Analysis of xx-top500-001-base.sdk
Contents
Original Sudoku
level: medium
position: .69..........4..3..8..........8..61.4.....9..5...2....2..9....5...6.1............ initial
Autosolve
position: .69.185..1..746839.84.9.1.69..8..61.4.8.6.95.5.6.29..82.198..658..6.129.69.....81 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D3: 2,3 => SOL * DIS # D9: 2,3 => CTR => D9: 4,5 * DIS # H1: 2 => CTR => H1: 4,7 * DIS # I8: 4,7 => CTR => I8: 3 * DIS # H1: 2,7 => CTR => H1: 4 * DIS # D6: 1,3 => CTR => D6: 4 * PRF # D6: 4 => SOL * DIS # E4: 3,7 => CTR => E4: 5 * PRF # E4: 5 => SOL * PRF # F4: 3,7 => SOL * DIS # I5: 3,7 => CTR => I5: 2 * DIS # F7: 3,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # F9: 3,7 => CTR => F9: 2,4,5 * DIS # G6: 4,7 => CTR => G6: 3 * DIS # H1: 2 => CTR => H1: 4,7 * CNT 16 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D3: 2,3 => SOL * STA D3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .69..........4..3..8..........8..61.4.....9..5...2....2..9....5...6.1............ | initial |
| .69.185..1..746839.84.9.1.69..8..61.4.8.6.95.5.6.29..82.198..658..6.129.69.....81 | autosolve |
| 369218547152746839784395126923857614478163952516429378231984765845671293697532481 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) A1: 3,7 B2: 2,5 C2: 2,5 A3: 3,7 D1: 2,3 I1: 4,7 H3: 2,7 D5: 1,3 F5: 3,7 H6: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,B6: 1.. / B5 = 1 => 0 pairs (X) / B6 = 1 => 11 pairs (_) D5,D6: 1.. / D5 = 1 => 11 pairs (_) / D6 = 1 => 0 pairs (X) B5,D5: 1.. / B5 = 1 => 0 pairs (X) / D5 = 1 => 11 pairs (_) B6,D6: 1.. / B6 = 1 => 11 pairs (_) / D6 = 1 => 0 pairs (X) B2,C2: 2.. / B2 = 2 => 0 pairs (X) / C2 = 2 => 9 pairs (_) H1,H3: 2.. / H1 = 2 => 0 pairs (X) / H3 = 2 => 9 pairs (_) I4,I5: 2.. / I4 = 2 => 0 pairs (X) / I5 = 2 => 10 pairs (_) D9,F9: 2.. / D9 = 2 => 0 pairs (X) / F9 = 2 => 11 pairs (_) D1,H1: 2.. / D1 = 2 => 9 pairs (_) / H1 = 2 => 0 pairs (X) B5,I5: 2.. / B5 = 2 => 0 pairs (X) / I5 = 2 => 10 pairs (_) C2,C4: 2.. / C2 = 2 => 9 pairs (_) / C4 = 2 => 0 pairs (X) F3,F9: 2.. / F3 = 2 => 0 pairs (X) / F9 = 2 => 11 pairs (_) A1,A3: 3.. / A1 = 3 => 9 pairs (_) / A3 = 3 => 0 pairs (X) A1,D1: 3.. / A1 = 3 => 9 pairs (_) / D1 = 3 => 0 pairs (X) H1,I1: 4.. / H1 = 4 => 10 pairs (_) / I1 = 4 => 0 pairs (X) F4,D6: 4.. / F4 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) B7,B8: 4.. / B7 = 4 => 0 pairs (X) / B8 = 4 => 12 pairs (_) F4,I4: 4.. / F4 = 4 => 0 pairs (X) / I4 = 4 => 0 pairs (_) B8,I8: 4.. / B8 = 4 => 12 pairs (_) / I8 = 4 => 0 pairs (X) D6,D9: 4.. / D6 = 4 => 0 pairs (*) / D9 = 4 => 0 pairs (X) H1,H6: 4.. / H1 = 4 => 10 pairs (_) / H6 = 4 => 0 pairs (X) B2,C2: 5.. / B2 = 5 => 9 pairs (_) / C2 = 5 => 0 pairs (X) D3,F3: 5.. / D3 = 5 => 11 pairs (_) / F3 = 5 => 0 pairs (*) E4,F4: 5.. / E4 = 5 => 0 pairs (*) / F4 = 5 => 0 pairs (X) B2,B8: 5.. / B2 = 5 => 9 pairs (_) / B8 = 5 => 0 pairs (X) D3,D9: 5.. / D3 = 5 => 11 pairs (_) / D9 = 5 => 0 pairs (*) A1,A3: 7.. / A1 = 7 => 0 pairs (X) / A3 = 7 => 9 pairs (_) A3,H3: 7.. / A3 = 7 => 9 pairs (_) / H3 = 7 => 0 pairs (X) * DURATION: 0:00:45.477027 START: 02:37:35.309447 END: 02:38:20.786474 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,C2,D1,D5,F5,H3,H6,I1) * .69.185..1..746839.84.9.1.69..8..61.4.8.6.95.5.6.29..82.198..658..6.129.69.....81 * PAIR D1: 2,3 BLK 2 D3: 2,3,5 # reduction candidate for 2,3 D3: 2,3 => SOLVED * 369218547152746839784395126923857614478163952516429378231984765845671293697532481 D3: 5 # 11 pairs F3: 2,3,5 # reduction candidate for 2,3 F3: 2,3 # 11 pairs * PAIR D1: 2,3 COL D D9: 2,3,4,5 # reduction candidate for 2,3 D9: 2,3 => CTR * .69.185471..7468397845931269..8..6144.816795251642937823198..658..6.129.69.....81 D9: 4,5 # 12 pairs * PAIR I1: 4,7 BLK 3 H1: 4,7,2 # reduction candidate for 4,7 H1: 2 => CTR * .69.185241..746839.84.9.1769..8.461.4.8.6.95.5.6.29.482.198..6584.6.129.69.4.2.81 H1: 4,7 # 9 pairs * PAIR I1: 4,7 COL I I4: 4,7,2,3 # reduction candidate for 4,7 I4: 4,7 # 17 pairs I8: 4,7,3 # reduction candidate for 4,7 I8: 4,7 => CTR * 3692185..1..7468397845931269..8.461.4.8.6795.5.6.29..82.198..658..6.129.69.....81 I8: 3 # 17 pairs * PAIR H3: 2,7 BLK 3 H1: 2,7,4 # reduction candidate for 2,7 H1: 2,7 => CTR * .69.185.4152746839.845931269..85461.4.8.6795.5.6.29.482.198..6584.6.129.69.4.2.81 H1: 4 # 10 pairs * PAIR D5: 1,3 BLK 5 D6: 1,3,4 # reduction candidate for 1,3 D6: 1,3 => CTR * .69.185..1..746839.845931269..85461.4.8.6795.5.6.29..82.198..658..6.129.69.4.2.81 D6: 4 => SOLVED * 369218547152746839784395126923857614478163952516429378231984765845671293697532481 * PAIR D5: 1,3 ROW 5 B5: 1,3,2,7 # reduction candidate for 1,3 B5: 2,7 # 15 pairs B5: 1,3 # 12 pairs * PAIR F5: 3,7 BLK 5 E4: 3,7,5 # reduction candidate for 3,7 E4: 3,7 => CTR * .69.1854715274683978459312692.8.56144.81679525164293782.198..6584.6.129369.....81 E4: 5 => SOLVED * 369218547152746839784395126923857614478163952516429378231984765845671293697532481 F4: 3,7,4,5 # reduction candidate for 3,7 F4: 3,7 => SOLVED * 369218547152746839784395126923857614478163952516429378231984765845671293697532481 F4: 4,5 # 11 pairs * PAIR F5: 3,7 ROW 5 B5: 3,7,1,2 # reduction candidate for 3,7 B5: 3,7 # 12 pairs I5: 3,7,2 # reduction candidate for 3,7 I5: 3,7 => CTR * .69.185..152746839.84.9.1.69..8.461242816.95.516329..82.198..658..6.129.69.4.2.81 I5: 2 # 10 pairs * PAIR F5: 3,7 COL F F7: 3,7,4 # reduction candidate for 3,7 F7: 3,7 => CTR * .69.185..1..746839.845921769..8.56144.8.6.95.5.6.29..82.198..658..6.129.69.....81 F7: 4 => SOLVED * 369218547152746839784395126923857614478163952516429378231984765845671293697532481 F9: 3,7,2,4,5 # reduction candidate for 3,7 F9: 3,7 => CTR * .69.185..1..746839.84.921769..8.56144.8.6.95.5.6.29..82.198..658..6.129.69.....81 F9: 2,4,5 # 10 pairs * PAIR H6: 4,7 BLK 6 I4: 4,7,2,3 # reduction candidate for 4,7 I4: 4,7 # 17 pairs G6: 4,7,3 # reduction candidate for 4,7 G6: 4,7 => CTR * 3692185..1..7468397845931269..8.461.4.8.6795.5.6.29..82.198..658..6.129.69.....81 G6: 3 # 17 pairs * PAIR H6: 4,7 COL H H1: 4,7,2 # reduction candidate for 4,7 H1: 2 => CTR * .69.185241..746839.84.9.1769..8.461.4.8.6.95.5.6.29.482.198..6584.6.129.69.4.2.81 H1: 4,7 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-001-base-pr-000.dot * REASONING * PRF # D3: 2,3 => SOL * DIS # D9: 2,3 => CTR => D9: 4,5 * DIS # H1: 2 => CTR => H1: 4,7 * DIS # I8: 4,7 => CTR => I8: 3 * DIS # H1: 2,7 => CTR => H1: 4 * DIS # D6: 1,3 => CTR => D6: 4 * PRF # D6: 4 => SOL * DIS # E4: 3,7 => CTR => E4: 5 * PRF # E4: 5 => SOL * PRF # F4: 3,7 => SOL * DIS # I5: 3,7 => CTR => I5: 2 * DIS # F7: 3,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # F9: 3,7 => CTR => F9: 2,4,5 * DIS # G6: 4,7 => CTR => G6: 3 * DIS # H1: 2 => CTR => H1: 4,7 * CNT 16 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,C2,D1,D5,F5,H3,H6,I1) * .69.185..1..746839.84.9.1.69..8..61.4.8.6.95.5.6.29..82.198..658..6.129.69.....81 * PAIR D1: 2,3 BLK 2 D3: 2,3,5 # reduction candidate for 2,3 D3: 2,3 => SOLVED * 369218547152746839784395126923857614478163952516429378231984765845671293697532481 * DURATION: 0:00:02.294293 START: 02:38:50.613474 END: 02:38:52.907767 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-001-base-pr-001.dot * REASONING * PRF # D3: 2,3 => SOL * STA D3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 001 solution: 369218547152746839784395126923857614478163952516429378231984765845671293697532481 info: 1305 FNBWY S8.f 21983 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 369218547152746839784395126923857614478163952516429378231984765845671293697532481 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 # D3: 2,3 => SOL * INC # D3: 5 => UNS * INC # F3: 2,3 => UNS * DIS # D9: 2,3 => CTR => D9: 4,5 * INC # D9: 4,5 => UNS * INC # H1: 4,7 => UNS * DIS # H1: 2 => CTR => H1: 4,7 * INC # I4: 4,7 => UNS * DIS # I8: 4,7 => CTR => I8: 3 * INC # I8: 3 => UNS * DIS # H1: 2,7 => CTR => H1: 4 * INC # H1: 4 => UNS * DIS # D6: 1,3 => CTR => D6: 4 * PRF # D6: 4 => SOL * INC # B5: 1,3 => UNS * INC # B5: 2,7 => UNS * DIS # E4: 3,7 => CTR => E4: 5 * PRF # E4: 5 => SOL * PRF # F4: 3,7 => SOL * INC # F4: 4,5 => UNS * INC # B5: 3,7 => UNS * DIS # I5: 3,7 => CTR => I5: 2 * INC # I5: 2 => UNS * DIS # F7: 3,7 => CTR => F7: 4 * PRF # F7: 4 => SOL * DIS # F9: 3,7 => CTR => F9: 2,4,5 * INC # F9: 2,4,5 => UNS * INC # I4: 4,7 => UNS * DIS # G6: 4,7 => CTR => G6: 3 * INC # G6: 3 => UNS * INC # H1: 4,7 => UNS * DIS # H1: 2 => CTR => H1: 4,7 * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # D3: 2,3 => SOL * STA D3: 2,3 * CNT 1 HDP CHAINS / 1 HYP OPENED