Analysis of xx-top500-285-base.sdk
Contents
Original Sudoku
level: medium
position: ...2.4.5..1............7...4......7.5...1.......6....9....8.6.13.7............2.. initial
Autosolve
position: 7..2.415..1....7.....1.79..4.1....7.57.41.3.....675419...78.6.13.79.1...1..54.2.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B9: 6,9 => CTR => B9: 8 * DIS # C9: 8 => CTR => C9: 6,9 * PRF # C6: 2,8 => SOL * DIS # A3: 2,8 => CTR => A3: 6 * PRF # I4: 5,8 => SOL * DIS # A2: 6 => CTR => A2: 2,9 * PRF # I8: 4 => SOL * PRF # I8: 4,8 => SOL * CNT 8 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B9: 6,9 => CTR => B9: 8 * PRF B9: 8 # C6: 2,8 => SOL * STA B9: 8 + C6: 2,8 * CNT 2 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...2.4.5..1............7...4......7.5...1.......6....9....8.6.13.7............2.. | initial |
| 7..2.415..1....7.....1.79..4.1....7.57.41.3.....675419...78.6.13.79.1...1..54.2.7 | autosolve |
| 798234156215896743643157928461329875579418362832675419954782631327961584186543297 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B3: 4,5 D2: 3,8 B4: 6,9 C5: 6,9 A6: 2,8 D4: 3,8 G4: 5,8 A7: 2,9 B7: 4,5 C7: 4,5 B8: 2,6 F7: 2,3 E8: 2,6 F9: 3,6 H7: 3,9 G8: 5,8 H8: 4,8 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,B8: 2.. / A7 = 2 => 0 pairs (X) / B8 = 2 => 0 pairs (_) F7,E8: 2.. / F7 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) A7,F7: 2.. / A7 = 2 => 0 pairs (X) / F7 = 2 => 0 pairs (_) B8,E8: 2.. / B8 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) B6,B8: 2.. / B6 = 2 => 0 pairs (X) / B8 = 2 => 0 pairs (_) E4,E8: 2.. / E4 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) B6,C6: 3.. / B6 = 3 => 0 pairs (*) / C6 = 3 => 0 pairs (X) D4,E4: 3.. / D4 = 3 => 18 pairs (_) / E4 = 3 => 0 pairs (X) F7,F9: 3.. / F7 = 3 => 0 pairs (X) / F9 = 3 => 0 pairs (_) H7,H9: 3.. / H7 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) F7,H7: 3.. / F7 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) F9,H9: 3.. / F9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) B1,B6: 3.. / B1 = 3 => 24 pairs (_) / B6 = 3 => 0 pairs (*) D2,D4: 3.. / D2 = 3 => 0 pairs (X) / D4 = 3 => 18 pairs (_) B7,C7: 4.. / B7 = 4 => 16 pairs (_) / C7 = 4 => 15 pairs (_) H8,I8: 4.. / H8 = 4 => 19 pairs (_) / I8 = 4 => 0 pairs (*) B3,B7: 4.. / B3 = 4 => 15 pairs (_) / B7 = 4 => 16 pairs (_) E2,E3: 5.. / E2 = 5 => 19 pairs (_) / E3 = 5 => 15 pairs (_) G4,I4: 5.. / G4 = 5 => 16 pairs (_) / I4 = 5 => 0 pairs (*) B7,C7: 5.. / B7 = 5 => 15 pairs (_) / C7 = 5 => 16 pairs (_) G8,I8: 5.. / G8 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) C2,E2: 5.. / C2 = 5 => 15 pairs (_) / E2 = 5 => 19 pairs (_) B3,B7: 5.. / B3 = 5 => 16 pairs (_) / B7 = 5 => 15 pairs (_) G4,G8: 5.. / G4 = 5 => 16 pairs (_) / G8 = 5 => 0 pairs (*) I4,I8: 5.. / I4 = 5 => 0 pairs (*) / I8 = 5 => 0 pairs (X) A2,A3: 6.. / A2 = 6 => 0 pairs (X) / A3 = 6 => 21 pairs (_) B4,C5: 6.. / B4 = 6 => 0 pairs (*) / C5 = 6 => 0 pairs (X) E8,F9: 6.. / E8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) E1,I1: 6.. / E1 = 6 => 0 pairs (X) / I1 = 6 => 0 pairs (_) B4,I4: 6.. / B4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) B8,E8: 6.. / B8 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) C5,C9: 6.. / C5 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) F2,F9: 6.. / F2 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) D2,F2: 8.. / D2 = 8 => 18 pairs (_) / F2 = 8 => 0 pairs (X) B9,C9: 8.. / B9 = 8 => 22 pairs (_) / C9 = 8 => 0 pairs (X) A3,A6: 8.. / A3 = 8 => 0 pairs (X) / A6 = 8 => 20 pairs (_) D2,D4: 8.. / D2 = 8 => 18 pairs (_) / D4 = 8 => 0 pairs (X) G4,G8: 8.. / G4 = 8 => 0 pairs (*) / G8 = 8 => 0 pairs (X) B4,C5: 9.. / B4 = 9 => 0 pairs (X) / C5 = 9 => 0 pairs (_) H7,H9: 9.. / H7 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) C5,F5: 9.. / C5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) A7,H7: 9.. / A7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) A2,A7: 9.. / A2 = 9 => 0 pairs (X) / A7 = 9 => 0 pairs (_) * DURATION: 0:01:34.970143 START: 12:39:51.192836 END: 12:41:26.162979 2017-05-04 * CP COUNT: (43) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,B3,B4,B7,B8,C5,C7,D2,D4,E8,F7,F9,G4,G8,H7,H8,H9) * 7..2.415..1....7.....1.79..4.1....7.57.41.3.....675419...78.6.13.79.1...1..54.2.7 * PAIR B3: 4,5 BLK 1 C2: 4,5,2,3,9 # reduction candidate for 4,5 C2: 4,5 # 19 pairs C3: 4,5,2,3,8 # reduction candidate for 4,5 C3: 4,5 # 20 pairs * PAIR B4: 6,9 COL B B9: 6,9,8 # reduction candidate for 6,9 B9: 6,9 => CTR * 7..2.415..1....7.....1.79..491....765764193.....6754199..782631327961..5168543297 B9: 8 # 22 pairs * PAIR C5: 6,9 COL C C9: 6,9,8 # reduction candidate for 6,9 C9: 8 => CTR * 7..2.415..1....7.....1.79..491....765764193.....6754199..782631327961..5168543297 C9: 6,9 # 22 pairs * PAIR A6: 2,8 BLK 4 B6: 2,8,3 # reduction candidate for 2,8 B6: 2,8 # 24 pairs C6: 2,8,3 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 798234156215896743643157928461329875579418362832675419954782631327961584186543297 C6: 3 # 24 pairs * PAIR A6: 2,8 COL A A3: 2,8,6 # reduction candidate for 2,8 A3: 2,8 => CTR * 7..2.415.61....7.....1.79..4.1....7.57.41.3.....6754199..782631327961...1..54.2.7 A3: 6 # 21 pairs * PAIR G4: 5,8 BLK 6 I4: 5,8,2,6 # reduction candidate for 5,8 I4: 5,8 => SOLVED * 798234156215896743643157928461329875579418362832675419954782631327961584186543297 I4: 2,6 # 18 pairs * PAIR A7: 2,9 COL A A2: 2,9,6 # reduction candidate for 2,9 A2: 6 => CTR * 7..2.415.61....7.....1.79..4.1....7.57.41.3.....6754199..782631327961...1..54.2.7 A2: 2,9 # 21 pairs * PAIR C7: 4,5 COL C C2: 4,5,2,3,9 # reduction candidate for 4,5 C2: 4,5 # 19 pairs C3: 4,5,2,3,8 # reduction candidate for 4,5 C3: 4,5 # 20 pairs * PAIR G8: 5,8 BLK 9 I8: 5,8,4 # reduction candidate for 5,8 I8: 4 => SOLVED * 798234156215896743643157928461329875579418362832675419954782631327961584186543297 I8: 5,8 # 19 pairs * PAIR H8: 4,8 BLK 9 I8: 4,8,5 # reduction candidate for 4,8 I8: 4,8 => SOLVED * 798234156215896743643157928461329875579418362832675419954782631327961584186543297 I8: 5 # 16 pairs * PAIR H8: 4,8 COL H H3: 4,8,2,6 # reduction candidate for 4,8 H3: 4,8 # 21 pairs H3: 2,6 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-285-base-pr-000.dot * REASONING * DIS # B9: 6,9 => CTR => B9: 8 * DIS # C9: 8 => CTR => C9: 6,9 * PRF # C6: 2,8 => SOL * DIS # A3: 2,8 => CTR => A3: 6 * PRF # I4: 5,8 => SOL * DIS # A2: 6 => CTR => A2: 2,9 * PRF # I8: 4 => SOL * PRF # I8: 4,8 => SOL * CNT 8 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A7,B3,B4,B7,B8,C5,C7,D2,D4,E8,F7,F9,G4,G8,H7,H8,H9) * 7..2.415..1....7.....1.79..4.1....7.57.41.3.....675419...78.6.13.79.1...1..54.2.7 * PAIR B3: 4,5 BLK 1 C2: 4,5,2,3,9 # reduction candidate for 4,5 C2: 4,5 # 19 pairs C3: 4,5,2,3,8 # reduction candidate for 4,5 C3: 4,5 # 20 pairs * PAIR B4: 6,9 COL B B9: 6,9,8 # reduction candidate for 6,9 B9: 6,9 => CTR * 7..2.415..1....7.....1.79..491....765764193.....6754199..782631327961..5168543297 * PAIR RESTART * PAIR A6: 2,8 BLK 4 C6: 2,8,3 # reduction candidate for 2,8 C6: 2,8 => SOLVED * 798234156215896743643157928461329875579418362832675419954782631327961584186543297 * DURATION: 0:00:07.369199 START: 12:41:55.100235 END: 12:42:02.469434 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-285-base-pr-001.dot * REASONING * DIS # B9: 6,9 => CTR => B9: 8 * PRF B9: 8 # C6: 2,8 => SOL * STA B9: 8 + C6: 2,8 * CNT 2 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 285 solution: 798234156215896743643157928461329875579418362832675419954782631327961584186543297 info: 2332 FNBHWY S8.f 7860 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 798234156215896743643157928461329875579418362832675419954782631327961584186543297 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 # C2: 4,5 => UNS * INC # C3: 4,5 => UNS * DIS # B9: 6,9 => CTR => B9: 8 * INC # B9: 8 => UNS * INC # C9: 6,9 => UNS * DIS # C9: 8 => CTR => C9: 6,9 * INC # B6: 2,8 => UNS * PRF # C6: 2,8 => SOL * INC # C6: 3 => UNS * DIS # A3: 2,8 => CTR => A3: 6 * INC # A3: 6 => UNS * PRF # I4: 5,8 => SOL * INC # I4: 2,6 => UNS * INC # A2: 2,9 => UNS * DIS # A2: 6 => CTR => A2: 2,9 * INC # C2: 4,5 => UNS * INC # C3: 4,5 => UNS * INC # I8: 5,8 => UNS * PRF # I8: 4 => SOL * PRF # I8: 4,8 => SOL * INC # I8: 5 => UNS * INC # H3: 4,8 => UNS * INC # H3: 2,6 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C2: 4,5 => UNS * INC # C3: 4,5 => UNS * DIS # B9: 6,9 => CTR => B9: 8 * PRF B9: 8 # C6: 2,8 => SOL * STA B9: 8 + C6: 2,8 * CNT 4 HDP CHAINS / 4 HYP OPENED