Analysis of xx-top500-146-base.sdk
Contents
Original Sudoku
level: medium
position: .21..........4...5..........3.1.6...7......4....2.....4.....1.75...8..........23. initial
Autosolve
position: .21.6....3.7.42.15.45.1..2.23417658971.....42.582.4..1483629157572381...1..457238 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A3: 8,9 => SOL * DIS # A3: 6 => CTR => A3: 8,9 * DIS # D1: 8,9 => CTR => D1: 5,7 * DIS # G1: 8,9 => CTR => G1: 4,7 * DIS # A3: 8 => CTR => A3: 6,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # D1: 8,9 => CTR => D1: 5,7 * PRF # D3: 8,9 => SOL * PRF # G2: 8,9 => SOL * DIS # G2: 6 => CTR => G2: 8,9 * DIS # F1: 3,8 => CTR => F1: 5 * PRF # F1: 5 => SOL * DIS # G1: 7,9 => CTR => G1: 4,8 * PRF # D1: 7,9 => SOL * DIS # D1: 5,8 => CTR => D1: 7,9 * DIS # A3: 8 => CTR => A3: 6,9 * DIS # D1: 5,8 => CTR => D1: 7,9 * PRF # D1: 7,9 => SOL * PRF # F1: 5,8 => SOL * DIS # F1: 3 => CTR => F1: 5,8 * PRF # G6: 3,6 => SOL * DIS # G6: 7 => CTR => G6: 3,6 * DIS # G6: 6,7 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # G8: 6,9 => SOL * DIS # G8: 4 => CTR => G8: 6,9 * DIS # G8: 4,6 => CTR => G8: 9 * PRF # G8: 9 => SOL * CNT 29 HDP CHAINS / 37 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A3: 8,9 => SOL * STA A3: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .21..........4...5..........3.1.6...7......4....2.....4.....1.75...8..........23. | initial |
| .21.6....3.7.42.15.45.1..2.23417658971.....42.582.4..1483629157572381...1..457238 | autosolve |
| 821765493367942815945813726234176589719538642658294371483629157572381964196457238 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (19) A1: 8,9 B2: 6,9 D2: 8,9 F3: 3,8 H1: 7,9 I1: 3,4 I3: 3,6 C5: 6,9 A6: 6,9 D5: 5,8 E5: 3,9 F5: 5,8 E6: 3,9 G5: 3,6 H6: 6,7 B9: 6,9 C9: 6,9 H8: 6,9 I8: 4,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 3.. / F1 = 3 => 0 pairs (X) / F3 = 3 => 0 pairs (_) I1,I3: 3.. / I1 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) E5,E6: 3.. / E5 = 3 => 0 pairs (*) / E6 = 3 => 0 pairs (X) G5,G6: 3.. / G5 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) F1,I1: 3.. / F1 = 3 => 0 pairs (X) / I1 = 3 => 0 pairs (_) F3,I3: 3.. / F3 = 3 => 0 pairs (*) / I3 = 3 => 0 pairs (X) E5,G5: 3.. / E5 = 3 => 0 pairs (*) / G5 = 3 => 0 pairs (X) E6,G6: 3.. / E6 = 3 => 0 pairs (X) / G6 = 3 => 0 pairs (_) G1,I1: 4.. / G1 = 4 => 0 pairs (*) / I1 = 4 => 0 pairs (X) G8,I8: 4.. / G8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) G1,G8: 4.. / G1 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) I1,I8: 4.. / I1 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) D1,F1: 5.. / D1 = 5 => 0 pairs (X) / F1 = 5 => 0 pairs (_) D5,F5: 5.. / D5 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) D1,D5: 5.. / D1 = 5 => 0 pairs (X) / D5 = 5 => 0 pairs (_) F1,F5: 5.. / F1 = 5 => 0 pairs (*) / F5 = 5 => 0 pairs (X) B2,A3: 6.. / B2 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) C5,A6: 6.. / C5 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) B9,C9: 6.. / B9 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) B2,G2: 6.. / B2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) C5,G5: 6.. / C5 = 6 => 0 pairs (X) / G5 = 6 => 0 pairs (_) A3,A6: 6.. / A3 = 6 => 0 pairs (X) / A6 = 6 => 0 pairs (_) B2,B9: 6.. / B2 = 6 => 0 pairs (*) / B9 = 6 => 0 pairs (X) C5,C9: 6.. / C5 = 6 => 0 pairs (X) / C9 = 6 => 0 pairs (_) H6,H8: 6.. / H6 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) I3,I8: 6.. / I3 = 6 => 0 pairs (*) / I8 = 6 => 0 pairs (X) D1,D3: 7.. / D1 = 7 => 0 pairs (*) / D3 = 7 => 0 pairs (X) G6,H6: 7.. / G6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) D3,G3: 7.. / D3 = 7 => 19 pairs (_) / G3 = 7 => 0 pairs (*) H1,H6: 7.. / H1 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) A1,A3: 8.. / A1 = 8 => 20 pairs (_) / A3 = 8 => 0 pairs (X) D5,F5: 8.. / D5 = 8 => 0 pairs (X) / F5 = 8 => 0 pairs (_) D2,G2: 8.. / D2 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) C5,A6: 9.. / C5 = 9 => 0 pairs (*) / A6 = 9 => 0 pairs (X) E5,E6: 9.. / E5 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) B9,C9: 9.. / B9 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) G8,H8: 9.. / G8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) C5,E5: 9.. / C5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A6,E6: 9.. / A6 = 9 => 0 pairs (X) / E6 = 9 => 0 pairs (_) B2,B9: 9.. / B2 = 9 => 0 pairs (X) / B9 = 9 => 0 pairs (_) C5,C9: 9.. / C5 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) H1,H8: 9.. / H1 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) * DURATION: 0:01:18.388178 START: 07:43:54.320698 END: 07:45:12.708876 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B2,B9,C5,C9,D2,D5,E5,E6,F3,F5,G5,H1,H6,H8,I1,I3,I8) * .21.6....3.7.42.15.45.1..2.23417658971.....42.582.4..1483629157572381...1..457238 * PAIR A1: 8,9 BLK 1 A3: 8,9,6 # reduction candidate for 8,9 A3: 8,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 A3: 6 => CTR * 821.6....397842615645.13.2.23417658971.....42.582.4..1483629157572381...1..457238 * PAIR A1: 8,9 ROW 1 D1: 8,9,5,7 # reduction candidate for 8,9 D1: 8,9 => CTR * .21.65..33.7.42.15.45713.2623417658971.5.8.42658294371483629157572381.641.6457238 D1: 5,7 # 20 pairs G1: 8,9,4,7 # reduction candidate for 8,9 G1: 8,9 => CTR * 8215639743.7942815.45718.2323417658971.8.5.42.582.47614836291575723814961..457238 G1: 4,7 # 20 pairs * PAIR B2: 6,9 BLK 1 A3: 6,9,8 # reduction candidate for 6,9 A3: 8 => CTR * .21.6....367.42.15845.13.2623417658971.....42658294371483629157572381.64196457238 A3: 6,9 # 20 pairs * PAIR B2: 6,9 ROW 2 G2: 6,9,8 # reduction candidate for 6,9 G2: 6,9 => CTR * .21.6....3.7842.15.45.13.2623417658971.5.8.42658294371483629157572381.641.6457238 G2: 8 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 * PAIR D2: 8,9 BLK 2 D1: 8,9,5,7 # reduction candidate for 8,9 D1: 8,9 => CTR * .21.65..33.7.42.15.45713.2623417658971.5.8.42658294371483629157572381.641.6457238 D1: 5,7 # 20 pairs D3: 8,9,7 # reduction candidate for 8,9 D3: 8,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 D3: 7 # 19 pairs * PAIR D2: 8,9 ROW 2 G2: 8,9,6 # reduction candidate for 8,9 G2: 8,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 G2: 6 => CTR * .21.6....3.7842615645.13.2.23417658971.....42.582.4..1483629157572381...1..457238 * PAIR F3: 3,8 BLK 2 F1: 3,8,5 # reduction candidate for 3,8 F1: 3,8 => CTR * .2156....367942815.4571..2.234176589719835642658294371483629157572381.64196457238 F1: 5 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 * PAIR H1: 7,9 BLK 3 G1: 7,9,4,8 # reduction candidate for 7,9 G1: 7,9 => CTR * 8215639743.7942815.45718.2323417658971.8.5.42.582.47614836291575723814961..457238 G1: 4,8 # 20 pairs G3: 7,9,6,8 # reduction candidate for 7,9 G3: 7,9 # 22 pairs * PAIR H1: 7,9 ROW 1 D1: 7,9,5,8 # reduction candidate for 7,9 D1: 7,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 D1: 5,8 => CTR * .21.6....367942815.4571..2.234176589719.3.642658294371483629157572381.64196457238 * PAIR A6: 6,9 COL A A3: 6,9,8 # reduction candidate for 6,9 A3: 8 => CTR * .21.6....367.42.15845.13.2623417658971.....42658294371483629157572381.64196457238 A3: 6,9 # 20 pairs * PAIR D5: 5,8 COL D D1: 5,8,7,9 # reduction candidate for 5,8 D1: 5,8 => CTR * .21.6....367942815.4571..2.234176589719.3.642658294371483629157572381.64196457238 D1: 7,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 * PAIR F5: 5,8 COL F F1: 5,8,3 # reduction candidate for 5,8 F1: 5,8 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 F1: 3 => CTR * 8215639743.794281594571862323417658971.8.5.42.582.4..14836291575723814961..457238 * PAIR G5: 3,6 BLK 6 G6: 3,6,7 # reduction candidate for 3,6 G6: 3,6 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 G6: 7 => CTR * 82196..7.3.7.42.1564571.923234176589716.9.342958234761483629157572381.96169457238 * PAIR H6: 6,7 BLK 6 G6: 6,7,3 # reduction candidate for 6,7 G6: 6,7 => CTR * 821.6....397842615645.13.2.234176589716.9.342958234..1483629157572381...169457238 G6: 3 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 * PAIR H8: 6,9 BLK 9 G8: 6,9,4 # reduction candidate for 6,9 G8: 6,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 G8: 4 => CTR * .21.63.743.7.42.1564571892323417658971.....42.582.47614836291575723814961..457238 * PAIR I8: 4,6 BLK 9 G8: 4,6,9 # reduction candidate for 4,6 G8: 4,6 => CTR * 82196..7.3.7.42.1564571.923234176589716.9.342958234761483629157572381.96169457238 G8: 9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-146-base-pr-000.dot * REASONING * PRF # A3: 8,9 => SOL * DIS # A3: 6 => CTR => A3: 8,9 * DIS # D1: 8,9 => CTR => D1: 5,7 * DIS # G1: 8,9 => CTR => G1: 4,7 * DIS # A3: 8 => CTR => A3: 6,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # D1: 8,9 => CTR => D1: 5,7 * PRF # D3: 8,9 => SOL * PRF # G2: 8,9 => SOL * DIS # G2: 6 => CTR => G2: 8,9 * DIS # F1: 3,8 => CTR => F1: 5 * PRF # F1: 5 => SOL * DIS # G1: 7,9 => CTR => G1: 4,8 * PRF # D1: 7,9 => SOL * DIS # D1: 5,8 => CTR => D1: 7,9 * DIS # A3: 8 => CTR => A3: 6,9 * DIS # D1: 5,8 => CTR => D1: 7,9 * PRF # D1: 7,9 => SOL * PRF # F1: 5,8 => SOL * DIS # F1: 3 => CTR => F1: 5,8 * PRF # G6: 3,6 => SOL * DIS # G6: 7 => CTR => G6: 3,6 * DIS # G6: 6,7 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # G8: 6,9 => SOL * DIS # G8: 4 => CTR => G8: 6,9 * DIS # G8: 4,6 => CTR => G8: 9 * PRF # G8: 9 => SOL * CNT 29 HDP CHAINS / 37 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A6,B2,B9,C5,C9,D2,D5,E5,E6,F3,F5,G5,H1,H6,H8,I1,I3,I8) * .21.6....3.7.42.15.45.1..2.23417658971.....42.582.4..1483629157572381...1..457238 * PAIR A1: 8,9 BLK 1 A3: 8,9,6 # reduction candidate for 8,9 A3: 8,9 => SOLVED * 821765493367942815945813726234176589719538642658294371483629157572381964196457238 * DURATION: 0:00:02.179676 START: 07:45:58.593143 END: 07:46:00.772819 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-146-base-pr-001.dot * REASONING * PRF # A3: 8,9 => SOL * STA A3: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 146 solution: 821765493367942815945813726234176589719538642658294371483629157572381964196457238 info: 1815 FNBWY S8.f 16992 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 821765493367942815945813726234176589719538642658294371483629157572381964196457238 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:
* PRF # A3: 8,9 => SOL * DIS # A3: 6 => CTR => A3: 8,9 * DIS # D1: 8,9 => CTR => D1: 5,7 * INC # D1: 5,7 => UNS * DIS # G1: 8,9 => CTR => G1: 4,7 * INC # G1: 4,7 => UNS * INC # A3: 6,9 => UNS * DIS # A3: 8 => CTR => A3: 6,9 * DIS # G2: 6,9 => CTR => G2: 8 * PRF # G2: 8 => SOL * DIS # D1: 8,9 => CTR => D1: 5,7 * INC # D1: 5,7 => UNS * PRF # D3: 8,9 => SOL * INC # D3: 7 => UNS * PRF # G2: 8,9 => SOL * DIS # G2: 6 => CTR => G2: 8,9 * DIS # F1: 3,8 => CTR => F1: 5 * PRF # F1: 5 => SOL * DIS # G1: 7,9 => CTR => G1: 4,8 * INC # G1: 4,8 => UNS * INC # G3: 7,9 => UNS * PRF # D1: 7,9 => SOL * DIS # D1: 5,8 => CTR => D1: 7,9 * INC # A3: 6,9 => UNS * DIS # A3: 8 => CTR => A3: 6,9 * DIS # D1: 5,8 => CTR => D1: 7,9 * PRF # D1: 7,9 => SOL * PRF # F1: 5,8 => SOL * DIS # F1: 3 => CTR => F1: 5,8 * PRF # G6: 3,6 => SOL * DIS # G6: 7 => CTR => G6: 3,6 * DIS # G6: 6,7 => CTR => G6: 3 * PRF # G6: 3 => SOL * PRF # G8: 6,9 => SOL * DIS # G8: 4 => CTR => G8: 6,9 * DIS # G8: 4,6 => CTR => G8: 9 * PRF # G8: 9 => SOL * CNT 37 HDP CHAINS / 37 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A3: 8,9 => SOL * STA A3: 8,9 * CNT 1 HDP CHAINS / 1 HYP OPENED