Analysis of xx-top500-051-base.sdk
Contents
Original Sudoku
level: medium
position: 6...7.3..1...9.....2.......7.3.........5...2........8.4.....7.....2..4.....8.5... initial
Autosolve
position: 6...7.3..1...9.....2..5....783.2....9..583.27...7.49834.....7.....2.74.....845... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A8: 3,8 => CTR => A8: 5 * DIS # D3: 1,4 => CTR => D3: 3,6 * DIS # I1: 1,4 => CTR => I1: 2,5,9 * DIS # G4: 1,6 => CTR => G4: 5 * DIS # G9: 1,6 => CTR => G9: 2 * CNT 5 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A8: 3,8 => CTR => A8: 5 * DIS A8: 5 # H1: 9 => CTR => H1: 1,4 * PRF A8: 5 + H1: 1,4 # C6: 1,6 => SOL * STA A8: 5 + H1: 1,4 + C6: 1,6 * CNT 3 HDP CHAINS / 7 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...7.3..1...9.....2.......7.3.........5...2........8.4.....7.....2..4.....8.5... | initial |
| 6...7.3..1...9.....2..5....783.2....9..583.27...7.49834.....7.....2.74.....845... | autosolve |
| 695478312134692875827351694783129546946583127251764983412936758568217439379845261 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A3: 3,8 D1: 1,4 A6: 2,5 E6: 1,6 G5: 1,6 C7: 2,8 A9: 2,3 I7: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F2: 2.. / F1 = 2 => 0 pairs (X) / F2 = 2 => 10 pairs (_) A6,C6: 2.. / A6 = 2 => 10 pairs (_) / C6 = 2 => 0 pairs (X) F1,I1: 2.. / F1 = 2 => 0 pairs (X) / I1 = 2 => 10 pairs (_) C7,I7: 2.. / C7 = 2 => 10 pairs (_) / I7 = 2 => 0 pairs (X) A6,A9: 2.. / A6 = 2 => 10 pairs (_) / A9 = 2 => 0 pairs (X) G2,G9: 2.. / G2 = 2 => 0 pairs (X) / G9 = 2 => 10 pairs (_) B2,A3: 3.. / B2 = 3 => 10 pairs (_) / A3 = 3 => 0 pairs (X) D2,D3: 3.. / D2 = 3 => 0 pairs (X) / D3 = 3 => 10 pairs (_) E7,E8: 3.. / E7 = 3 => 9 pairs (_) / E8 = 3 => 12 pairs (_) B2,D2: 3.. / B2 = 3 => 10 pairs (_) / D2 = 3 => 0 pairs (X) A3,D3: 3.. / A3 = 3 => 0 pairs (X) / D3 = 3 => 10 pairs (_) B5,C5: 4.. / B5 = 4 => 10 pairs (_) / C5 = 4 => 9 pairs (_) H4,I4: 4.. / H4 = 4 => 8 pairs (_) / I4 = 4 => 8 pairs (_) B7,H7: 5.. / B7 = 5 => 0 pairs (X) / H7 = 5 => 8 pairs (_) A6,A8: 5.. / A6 = 5 => 0 pairs (X) / A8 = 5 => 10 pairs (_) G2,G4: 5.. / G2 = 5 => 0 pairs (X) / G4 = 5 => 8 pairs (_) H2,H3: 7.. / H2 = 7 => 8 pairs (_) / H3 = 7 => 8 pairs (_) B9,C9: 7.. / B9 = 7 => 8 pairs (_) / C9 = 7 => 0 pairs (X) C3,H3: 7.. / C3 = 7 => 8 pairs (_) / H3 = 7 => 8 pairs (_) B2,B9: 7.. / B2 = 7 => 0 pairs (X) / B9 = 7 => 8 pairs (_) G2,G3: 8.. / G2 = 8 => 10 pairs (_) / G3 = 8 => 0 pairs (X) I7,I8: 8.. / I7 = 8 => 10 pairs (_) / I8 = 8 => 0 pairs (X) C1,F1: 8.. / C1 = 8 => 0 pairs (X) / F1 = 8 => 10 pairs (_) C7,I7: 8.. / C7 = 8 => 0 pairs (X) / I7 = 8 => 10 pairs (_) A3,A8: 8.. / A3 = 8 => 10 pairs (_) / A8 = 8 => 0 pairs (X) D4,F4: 9.. / D4 = 9 => 10 pairs (_) / F4 = 9 => 10 pairs (_) D7,F7: 9.. / D7 = 9 => 10 pairs (_) / F7 = 9 => 10 pairs (_) D4,D7: 9.. / D4 = 9 => 10 pairs (_) / D7 = 9 => 10 pairs (_) F4,F7: 9.. / F4 = 9 => 10 pairs (_) / F7 = 9 => 10 pairs (_) * DURATION: 0:00:44.412151 START: 04:24:28.800225 END: 04:25:13.212376 2017-05-04 * CP COUNT: (29) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A9,C7,D1,E6,G5,I7) * 6...7.3..1...9.....2..5....783.2....9..583.27...7.49834.....7.....2.74.....845... * PAIR A3: 3,8 COL A A8: 3,8,5 # reduction candidate for 3,8 A8: 3,8 => CTR * 6...7.3..1...9.....2..5....783.2....9..583.275.27.49834.8...7.23..2.74.82..845.3. A8: 5 # 10 pairs * PAIR D1: 1,4 BLK 2 D3: 1,4,3,6 # reduction candidate for 1,4 D3: 1,4 => CTR * 6...7.3..1..39....32..5....783.2....9..583.27...7.49834.....7..8..2.74..2..845... D3: 3,6 # 10 pairs * PAIR D1: 1,4 ROW 1 H1: 1,4,5,9 # reduction candidate for 1,4 H1: 1,4 # 11 pairs I1: 1,4,2,5,9 # reduction candidate for 1,4 I1: 1,4 => CTR * 6.8.723..1...9....32..5....783.2....9..583.27...7.49834.2...7.....2.74.....845... I1: 2,5,9 # 8 pairs * PAIR A6: 2,5 BLK 4 C6: 2,5,1,6 # reduction candidate for 2,5 C6: 1,6 # 12 pairs C6: 2,5 # 10 pairs * PAIR E6: 1,6 BLK 5 D4: 1,6,9 # reduction candidate for 1,6 D4: 1,6 # 10 pairs F4: 1,6,9 # reduction candidate for 1,6 F4: 1,6 # 10 pairs * PAIR E6: 1,6 ROW 6 B6: 1,6,5 # reduction candidate for 1,6 B6: 1,6 # 10 pairs C6: 1,6,2,5 # reduction candidate for 1,6 C6: 1,6 # 12 pairs * PAIR E6: 1,6 COL E E7: 1,6,3 # reduction candidate for 1,6 E7: 1,6 # 12 pairs E8: 1,6,3 # reduction candidate for 1,6 E8: 1,6 # 9 pairs * PAIR G5: 1,6 BLK 6 G4: 1,6,5 # reduction candidate for 1,6 G4: 1,6 => CTR * 6...7.3..1...9.5...2..5.8..783.2....9..583.27...7.49834.....7..8..2.74.....8452.. G4: 5 # 8 pairs H4: 1,6,4,5 # reduction candidate for 1,6 H4: 1,6 # 9 pairs I4: 1,6,4,5 # reduction candidate for 1,6 I4: 1,6 # 9 pairs * PAIR G5: 1,6 ROW 5 B5: 1,6,4 # reduction candidate for 1,6 B5: 1,6 # 9 pairs C5: 1,6,4 # reduction candidate for 1,6 C5: 1,6 # 10 pairs * PAIR G5: 1,6 COL G G3: 1,6,8 # reduction candidate for 1,6 G3: 1,6 # 10 pairs G9: 1,6,2 # reduction candidate for 1,6 G9: 1,6 => CTR * 6...723..1...982..32..5.8..783.2.5..9..583.275.27.49834.....7..8..2.74.....845... G9: 2 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-051-base-pr-000.dot * REASONING * DIS # A8: 3,8 => CTR => A8: 5 * DIS # D3: 1,4 => CTR => D3: 3,6 * DIS # I1: 1,4 => CTR => I1: 2,5,9 * DIS # G4: 1,6 => CTR => G4: 5 * DIS # G9: 1,6 => CTR => G9: 2 * CNT 5 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A6,A9,C7,D1,E6,G5,I7) * 6...7.3..1...9.....2..5....783.2....9..583.27...7.49834.....7.....2.74.....845... * PAIR A3: 3,8 COL A A8: 3,8,5 # reduction candidate for 3,8 A8: 3,8 => CTR * 6...7.3..1...9.....2..5....783.2....9..583.275.27.49834.8...7.23..2.74.82..845.3. * PAIR RESTART * PAIR D1: 1,4 ROW 1 H1: 1,4,9 # reduction candidate for 1,4 H1: 9 => CTR * 6..17839213.492865829356174783.2.5419..5836272..7149834.2.317585.82.743.37.8452.. * PAIR RESTART * PAIR E6: 1,6 BLK 5 D4: 1,6,9 # reduction candidate for 1,6 D4: 1,6 # 17 pairs F4: 1,6,9 # reduction candidate for 1,6 F4: 1,6 # 17 pairs * PAIR E6: 1,6 ROW 6 B6: 1,6,5 # reduction candidate for 1,6 B6: 1,6 # 16 pairs C6: 1,6,5 # reduction candidate for 1,6 C6: 1,6 => SOLVED * 695478312134692875827351694783129546946583127251764983412936758568217439379845261 * DURATION: 0:00:10.798666 START: 04:25:33.324291 END: 04:25:44.122957 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-051-base-pr-001.dot * REASONING * DIS # A8: 3,8 => CTR => A8: 5 * DIS A8: 5 # H1: 9 => CTR => H1: 1,4 * PRF A8: 5 + H1: 1,4 # C6: 1,6 => SOL * STA A8: 5 + H1: 1,4 + C6: 1,6 * CNT 3 HDP CHAINS / 7 HYP OPENED
Header Info
Top 500 Minimum 17 051 solution: 695478312134692875827351694783129546946583127251764983412936758568217439379845261 info: 1387 FNBTHXY S8.f 34718 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 695478312134692875827351694783129546946583127251764983412936758568217439379845261 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 # A8: 3,8 => CTR => A8: 5 * INC # A8: 5 => UNS * DIS # D3: 1,4 => CTR => D3: 3,6 * INC # D3: 3,6 => UNS * INC # H1: 1,4 => UNS * DIS # I1: 1,4 => CTR => I1: 2,5,9 * INC # I1: 2,5,9 => UNS * INC # C6: 2,5 => UNS * INC # C6: 1,6 => UNS * INC # D4: 1,6 => UNS * INC # F4: 1,6 => UNS * INC # B6: 1,6 => UNS * INC # C6: 1,6 => UNS * INC # E7: 1,6 => UNS * INC # E8: 1,6 => UNS * DIS # G4: 1,6 => CTR => G4: 5 * INC # G4: 5 => UNS * INC # H4: 1,6 => UNS * INC # I4: 1,6 => UNS * INC # B5: 1,6 => UNS * INC # C5: 1,6 => UNS * INC # G3: 1,6 => UNS * DIS # G9: 1,6 => CTR => G9: 2 * INC # G9: 2 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A8: 3,8 => CTR => A8: 5 * INC A8: 5 # H1: 1,4 => UNS * DIS A8: 5 # H1: 9 => CTR => H1: 1,4 * INC A8: 5 + H1: 1,4 # D4: 1,6 => UNS * INC A8: 5 + H1: 1,4 # F4: 1,6 => UNS * INC A8: 5 + H1: 1,4 # B6: 1,6 => UNS * PRF A8: 5 + H1: 1,4 # C6: 1,6 => SOL * STA A8: 5 + H1: 1,4 + C6: 1,6 * CNT 7 HDP CHAINS / 7 HYP OPENED