 # reduction candidate for 3,7 D3: 3,7 => CTR * 743968215.251.46...61.52..41.7546.2.4..2.17562568..14.6...154.2574629381312487569 D3: 9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * PAIR H7: 7,9 COL H H2: 7,9,3 # reduction candidate for 7,9 H2: 7,9 => CTR * ....68215.251346...61.52.341.75.6.2....2.17562568731496..3154.2574629381.1248.56. H2: 3 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 H3: 7,9,3 # reduction candidate for 7,9 H3: 7,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 H3: 3 => CTR * ....68215.251346...61.52.341.75.6.2....2.17562568731496..3154.2574629381.1248.56. * PAIR I9: 7,9 COL I I2: 7,9,8 # reduction candidate for 7,9 I2: 7,9 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 I2: 8 => CTR * ....68215.251.46.8861.529.41.75.682....2.17562568..14.6...15492574629381912483567 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-160-base-pr-000.dot * REASONING * DIS # A1: 3,9 => CTR => A1: 4,7 * DIS # B1: 3,9 => CTR => B1: 4 * DIS # A2: 3,9 => CTR => A2: 7,8 * PRF # A2: 7,8 => SOL * PRF # A3: 3,9 => SOL * DIS # D1: 7 => CTR => D1: 3,9 * PRF # D1: 3,7 => SOL * DIS # D1: 9 => CTR => D1: 3,7 * DIS # D3: 3,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # A2: 3,7 => CTR => A2: 8,9 * PRF # H2: 3,7 => SOL * DIS # H2: 9 => CTR => H2: 3,7 * DIS # E6: 3,7 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # I2: 8,9 => SOL * DIS # I2: 7 => CTR => I2: 8,9 * DIS # A3: 8,9 => CTR => A3: 3,7 * PRF # A3: 3,7 => SOL * DIS # E6: 3,7 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 3 => CTR => I4: 8,9 * DIS # I4: 3,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # E6: 3,9 => SOL * DIS # E6: 7 => CTR => E6: 3,9 * DIS # A1: 3,9 => CTR => A1: 4,7 * DIS # A2: 3,9 => CTR => A2: 7,8 * PRF # A2: 7,8 => SOL * PRF # A3: 3,9 => SOL * DIS # A5: 3,9 => CTR => A5: 4 * PRF # D1: 3,7 => SOL * DIS # D1: 9 => CTR => D1: 3,7 * DIS # D3: 3,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # H2: 7,9 => CTR => H2: 3 * PRF # H2: 3 => SOL * PRF # H3: 7,9 => SOL * DIS # H3: 3 => CTR => H3: 7,9 * PRF # I2: 7,9 => SOL * DIS # I2: 8 => CTR => I2: 7,9 * CNT 42 HDP CHAINS / 54 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,C1,D7,E2,F6,F9,G3,G4,H7,I6,I9) * ....68215.251.46...61.52..41.75.6.2....2.17562568..14.6...154.2574629381.1248.56. * PAIR C1: 3,9 BLK 1 A1: 3,9,4,7 # reduction candidate for 3,9 A1: 3,9 => CTR * .4.768215.251346...619528341.75469284..2917562568..14.6...154.2574629381.1248.56. B1: 3,9,4 # reduction candidate for 3,9 B1: 3,9 => CTR * 4..768215.251346...619528341.75.6928...2.17562568..14.6...154.2574629381.1248.56. A2: 3,9,8 # reduction candidate for 3,9 A2: 3,9 => CTR * 74..68215.251.46.8861.529.41.754682.4..2.17562568..14.6...15492574629381912483567 A2: 8 => SOLVED * 749368215825174639361952874137546928498231756256897143683715492574629381912483567 * DURATION: 0:00:03.705195 START: 08:14:49.145963 END: 08:14:52.851158 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-160-base-pr-001.dot * REASONING * DIS # A1: 3,9 => CTR => A1: 4,7 * DIS A1: 4,7 # B1: 3,9 => CTR => B1: 4 * DIS A1: 4,7 + B1: 4 # A2: 3,9 => CTR => A2: 8 * PRF A1: 4,7 + B1: 4 + A2: 8 => SOL * STA A1: 4,7 + B1: 4 + A2: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 160 solution: 749368215825174639361952874137546928498231756256897143683715492574629381912483567 info: 1819 FNBWX S8.f 41545 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 749368215825174639361952874137546928498231756256897143683715492574629381912483567 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:
* DIS # A1: 3,9 => CTR => A1: 4,7 * INC # A1: 4,7 => UNS * DIS # B1: 3,9 => CTR => B1: 4 * INC # B1: 4 => UNS * DIS # A2: 3,9 => CTR => A2: 7,8 * PRF # A2: 7,8 => SOL * PRF # A3: 3,9 => SOL * INC # A3: 7,8 => UNS * INC # D1: 3,9 => UNS * DIS # D1: 7 => CTR => D1: 3,9 * INC # C5: 3,9 => UNS * INC # C7: 3,9 => UNS * PRF # D1: 3,7 => SOL * DIS # D1: 9 => CTR => D1: 3,7 * DIS # D3: 3,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # A2: 3,7 => CTR => A2: 8,9 * INC # A2: 8,9 => UNS * PRF # H2: 3,7 => SOL * DIS # H2: 9 => CTR => H2: 3,7 * DIS # E6: 3,7 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # I2: 8,9 => SOL * DIS # I2: 7 => CTR => I2: 8,9 * DIS # A3: 8,9 => CTR => A3: 3,7 * PRF # A3: 3,7 => SOL * DIS # E6: 3,7 => CTR => E6: 9 * PRF # E6: 9 => SOL * PRF # I4: 8,9 => SOL * DIS # I4: 3 => CTR => I4: 8,9 * DIS # I4: 3,9 => CTR => I4: 8 * PRF # I4: 8 => SOL * PRF # E6: 3,9 => SOL * DIS # E6: 7 => CTR => E6: 3,9 * INC # B7: 3,9 => UNS * INC # C7: 3,9 => UNS * DIS # A1: 3,9 => CTR => A1: 4,7 * INC # A1: 4,7 => UNS * DIS # A2: 3,9 => CTR => A2: 7,8 * PRF # A2: 7,8 => SOL * PRF # A3: 3,9 => SOL * INC # A3: 7,8 => UNS * DIS # A5: 3,9 => CTR => A5: 4 * INC # A5: 4 => UNS * PRF # D1: 3,7 => SOL * DIS # D1: 9 => CTR => D1: 3,7 * DIS # D3: 3,7 => CTR => D3: 9 * PRF # D3: 9 => SOL * DIS # H2: 7,9 => CTR => H2: 3 * PRF # H2: 3 => SOL * PRF # H3: 7,9 => SOL * DIS # H3: 3 => CTR => H3: 7,9 * PRF # I2: 7,9 => SOL * DIS # I2: 8 => CTR => I2: 7,9 * CNT 54 HDP CHAINS / 54 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A1: 3,9 => CTR => A1: 4,7 * DIS A1: 4,7 # B1: 3,9 => CTR => B1: 4 * DIS A1: 4,7 + B1: 4 # A2: 3,9 => CTR => A2: 8 * PRF A1: 4,7 + B1: 4 + A2: 8 => SOL * STA A1: 4,7 + B1: 4 + A2: 8 * CNT 4 HDP CHAINS / 3 HYP OPENED