Analysis of xx-top500-057-base.sdk
Contents
Original Sudoku
level: medium
position: ...6..39..1.2.....7........5...87....6.....1..........4.....7........5.8.2.1..... initial
Autosolve
position: ...67139..1.2...7.7.....1..5.1.872...6.....17.7..16...4.....7.11..7..5.8.271..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 2,8 => CTR => C1: 4,5 * PRF # A6: 2,8 => SOL * DIS # A6: 3,9 => CTR => A6: 2,8 * DIS # F3: 5,8 => CTR => F3: 3,4,9 * DIS # B7: 3,9 => CTR => B7: 5,8 * DIS # C7: 3,9 => CTR => C7: 5,6,8 * DIS # E8: 3,9 => CTR => E8: 2,4,6 * DIS # F8: 3,9 => CTR => F8: 2,4 * DIS # B4: 3,9 => CTR => B4: 4 * CNT 9 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 2,8 => CTR => C1: 4,5 * PRF C1: 4,5 # A6: 2,8 => SOL * STA C1: 4,5 + A6: 2,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...6..39..1.2.....7........5...87....6.....1..........4.....7........5.8.2.1..... | initial |
| ...67139..1.2...7.7.....1..5.1.872...6.....17.7..16...4.....7.11..7..5.8.271..... | autosolve |
| 854671392619235874732894156541987263968523417273416985485369721196742538327158649 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) A1: 2,8 C3: 2,6 H3: 5,8 I3: 2,6 H6: 5,8 B8: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I1,I3: 2.. / I1 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) A6,C6: 2.. / A6 = 2 => 0 pairs (*) / C6 = 2 => 0 pairs (X) E5,F5: 2.. / E5 = 2 => 6 pairs (_) / F5 = 2 => 6 pairs (_) H7,H8: 2.. / H7 = 2 => 6 pairs (_) / H8 = 2 => 7 pairs (_) C3,I3: 2.. / C3 = 2 => 0 pairs (*) / I3 = 2 => 0 pairs (X) A1,A6: 2.. / A1 = 2 => 0 pairs (X) / A6 = 2 => 0 pairs (_) H6,I6: 5.. / H6 = 5 => 0 pairs (X) / I6 = 5 => 0 pairs (_) B7,C7: 5.. / B7 = 5 => 0 pairs (X) / C7 = 5 => 6 pairs (_) E9,F9: 5.. / E9 = 5 => 6 pairs (_) / F9 = 5 => 0 pairs (X) D3,D5: 5.. / D3 = 5 => 0 pairs (X) / D5 = 5 => 6 pairs (_) H3,H6: 5.. / H3 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) H4,I4: 6.. / H4 = 6 => 0 pairs (*) / I4 = 6 => 0 pairs (X) C3,I3: 6.. / C3 = 6 => 0 pairs (X) / I3 = 6 => 0 pairs (_) A2,A9: 6.. / A2 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) G2,G9: 6.. / G2 = 6 => 0 pairs (X) / G9 = 6 => 0 pairs (_) G2,H3: 8.. / G2 = 8 => 0 pairs (*) / H3 = 8 => 0 pairs (X) F2,G2: 8.. / F2 = 8 => 0 pairs (X) / G2 = 8 => 0 pairs (_) A9,F9: 8.. / A9 = 8 => 0 pairs (X) / F9 = 8 => 0 pairs (_) B1,B7: 8.. / B1 = 8 => 0 pairs (X) / B7 = 8 => 0 pairs (_) D3,D7: 8.. / D3 = 8 => 0 pairs (*) / D7 = 8 => 0 pairs (X) H3,H6: 8.. / H3 = 8 => 0 pairs (X) / H6 = 8 => 0 pairs (_) G9,I9: 9.. / G9 = 9 => 0 pairs (X) / I9 = 9 => 8 pairs (_) * DURATION: 0:00:39.705048 START: 04:38:06.676613 END: 04:38:46.381661 2017-05-04 * CP COUNT: (22) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,C3,H3,H6,I3) * ...67139..1.2...7.7.....1..5.1.872...6.....17.7..16...4.....7.11..7..5.8.271..... * PAIR A1: 2,8 BLK 1 C1: 2,8,4,5 # reduction candidate for 2,8 C1: 2,8 => CTR * ...67139..1.2...7.7.6...1.25.1.872...6.....17.7..16...485...7.11..7..5.86271.8... C1: 4,5 # 7 pairs * PAIR A1: 2,8 COL A A6: 2,8,3,9 # reduction candidate for 2,8 A6: 2,8 => SOLVED * 854671392619235874732894156541987263968523417273416985485369721196742538327158649 A6: 3,9 => CTR * 2..67139..1.2...7.7.6...1.25.1.872...6.....17.72.16...4.....7.11..7..5.86271.8... * PAIR H3: 5,8 ROW 3 D3: 5,8,3,4,9 # reduction candidate for 5,8 D3: 5,8 # 9 pairs F3: 5,8,3,4,9 # reduction candidate for 5,8 F3: 5,8 => CTR * 28.67139.61.2...7.7.....1..5.1.872...6.5...17.7..16...4..8..7.11..7..5.88271..... F3: 3,4,9 # 6 pairs * PAIR B8: 3,9 BLK 7 B7: 3,9,5,8 # reduction candidate for 3,9 B7: 3,9 => CTR * 28467139561.2...7.75....18.541.872...6.5...17.7..16.5.4.58..7.11..7..5.88271..... B7: 5,8 # 7 pairs C7: 3,9,5,6,8 # reduction candidate for 3,9 C7: 3,9 => CTR * 28.67139.61.2...7.7.....1..5.1.872...6.....17.7..16...45....7.11..7..5.88271..... C7: 5,6,8 # 6 pairs C8: 3,9,6 # reduction candidate for 3,9 C8: 3,9 # 10 pairs * PAIR B8: 3,9 ROW 8 E8: 3,9,2,4,6 # reduction candidate for 3,9 E8: 3,9 => CTR * 8546713926192.3874732...1.65.1.8726.96..2..1727..169..485.6.7.119673.5.83271.8649 E8: 2,4,6 # 6 pairs F8: 3,9,2,4 # reduction candidate for 3,9 F8: 3,9 => CTR * 85467139261923.87473289415654198726.96.....1727..169..485.6.7.11967.35.83271.8649 F8: 2,4 # 7 pairs * PAIR B8: 3,9 COL B B3: 3,9,4,5 # reduction candidate for 3,9 B3: 3,9 # 12 pairs B4: 3,9,4 # reduction candidate for 3,9 B4: 3,9 => CTR * ...67139..1.2...7.7.6...1.25.1.872...6.....17.7..16...4.....7.11..7..5.86271.8... B4: 4 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-057-base-pr-000.dot * REASONING * DIS # C1: 2,8 => CTR => C1: 4,5 * PRF # A6: 2,8 => SOL * DIS # A6: 3,9 => CTR => A6: 2,8 * DIS # F3: 5,8 => CTR => F3: 3,4,9 * DIS # B7: 3,9 => CTR => B7: 5,8 * DIS # C7: 3,9 => CTR => C7: 5,6,8 * DIS # E8: 3,9 => CTR => E8: 2,4,6 * DIS # F8: 3,9 => CTR => F8: 2,4 * DIS # B4: 3,9 => CTR => B4: 4 * CNT 9 HDP CHAINS / 19 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,B8,C3,H3,H6,I3) * ...67139..1.2...7.7.....1..5.1.872...6.....17.7..16...4.....7.11..7..5.8.271..... * PAIR A1: 2,8 BLK 1 C1: 2,8,4,5 # reduction candidate for 2,8 C1: 2,8 => CTR * ...67139..1.2...7.7.6...1.25.1.872...6.....17.7..16...485...7.11..7..5.86271.8... * PAIR A1: 2,8 COL A A6: 2,8,3,9 # reduction candidate for 2,8 A6: 2,8 => SOLVED * 854671392619235874732894156541987263968523417273416985485369721196742538327158649 * DURATION: 0:00:04.371649 START: 04:39:04.546092 END: 04:39:08.917741 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-057-base-pr-001.dot * REASONING * DIS # C1: 2,8 => CTR => C1: 4,5 * PRF C1: 4,5 # A6: 2,8 => SOL * STA C1: 4,5 + A6: 2,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 057 solution: 854671392619235874732894156541987263968523417273416985485369721196742538327158649 info: 1427 FNBHWXY S8.f 10625 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 854671392619235874732894156541987263968523417273416985485369721196742538327158649 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 # C1: 2,8 => CTR => C1: 4,5 * INC # C1: 4,5 => UNS * PRF # A6: 2,8 => SOL * DIS # A6: 3,9 => CTR => A6: 2,8 * INC # D3: 5,8 => UNS * DIS # F3: 5,8 => CTR => F3: 3,4,9 * INC # F3: 3,4,9 => UNS * DIS # B7: 3,9 => CTR => B7: 5,8 * INC # B7: 5,8 => UNS * DIS # C7: 3,9 => CTR => C7: 5,6,8 * INC # C7: 5,6,8 => UNS * INC # C8: 3,9 => UNS * DIS # E8: 3,9 => CTR => E8: 2,4,6 * INC # E8: 2,4,6 => UNS * DIS # F8: 3,9 => CTR => F8: 2,4 * INC # F8: 2,4 => UNS * INC # B3: 3,9 => UNS * DIS # B4: 3,9 => CTR => B4: 4 * INC # B4: 4 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 2,8 => CTR => C1: 4,5 * PRF C1: 4,5 # A6: 2,8 => SOL * STA C1: 4,5 + A6: 2,8 * CNT 2 HDP CHAINS / 2 HYP OPENED