Analysis of xx-top500-108-base.sdk
Contents
Original Sudoku
level: medium
position: ...4..52.1.8................5.34....3.......8...2...1..4....3..6...7.........1... initial
Autosolve
position: .3.41852.1.8.5..34.....318.85134.2..3.21..458...285.13.4.8..3.161357489228..31.45 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F5: 6,9 => SOL * PRF # B5: 7 => SOL * DIS # I4: 6,7 => CTR => I4: 9 * DIS # F4: 9 => CTR => F4: 6,7 * DIS # G2: 6,7 => CTR => G2: 9 * CNT 5 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F5: 6,9 => SOL * STA F5: 6,9 * CNT 1 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4..52.1.8................5.34....3.......8...2...1..4....3..6...7.........1... | initial |
| .3.41852.1.8.5..34.....318.85134.2..3.21..458...285.13.4.8..3.161357489228..31.45 | autosolve |
| 739418526168752934524693187851347269372169458496285713945826371613574892287931645 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 7,9 A3: 4,5 C3: 4,5 E5: 6,9 H4: 6,7 C9: 7,9 D9: 6,9 H7: 6,7 G9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,B3: 2.. / B2 = 2 => 11 pairs (_) / B3 = 2 => 11 pairs (_) F2,E3: 2.. / F2 = 2 => 11 pairs (_) / E3 = 2 => 11 pairs (_) E7,F7: 2.. / E7 = 2 => 11 pairs (_) / F7 = 2 => 11 pairs (_) B2,F2: 2.. / B2 = 2 => 11 pairs (_) / F2 = 2 => 11 pairs (_) B3,E3: 2.. / B3 = 2 => 11 pairs (_) / E3 = 2 => 11 pairs (_) E3,E7: 2.. / E3 = 2 => 11 pairs (_) / E7 = 2 => 11 pairs (_) F2,F7: 2.. / F2 = 2 => 11 pairs (_) / F7 = 2 => 11 pairs (_) A3,C3: 4.. / A3 = 4 => 10 pairs (_) / C3 = 4 => 8 pairs (_) A6,C6: 4.. / A6 = 4 => 8 pairs (_) / C6 = 4 => 10 pairs (_) A3,A6: 4.. / A3 = 4 => 10 pairs (_) / A6 = 4 => 8 pairs (_) C3,C6: 4.. / C3 = 4 => 8 pairs (_) / C6 = 4 => 10 pairs (_) A3,C3: 5.. / A3 = 5 => 8 pairs (_) / C3 = 5 => 10 pairs (_) A7,C7: 5.. / A7 = 5 => 10 pairs (_) / C7 = 5 => 8 pairs (_) A3,A7: 5.. / A3 = 5 => 8 pairs (_) / A7 = 5 => 10 pairs (_) C3,C7: 5.. / C3 = 5 => 10 pairs (_) / C7 = 5 => 8 pairs (_) H7,G9: 6.. / H7 = 6 => 18 pairs (_) / G9 = 6 => 18 pairs (_) C1,I1: 6.. / C1 = 6 => 10 pairs (_) / I1 = 6 => 16 pairs (_) D9,G9: 6.. / D9 = 6 => 18 pairs (_) / G9 = 6 => 18 pairs (_) C1,C6: 6.. / C1 = 6 => 10 pairs (_) / C6 = 6 => 16 pairs (_) H4,H7: 6.. / H4 = 6 => 18 pairs (_) / H7 = 6 => 18 pairs (_) D2,D3: 7.. / D2 = 7 => 12 pairs (_) / D3 = 7 => 11 pairs (_) F4,F5: 7.. / F4 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) H7,G9: 7.. / H7 = 7 => 18 pairs (_) / G9 = 7 => 18 pairs (_) B5,F5: 7.. / B5 = 7 => 0 pairs (*) / F5 = 7 => 0 pairs (X) C9,G9: 7.. / C9 = 7 => 18 pairs (_) / G9 = 7 => 18 pairs (_) H4,H7: 7.. / H4 = 7 => 18 pairs (_) / H7 = 7 => 18 pairs (_) I4,G6: 9.. / I4 = 9 => 17 pairs (_) / G6 = 9 => 0 pairs (X) F4,I4: 9.. / F4 = 9 => 0 pairs (X) / I4 = 9 => 17 pairs (_) C9,D9: 9.. / C9 = 9 => 18 pairs (_) / D9 = 9 => 18 pairs (_) G2,G6: 9.. / G2 = 9 => 17 pairs (_) / G6 = 9 => 0 pairs (X) * DURATION: 0:00:53.796770 START: 06:27:33.331282 END: 06:28:27.128052 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,C3,C9,D9,E5,G9,H4,H7) * .3.41852.1.8.5..34.....318.85134.2..3.21..458...285.13.4.8..3.161357489228..31.45 * PAIR A1: 7,9 BLK 1 C1: 7,9,6 # reduction candidate for 7,9 C1: 7,9 # 16 pairs B2: 7,9,2,6 # reduction candidate for 7,9 B2: 7,9 # 13 pairs B3: 7,9,2,6 # reduction candidate for 7,9 B3: 7,9 # 13 pairs * PAIR A1: 7,9 ROW 1 I1: 7,9,6 # reduction candidate for 7,9 I1: 6 # 16 pairs I1: 7,9 # 10 pairs * PAIR A1: 7,9 COL A A6: 7,9,4 # reduction candidate for 7,9 A6: 7,9 # 10 pairs A7: 7,9,5 # reduction candidate for 7,9 A7: 7,9 # 8 pairs * PAIR E5: 6,9 BLK 5 F4: 6,9,7 # reduction candidate for 6,9 F4: 6,9 # 12 pairs F5: 6,9,7 # reduction candidate for 6,9 F5: 6,9 => SOLVED * 739418526168752934524693187851347269372169458496285713945826371613574892287931645 F5: 7 # 12 pairs * PAIR E5: 6,9 ROW 5 B5: 6,9,7 # reduction candidate for 6,9 B5: 7 => SOLVED * 739418526168752934524693187851347269372169458496285713945826371613574892287931645 B5: 6,9 # 12 pairs * PAIR E5: 6,9 COL E E3: 6,9,2 # reduction candidate for 6,9 E3: 6,9 # 11 pairs E7: 6,9,2 # reduction candidate for 6,9 E7: 6,9 # 11 pairs * PAIR H4: 6,7 BLK 6 I4: 6,7,9 # reduction candidate for 6,7 I4: 6,7 => CTR * .3.41852.1.895..34...7231898513492..392167458...285913.4.892361613574892289631745 I4: 9 # 17 pairs G6: 6,7,9 # reduction candidate for 6,7 G6: 6,7 # 17 pairs * PAIR H4: 6,7 ROW 4 F4: 6,7,9 # reduction candidate for 6,7 F4: 9 => CTR * .3.41852.1.895..34...7231898513492..392167458...285913.4.892361613574892289631745 F4: 6,7 # 17 pairs * PAIR C9: 7,9 BLK 7 A7: 7,9,5 # reduction candidate for 7,9 A7: 7,9 # 8 pairs C7: 7,9,5 # reduction candidate for 7,9 C7: 7,9 # 10 pairs * PAIR C9: 7,9 COL C C1: 7,9,6 # reduction candidate for 7,9 C1: 7,9 # 16 pairs C6: 7,9,4,6 # reduction candidate for 7,9 C6: 7,9 # 10 pairs * PAIR D9: 6,9 BLK 8 E7: 6,9,2 # reduction candidate for 6,9 E7: 6,9 # 11 pairs F7: 6,9,2 # reduction candidate for 6,9 F7: 6,9 # 11 pairs * PAIR D9: 6,9 COL D D2: 6,9,7 # reduction candidate for 6,9 D2: 6,9 # 11 pairs D3: 6,9,7 # reduction candidate for 6,9 D3: 6,9 # 12 pairs * PAIR G9: 6,7 COL G G2: 6,7,9 # reduction candidate for 6,7 G2: 6,7 => CTR * .3.41852.1.895..34...7231898513492..392167458...285913.4.892361613574892289631745 G2: 9 # 17 pairs G6: 6,7,9 # reduction candidate for 6,7 G6: 6,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-108-base-pr-000.dot * REASONING * PRF # F5: 6,9 => SOL * PRF # B5: 7 => SOL * DIS # I4: 6,7 => CTR => I4: 9 * DIS # F4: 9 => CTR => F4: 6,7 * DIS # G2: 6,7 => CTR => G2: 9 * CNT 5 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,C3,C9,D9,E5,G9,H4,H7) * .3.41852.1.8.5..34.....318.85134.2..3.21..458...285.13.4.8..3.161357489228..31.45 * PAIR A1: 7,9 BLK 1 C1: 7,9,6 # reduction candidate for 7,9 C1: 7,9 # 16 pairs B2: 7,9,2,6 # reduction candidate for 7,9 B2: 7,9 # 13 pairs B3: 7,9,2,6 # reduction candidate for 7,9 B3: 7,9 # 13 pairs * PAIR A1: 7,9 ROW 1 I1: 7,9,6 # reduction candidate for 7,9 I1: 6 # 16 pairs I1: 7,9 # 10 pairs * PAIR A1: 7,9 COL A A6: 7,9,4 # reduction candidate for 7,9 A6: 7,9 # 10 pairs A7: 7,9,5 # reduction candidate for 7,9 A7: 7,9 # 8 pairs * PAIR E5: 6,9 BLK 5 F4: 6,9,7 # reduction candidate for 6,9 F4: 6,9 # 12 pairs F5: 6,9,7 # reduction candidate for 6,9 F5: 6,9 => SOLVED * 739418526168752934524693187851347269372169458496285713945826371613574892287931645 * DURATION: 0:00:10.077442 START: 06:28:57.958293 END: 06:29:08.035735 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-108-base-pr-001.dot * REASONING * PRF # F5: 6,9 => SOL * STA F5: 6,9 * CNT 1 HDP CHAINS / 9 HYP OPENED
Header Info
Top 500 Minimum 17 108 solution: 739418526168752934524693187851347269372169458496285713945826371613574892287931645 info: 1629 FNBHWXY S8.f 9130 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 739418526168752934524693187851347269372169458496285713945826371613574892287931645 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 # C1: 7,9 => UNS * INC # B2: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # I1: 7,9 => UNS * INC # I1: 6 => UNS * INC # A6: 7,9 => UNS * INC # A7: 7,9 => UNS * INC # F4: 6,9 => UNS * PRF # F5: 6,9 => SOL * INC # F5: 7 => UNS * INC # B5: 6,9 => UNS * PRF # B5: 7 => SOL * INC # E3: 6,9 => UNS * INC # E7: 6,9 => UNS * DIS # I4: 6,7 => CTR => I4: 9 * INC # I4: 9 => UNS * INC # G6: 6,7 => UNS * INC # F4: 6,7 => UNS * DIS # F4: 9 => CTR => F4: 6,7 * INC # A7: 7,9 => UNS * INC # C7: 7,9 => UNS * INC # C1: 7,9 => UNS * INC # C6: 7,9 => UNS * INC # E7: 6,9 => UNS * INC # F7: 6,9 => UNS * INC # D2: 6,9 => UNS * INC # D3: 6,9 => UNS * DIS # G2: 6,7 => CTR => G2: 9 * INC # G2: 9 => UNS * INC # G6: 6,7 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 7,9 => UNS * INC # B2: 7,9 => UNS * INC # B3: 7,9 => UNS * INC # I1: 7,9 => UNS * INC # I1: 6 => UNS * INC # A6: 7,9 => UNS * INC # A7: 7,9 => UNS * INC # F4: 6,9 => UNS * PRF # F5: 6,9 => SOL * STA F5: 6,9 * CNT 9 HDP CHAINS / 9 HYP OPENED