Analysis of xx-top500-030-base.sdk
Contents
Original Sudoku
level: medium
position: .7..3.4..8......9..........6..8.9.....1...5.3...2......53.7..........1.........8. initial
Autosolve
position: .7..3.4588.....39.3...8..7.632859714981...523547213869.53.7894...8...13....3...8. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 1,2 => SOL * DIS # F1: 6 => CTR => F1: 1,2 * PRF # B3: 1,2 => SOL * DIS # D1: 1 => CTR => D1: 6,9 * PRF # B3: 2,6 => SOL * PRF # E2: 4,6 => SOL * DIS # E2: 2 => CTR => E2: 4,6 * DIS # E8: 4,6 => CTR => E8: 2,9 * DIS # E9: 4,6 => CTR => E9: 2,9 * PRF # E9: 2,9 => SOL * DIS # B9: 6,9 => CTR => B9: 1,2 * DIS # B9: 6,9 => CTR => B9: 1,2 * PRF # E9: 6,9 => SOL * DIS # F9: 1,6 => CTR => F9: 2,4,5 * PRF # F9: 2,4,5 => SOL * PRF # D1: 1,6 => SOL * DIS # D2: 1,6 => CTR => D2: 4,5,7 * DIS # B9: 2,6 => CTR => B9: 1,9 * DIS # E9: 2,6 => CTR => E9: 4,9 * DIS # F9: 2,6 => CTR => F9: 1,4,5 * CNT 20 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .7..3.4..8......9..........6..8.9.....1...5.3...2......53.7..........1.........8. | initial |
| .7..3.4588.....39.3...8..7.632859714981...523547213869.53.7894...8...13....3...8. | autosolve |
| 179632458865741392324985671632859714981467523547213869253178946498526137716394285 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A1: 1,2 C1: 6,9 C2: 4,5 C3: 4,5 G3: 2,6 E5: 4,6 A7: 1,2 A8: 4,7 A9: 4,7 C9: 6,9 D7: 1,6 I7: 2,6 I8: 5,7 G9: 2,6 I9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 1.. / I2 = 1 => 18 pairs (_) / I3 = 1 => 16 pairs (_) A7,B9: 1.. / A7 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) D7,F9: 1.. / D7 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) A7,D7: 1.. / A7 = 1 => 0 pairs (X) / D7 = 1 => 0 pairs (_) B9,F9: 1.. / B9 = 1 => 0 pairs (*) / F9 = 1 => 0 pairs (X) A1,A7: 1.. / A1 = 1 => 0 pairs (*) / A7 = 1 => 0 pairs (X) I7,G9: 2.. / I7 = 2 => 0 pairs (X) / G9 = 2 => 0 pairs (_) A1,F1: 2.. / A1 = 2 => 0 pairs (X) / F1 = 2 => 0 pairs (_) A7,I7: 2.. / A7 = 2 => 0 pairs (*) / I7 = 2 => 0 pairs (X) A1,A7: 2.. / A1 = 2 => 0 pairs (X) / A7 = 2 => 0 pairs (_) G3,G9: 2.. / G3 = 2 => 0 pairs (X) / G9 = 2 => 0 pairs (_) C2,C3: 4.. / C2 = 4 => 16 pairs (_) / C3 = 4 => 13 pairs (_) A8,A9: 4.. / A8 = 4 => 12 pairs (_) / A9 = 4 => 0 pairs (X) C2,C3: 5.. / C2 = 5 => 13 pairs (_) / C3 = 5 => 16 pairs (_) I8,I9: 5.. / I8 = 5 => 0 pairs (X) / I9 = 5 => 12 pairs (_) F9,I9: 5.. / F9 = 5 => 0 pairs (X) / I9 = 5 => 12 pairs (_) I7,G9: 6.. / I7 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) D7,I7: 6.. / D7 = 6 => 0 pairs (X) / I7 = 6 => 0 pairs (_) C1,C9: 6.. / C1 = 6 => 16 pairs (_) / C9 = 6 => 0 pairs (*) G3,G9: 6.. / G3 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) D2,F2: 7.. / D2 = 7 => 16 pairs (_) / F2 = 7 => 16 pairs (_) D5,F5: 7.. / D5 = 7 => 16 pairs (_) / F5 = 7 => 16 pairs (_) A8,A9: 7.. / A8 = 7 => 0 pairs (X) / A9 = 7 => 12 pairs (_) I8,I9: 7.. / I8 = 7 => 12 pairs (_) / I9 = 7 => 0 pairs (X) A8,I8: 7.. / A8 = 7 => 0 pairs (X) / I8 = 7 => 12 pairs (_) A9,I9: 7.. / A9 = 7 => 12 pairs (_) / I9 = 7 => 0 pairs (X) D2,D5: 7.. / D2 = 7 => 16 pairs (_) / D5 = 7 => 16 pairs (_) F2,F5: 7.. / F2 = 7 => 16 pairs (_) / F5 = 7 => 16 pairs (_) C1,B3: 9.. / C1 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) D1,D3: 9.. / D1 = 9 => 16 pairs (_) / D3 = 9 => 0 pairs (*) E8,E9: 9.. / E8 = 9 => 16 pairs (_) / E9 = 9 => 0 pairs (*) C1,D1: 9.. / C1 = 9 => 0 pairs (*) / D1 = 9 => 0 pairs (X) B3,D3: 9.. / B3 = 9 => 16 pairs (_) / D3 = 9 => 0 pairs (*) B8,E8: 9.. / B8 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) C1,C9: 9.. / C1 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) * DURATION: 0:01:02.557483 START: 03:39:32.644274 END: 03:40:35.201757 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,A8,A9,C1,C2,C3,C9,D7,E5,G3,G9,I7,I8,I9) * .7..3.4588.....39.3...8..7.632859714981...523547213869.53.7894...8...13....3...8. * PAIR A1: 1,2 BLK 1 B2: 1,2,6 # reduction candidate for 1,2 B2: 1,2 # 17 pairs B3: 1,2,6,9 # reduction candidate for 1,2 B3: 1,2 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 B3: 6,9 # 17 pairs * PAIR A1: 1,2 ROW 1 F1: 1,2,6 # reduction candidate for 1,2 F1: 6 => CTR * 27.1364588.....39.3..98..7.632859714981...523547213869153678942.68.9213....3...8. F1: 1,2 # 17 pairs * PAIR C1: 6,9 BLK 1 B3: 6,9,1,2 # reduction candidate for 6,9 B3: 1,2 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 B3: 6,9 # 17 pairs * PAIR C1: 6,9 ROW 1 D1: 6,9,1 # reduction candidate for 6,9 D1: 1 => CTR * .791364588.....39.3..98..7.632859714981...523547213869153678942.68...13....3...8. D1: 6,9 # 17 pairs * PAIR C2: 4,5 ROW 2 D2: 4,5,1,6,7 # reduction candidate for 4,5 D2: 4,5 # 18 pairs F2: 4,5,1,2,6,7 # reduction candidate for 4,5 F2: 4,5 # 18 pairs * PAIR C3: 4,5 ROW 3 D3: 4,5,1,6,9 # reduction candidate for 4,5 D3: 4,5 # 17 pairs F3: 4,5,1,2,6 # reduction candidate for 4,5 F3: 4,5 # 19 pairs * PAIR G3: 2,6 BLK 3 I2: 2,6,1 # reduction candidate for 2,6 I2: 2,6 # 16 pairs I3: 2,6,1 # reduction candidate for 2,6 I3: 2,6 # 18 pairs * PAIR G3: 2,6 ROW 3 B3: 2,6,1,9 # reduction candidate for 2,6 B3: 2,6 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 B3: 1,9 # 16 pairs F3: 2,6,1,4,5 # reduction candidate for 2,6 F3: 2,6 # 19 pairs * PAIR E5: 4,6 BLK 5 D5: 4,6,7 # reduction candidate for 4,6 D5: 4,6 # 16 pairs F5: 4,6,7 # reduction candidate for 4,6 F5: 4,6 # 16 pairs * PAIR E5: 4,6 COL E E2: 4,6,2 # reduction candidate for 4,6 E2: 4,6 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 E2: 2 => CTR * 27..3.4588...2.39.3...8..7.632859714981...523547213869153678942.68.9213..29341685 E8: 4,6,2,9 # reduction candidate for 4,6 E8: 4,6 => CTR * 279.3.4588...2.39.3..98.672632859714981...523547213869153.7894..98..213...639.28. E8: 2,9 # 16 pairs E9: 4,6,2,9 # reduction candidate for 4,6 E9: 4,6 => CTR * 27..3.4588...2.39.3...8..7.632859714981...523547213869153678942.68.9213..29341685 E9: 2,9 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 * PAIR A7: 1,2 BLK 7 B9: 1,2,6,9 # reduction candidate for 1,2 B9: 6,9 => CTR * .7..3.4588.....39.3...8..7.632859714981...523547213869153678942..8...13....3...8. B9: 1,2 # 17 pairs * PAIR C9: 6,9 BLK 7 B8: 6,9,2 # reduction candidate for 6,9 B8: 6,9 # 17 pairs B9: 6,9,1,2 # reduction candidate for 6,9 B9: 6,9 => CTR * .7..3.4588.....39.3...8..7.632859714981...523547213869153678942..8...13....3...8. B9: 1,2 # 17 pairs * PAIR C9: 6,9 ROW 9 E9: 6,9,2,4 # reduction candidate for 6,9 E9: 6,9 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 E9: 2,4 # 17 pairs * PAIR D7: 1,6 BLK 8 F9: 1,6,2,4,5 # reduction candidate for 1,6 F9: 1,6 => CTR * 27..3.4588...2.39.3...8..7.632859714981.6.523547213869153678942468592137729341685 F9: 2,4,5 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 * PAIR D7: 1,6 COL D D1: 1,6,9 # reduction candidate for 1,6 D1: 1,6 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 D1: 9 # 16 pairs D2: 1,6,4,5,7 # reduction candidate for 1,6 D2: 1,6 => CTR * .7.93.4588.5.4739.39458..7.632859714981764523547213869.531789467.849613541.3.5.87 D2: 4,5,7 # 15 pairs D3: 1,6,4,5,9 # reduction candidate for 1,6 D3: 1,6 # 22 pairs * PAIR I7: 2,6 COL I I2: 2,6,1 # reduction candidate for 2,6 I2: 2,6 # 16 pairs I3: 2,6,1 # reduction candidate for 2,6 I3: 2,6 # 18 pairs * PAIR G9: 2,6 ROW 9 B9: 2,6,1,9 # reduction candidate for 2,6 B9: 2,6 => CTR * .7..3.4588.....39.3...8..7.632859714981...523547213869153678942.68.9213..29341685 B9: 1,9 # 16 pairs E9: 2,6,4,9 # reduction candidate for 2,6 E9: 2,6 => CTR * .7693.4588.....39.39..8..7.632859714981...523547213869.53178946.68.9213..1936.28. E9: 4,9 # 16 pairs F9: 2,6,1,4,5 # reduction candidate for 2,6 F9: 2,6 => CTR * 17..324588.....39.3...8.67.632859714981...523547213869253178946..8.2.13771.3..285 F9: 1,4,5 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-030-base-pr-000.dot * REASONING * PRF # B3: 1,2 => SOL * DIS # F1: 6 => CTR => F1: 1,2 * PRF # B3: 1,2 => SOL * DIS # D1: 1 => CTR => D1: 6,9 * PRF # B3: 2,6 => SOL * PRF # E2: 4,6 => SOL * DIS # E2: 2 => CTR => E2: 4,6 * DIS # E8: 4,6 => CTR => E8: 2,9 * DIS # E9: 4,6 => CTR => E9: 2,9 * PRF # E9: 2,9 => SOL * DIS # B9: 6,9 => CTR => B9: 1,2 * DIS # B9: 6,9 => CTR => B9: 1,2 * PRF # E9: 6,9 => SOL * DIS # F9: 1,6 => CTR => F9: 2,4,5 * PRF # F9: 2,4,5 => SOL * PRF # D1: 1,6 => SOL * DIS # D2: 1,6 => CTR => D2: 4,5,7 * DIS # B9: 2,6 => CTR => B9: 1,9 * DIS # E9: 2,6 => CTR => E9: 4,9 * DIS # F9: 2,6 => CTR => F9: 1,4,5 * CNT 20 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A7,A8,A9,C1,C2,C3,C9,D7,E5,G3,G9,I7,I8,I9) * .7..3.4588.....39.3...8..7.632859714981...523547213869.53.7894...8...13....3...8. * PAIR A1: 1,2 BLK 1 B2: 1,2,6 # reduction candidate for 1,2 B2: 1,2 # 17 pairs B3: 1,2,6,9 # reduction candidate for 1,2 B3: 1,2 => SOLVED * 179632458865741392324985671632859714981467523547213869253178946498526137716394285 * DURATION: 0:00:03.077389 START: 03:41:23.416095 END: 03:41:26.493484 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-030-base-pr-001.dot * REASONING * PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 030 solution: 179632458865741392324985671632859714981467523547213869253178946498526137716394285 info: 1326 FNBTWXY S8.f 22434 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 179632458865741392324985671632859714981467523547213869253178946498526137716394285 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 # B2: 1,2 => UNS * PRF # B3: 1,2 => SOL * INC # B3: 6,9 => UNS * INC # F1: 1,2 => UNS * DIS # F1: 6 => CTR => F1: 1,2 * INC # B3: 6,9 => UNS * PRF # B3: 1,2 => SOL * INC # D1: 6,9 => UNS * DIS # D1: 1 => CTR => D1: 6,9 * INC # D2: 4,5 => UNS * INC # F2: 4,5 => UNS * INC # D3: 4,5 => UNS * INC # F3: 4,5 => UNS * INC # I2: 2,6 => UNS * INC # I3: 2,6 => UNS * PRF # B3: 2,6 => SOL * INC # B3: 1,9 => UNS * INC # F3: 2,6 => UNS * INC # D5: 4,6 => UNS * INC # F5: 4,6 => UNS * PRF # E2: 4,6 => SOL * DIS # E2: 2 => CTR => E2: 4,6 * DIS # E8: 4,6 => CTR => E8: 2,9 * INC # E8: 2,9 => UNS * DIS # E9: 4,6 => CTR => E9: 2,9 * PRF # E9: 2,9 => SOL * INC # B9: 1,2 => UNS * DIS # B9: 6,9 => CTR => B9: 1,2 * INC # B8: 6,9 => UNS * DIS # B9: 6,9 => CTR => B9: 1,2 * INC # B9: 1,2 => UNS * PRF # E9: 6,9 => SOL * INC # E9: 2,4 => UNS * DIS # F9: 1,6 => CTR => F9: 2,4,5 * PRF # F9: 2,4,5 => SOL * PRF # D1: 1,6 => SOL * INC # D1: 9 => UNS * DIS # D2: 1,6 => CTR => D2: 4,5,7 * INC # D2: 4,5,7 => UNS * INC # D3: 1,6 => UNS * INC # I2: 2,6 => UNS * INC # I3: 2,6 => UNS * DIS # B9: 2,6 => CTR => B9: 1,9 * INC # B9: 1,9 => UNS * DIS # E9: 2,6 => CTR => E9: 4,9 * INC # E9: 4,9 => UNS * DIS # F9: 2,6 => CTR => F9: 1,4,5 * INC # F9: 1,4,5 => UNS * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B2: 1,2 => UNS * PRF # B3: 1,2 => SOL * STA B3: 1,2 * CNT 2 HDP CHAINS / 2 HYP OPENED