Analysis of xx-top500-117-base.sdk
Contents
Original Sudoku
level: medium
position: .8..1.3.....6...4.....5.....4.2....7....3.1...........1..7........4...2.5.3...... initial
Autosolve
position: 785914362.3167..454..35.71.34.2.1.57.5.83.194.1.54.2..1.47.5....7.4.35215.31..47. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 2,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # C3: 2 => CTR => C3: 6,9 * DIS # B9: 6,9 => CTR => B9: 2 * PRF # G7: 8,9 => SOL * DIS # G7: 6 => CTR => G7: 8,9 * PRF # I7: 8,9 => SOL * DIS # C5: 7 => CTR => C5: 2,6 * DIS # F6: 7 => CTR => F6: 6,9 * DIS # C4: 6,9 => CTR => C4: 8 * PRF # C4: 8 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 9 => CTR => F6: 6,7 * DIS # C5: 6,7 => CTR => C5: 2 * PRF # I6: 3 => SOL * PRF # C4: 6,8 => SOL * DIS # C4: 9 => CTR => C4: 6,8 * DIS # G7: 9 => CTR => G7: 6,8 * PRF # I6: 3,8 => SOL * DIS # I6: 6 => CTR => I6: 3,8 * DIS # A8: 6,9 => CTR => A8: 8 * DIS # B9: 6,9 => CTR => B9: 2 * DIS # F6: 7 => CTR => F6: 6,9 * PRF # I7: 6,9 => SOL * CNT 24 HDP CHAINS / 40 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 2,9 => CTR => C3: 6 * PRF C3: 6 => SOL * STA C3: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .8..1.3.....6...4.....5.....4.2....7....3.1...........1..7........4...2.5.3...... | initial |
| 785914362.3167..454..35.71.34.2.1.57.5.83.194.1.54.2..1.47.5....7.4.35215.31..47. | autosolve |
| 785914362231678945496352718348291657652837194917546283164725839879463521523189476 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A2: 2,9 B3: 6,9 F2: 2,8 F3: 2,8 G2: 8,9 I3: 8,9 A5: 2,6 E4: 6,9 F5: 6,7 G4: 6,8 H6: 3,8 E7: 2,8 E8: 6,9 E9: 2,8 F9: 6,9 H7: 3,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,C3: 2.. / A2 = 2 => 16 pairs (_) / C3 = 2 => 0 pairs (X) F2,F3: 2.. / F2 = 2 => 0 pairs (X) / F3 = 2 => 16 pairs (_) A5,C5: 2.. / A5 = 2 => 0 pairs (X) / C5 = 2 => 16 pairs (_) B7,B9: 2.. / B7 = 2 => 0 pairs (X) / B9 = 2 => 16 pairs (_) E7,E9: 2.. / E7 = 2 => 16 pairs (_) / E9 = 2 => 0 pairs (X) A2,F2: 2.. / A2 = 2 => 16 pairs (_) / F2 = 2 => 0 pairs (X) C3,F3: 2.. / C3 = 2 => 0 pairs (X) / F3 = 2 => 16 pairs (_) B7,E7: 2.. / B7 = 2 => 0 pairs (X) / E7 = 2 => 16 pairs (_) B9,E9: 2.. / B9 = 2 => 16 pairs (_) / E9 = 2 => 0 pairs (X) A2,A5: 2.. / A2 = 2 => 16 pairs (_) / A5 = 2 => 0 pairs (X) C3,C5: 2.. / C3 = 2 => 0 pairs (X) / C5 = 2 => 16 pairs (_) H6,I6: 3.. / H6 = 3 => 16 pairs (_) / I6 = 3 => 0 pairs (*) H7,I7: 3.. / H7 = 3 => 0 pairs (*) / I7 = 3 => 0 pairs (X) H6,H7: 3.. / H6 = 3 => 16 pairs (_) / H7 = 3 => 0 pairs (*) I6,I7: 3.. / I6 = 3 => 0 pairs (*) / I7 = 3 => 0 pairs (X) B3,C3: 6.. / B3 = 6 => 0 pairs (X) / C3 = 6 => 0 pairs (_) G4,I6: 6.. / G4 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) E8,F9: 6.. / E8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) E4,E8: 6.. / E4 = 6 => 0 pairs (X) / E8 = 6 => 0 pairs (_) G4,G7: 6.. / G4 = 6 => 0 pairs (*) / G7 = 6 => 0 pairs (X) C5,C6: 7.. / C5 = 7 => 0 pairs (X) / C6 = 7 => 19 pairs (_) F5,F6: 7.. / F5 = 7 => 19 pairs (_) / F6 = 7 => 0 pairs (X) C5,F5: 7.. / C5 = 7 => 0 pairs (X) / F5 = 7 => 19 pairs (_) C6,F6: 7.. / C6 = 7 => 19 pairs (_) / F6 = 7 => 0 pairs (X) F2,F3: 8.. / F2 = 8 => 16 pairs (_) / F3 = 8 => 0 pairs (X) G2,I3: 8.. / G2 = 8 => 0 pairs (X) / I3 = 8 => 16 pairs (_) A8,C8: 8.. / A8 = 8 => 20 pairs (_) / C8 = 8 => 0 pairs (X) E7,E9: 8.. / E7 = 8 => 0 pairs (X) / E9 = 8 => 16 pairs (_) F2,G2: 8.. / F2 = 8 => 16 pairs (_) / G2 = 8 => 0 pairs (X) F3,I3: 8.. / F3 = 8 => 0 pairs (X) / I3 = 8 => 16 pairs (_) C4,G4: 8.. / C4 = 8 => 0 pairs (*) / G4 = 8 => 0 pairs (X) E9,I9: 8.. / E9 = 8 => 16 pairs (_) / I9 = 8 => 0 pairs (X) A6,A8: 8.. / A6 = 8 => 0 pairs (X) / A8 = 8 => 20 pairs (_) H6,H7: 8.. / H6 = 8 => 0 pairs (*) / H7 = 8 => 0 pairs (X) G2,I3: 9.. / G2 = 9 => 16 pairs (_) / I3 = 9 => 0 pairs (X) E4,F6: 9.. / E4 = 9 => 0 pairs (*) / F6 = 9 => 0 pairs (X) E8,F9: 9.. / E8 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) A2,G2: 9.. / A2 = 9 => 0 pairs (X) / G2 = 9 => 16 pairs (_) C4,E4: 9.. / C4 = 9 => 0 pairs (X) / E4 = 9 => 0 pairs (_) E4,E8: 9.. / E4 = 9 => 0 pairs (*) / E8 = 9 => 0 pairs (X) F6,F9: 9.. / F6 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) G2,G7: 9.. / G2 = 9 => 16 pairs (_) / G7 = 9 => 0 pairs (X) * DURATION: 0:01:44.326248 START: 06:46:22.361476 END: 06:48:06.687724 2017-05-04 * CP COUNT: (42) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,E4,E7,E8,E9,F2,F3,F5,F9,G2,G4,H6,H7,I3) * 785914362.3167..454..35.71.34.2.1.57.5.83.194.1.54.2..1.47.5....7.4.35215.31..47. * PAIR A2: 2,9 BLK 1 C3: 2,9,6 # reduction candidate for 2,9 C3: 2,9 => CTR * 78591436293167..4546.35.71.34.261857.5.837194.175492361.47.5683.784935215.3186479 C3: 6 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 * PAIR B3: 6,9 BLK 1 C3: 6,9,2 # reduction candidate for 6,9 C3: 2 => CTR * 7859143629316728454623587193482.1.5725.83.194.1.54.2..1.47.59.6.7.4.3521593126478 C3: 6,9 # 16 pairs * PAIR B3: 6,9 COL B B7: 6,9,2 # reduction candidate for 6,9 B7: 6,9 # 16 pairs B9: 6,9,2 # reduction candidate for 6,9 B9: 6,9 => CTR * 785914362.3167.8454..358719348291657.5.83.194.1.54.28312478593687946352156312.478 B9: 2 # 16 pairs * PAIR G2: 8,9 COL G G7: 8,9,6 # reduction candidate for 8,9 G7: 8,9 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 G7: 6 => CTR * 7859143622316789454..35271834.2.1857652837194.1754923619472568387.4.35215.318.479 * PAIR I3: 8,9 COL I I7: 8,9,3,6 # reduction candidate for 8,9 I7: 8,9 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 I7: 3,6 # 17 pairs I9: 8,9,6 # reduction candidate for 8,9 I9: 8,9 # 20 pairs * PAIR A5: 2,6 BLK 4 C5: 2,6,7 # reduction candidate for 2,6 C5: 7 => CTR * 785914362.3167..454.235871934.2.1.57257836194.1.5472..1.47.59...7.4635215931..47. C5: 2,6 # 19 pairs * PAIR E4: 6,9 BLK 5 F6: 6,9,7 # reduction candidate for 6,9 F6: 7 => CTR * 785914362.3167..454..35.71.34.291.572578361946195472..1.47.5....7.4635215.31.947. F6: 6,9 # 19 pairs * PAIR E4: 6,9 ROW 4 C4: 6,9,8 # reduction candidate for 6,9 C4: 6,9 => CTR * 785914362.316789454..35271834.2.1857.52837194.17549236194725683.78493521523186479 C4: 8 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 * PAIR F5: 6,7 BLK 5 F6: 6,7,9 # reduction candidate for 6,7 F6: 6,7 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 F6: 9 => CTR * 78591436293167284546235.71.34.2.1.57.5.837194.175492..1.47.5....7.4935215.31.647. * PAIR F5: 6,7 ROW 5 C5: 6,7,2 # reduction candidate for 6,7 C5: 6,7 => CTR * 7859143629316728454623587193482.1.5725.83.194.1.54.2..1.47.59...7.4.3521593126478 C5: 2 # 16 pairs * PAIR G4: 6,8 BLK 6 I6: 6,8,3 # reduction candidate for 6,8 I6: 3 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 I6: 6,8 # 16 pairs * PAIR G4: 6,8 ROW 4 C4: 6,8,9 # reduction candidate for 6,8 C4: 6,8 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 C4: 9 => CTR * 785914362.3167..454..35.71.349261857.5.837194.175492361.47.5683.784935215.3186479 * PAIR G4: 6,8 COL G G7: 6,8,9 # reduction candidate for 6,8 G7: 9 => CTR * 78591436293167284546235871934829165725.83.19461954.2..1.47.59...7.4635215.31.947. G7: 6,8 # 16 pairs * PAIR H6: 3,8 BLK 6 I6: 3,8,6 # reduction candidate for 3,8 I6: 3,8 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 I6: 6 => CTR * 785914362.3167.9454..35.71834.2.1857.5.83.194.1.549236194725683.7.493521523186479 * PAIR E8: 6,9 ROW 8 A8: 6,9,8 # reduction candidate for 6,9 A8: 6,9 => CTR * 785914362.3167.9454..35.71834.2.1857.5.83.19481.549236194725683678493521523186479 A8: 8 # 20 pairs C8: 6,9,8 # reduction candidate for 6,9 C8: 6,9 # 20 pairs * PAIR F9: 6,9 ROW 9 B9: 6,9,2 # reduction candidate for 6,9 B9: 6,9 => CTR * 785914362.3167.8454..358719348291657.5.83.194.1.54.28312478593687946352156312.478 B9: 2 # 16 pairs I9: 6,9,8 # reduction candidate for 6,9 I9: 6,9 # 16 pairs * PAIR F9: 6,9 COL F F6: 6,9,7 # reduction candidate for 6,9 F6: 7 => CTR * 785914362.3167..454..35.71.34.291.572578361946195472..1.47.5....7.4635215.31.947. F6: 6,9 # 19 pairs * PAIR H7: 3,8 BLK 9 I7: 3,8,6,9 # reduction candidate for 3,8 I7: 6,9 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 I7: 3,8 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-117-base-pr-000.dot * REASONING * DIS # C3: 2,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * DIS # C3: 2 => CTR => C3: 6,9 * DIS # B9: 6,9 => CTR => B9: 2 * PRF # G7: 8,9 => SOL * DIS # G7: 6 => CTR => G7: 8,9 * PRF # I7: 8,9 => SOL * DIS # C5: 7 => CTR => C5: 2,6 * DIS # F6: 7 => CTR => F6: 6,9 * DIS # C4: 6,9 => CTR => C4: 8 * PRF # C4: 8 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 9 => CTR => F6: 6,7 * DIS # C5: 6,7 => CTR => C5: 2 * PRF # I6: 3 => SOL * PRF # C4: 6,8 => SOL * DIS # C4: 9 => CTR => C4: 6,8 * DIS # G7: 9 => CTR => G7: 6,8 * PRF # I6: 3,8 => SOL * DIS # I6: 6 => CTR => I6: 3,8 * DIS # A8: 6,9 => CTR => A8: 8 * DIS # B9: 6,9 => CTR => B9: 2 * DIS # F6: 7 => CTR => F6: 6,9 * PRF # I7: 6,9 => SOL * CNT 24 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B3,E4,E7,E8,E9,F2,F3,F5,F9,G2,G4,H6,H7,I3) * 785914362.3167..454..35.71.34.2.1.57.5.83.194.1.54.2..1.47.5....7.4.35215.31..47. * PAIR A2: 2,9 BLK 1 C3: 2,9,6 # reduction candidate for 2,9 C3: 2,9 => CTR * 78591436293167..4546.35.71.34.261857.5.837194.175492361.47.5683.784935215.3186479 C3: 6 => SOLVED * 785914362231678945496352718348291657652837194917546283164725839879463521523189476 * DURATION: 0:00:03.931309 START: 06:49:05.268696 END: 06:49:09.200005 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-117-base-pr-001.dot * REASONING * DIS # C3: 2,9 => CTR => C3: 6 * PRF C3: 6 => SOL * STA C3: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 117 solution: 785914362231678945496352718348291657652837194917546283164725839879463521523189476 info: 1765 FNBTHWXY S8.f 23521 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 785914362231678945496352718348291657652837194917546283164725839879463521523189476 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 # C3: 2,9 => CTR => C3: 6 * PRF # C3: 6 => SOL * INC # C3: 6,9 => UNS * DIS # C3: 2 => CTR => C3: 6,9 * INC # B7: 6,9 => UNS * DIS # B9: 6,9 => CTR => B9: 2 * INC # B9: 2 => UNS * PRF # G7: 8,9 => SOL * DIS # G7: 6 => CTR => G7: 8,9 * PRF # I7: 8,9 => SOL * INC # I7: 3,6 => UNS * INC # I9: 8,9 => UNS * INC # C5: 2,6 => UNS * DIS # C5: 7 => CTR => C5: 2,6 * INC # F6: 6,9 => UNS * DIS # F6: 7 => CTR => F6: 6,9 * DIS # C4: 6,9 => CTR => C4: 8 * PRF # C4: 8 => SOL * PRF # F6: 6,7 => SOL * DIS # F6: 9 => CTR => F6: 6,7 * DIS # C5: 6,7 => CTR => C5: 2 * INC # C5: 2 => UNS * INC # I6: 6,8 => UNS * PRF # I6: 3 => SOL * PRF # C4: 6,8 => SOL * DIS # C4: 9 => CTR => C4: 6,8 * INC # G7: 6,8 => UNS * DIS # G7: 9 => CTR => G7: 6,8 * PRF # I6: 3,8 => SOL * DIS # I6: 6 => CTR => I6: 3,8 * DIS # A8: 6,9 => CTR => A8: 8 * INC # A8: 8 => UNS * INC # C8: 6,9 => UNS * DIS # B9: 6,9 => CTR => B9: 2 * INC # B9: 2 => UNS * INC # I9: 6,9 => UNS * INC # F6: 6,9 => UNS * DIS # F6: 7 => CTR => F6: 6,9 * INC # I7: 3,8 => UNS * PRF # I7: 6,9 => SOL * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C3: 2,9 => CTR => C3: 6 * PRF C3: 6 => SOL * STA C3: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED