Analysis of xx-top500-377-base.sdk
Contents
Original Sudoku
level: medium
position: .84.6.......7...3..........73.1...........6.1......8....6.4.2..1..3...5.......... initial
Autosolve
position: .84.631.761.7...3..73....6.73.186.4.8.5.3.671461.7.8.33568472191483..756..76..384 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 2,9 => CTR => F2: 4,5,8 * DIS # G2: 5,9 => CTR => G2: 4 * DIS # E3: 2,9 => CTR => E3: 1,5 * DIS # F2: 2,9 => CTR => F2: 4,5,8 * PRF # F3: 2,9 => SOL * DIS # E3: 2,9 => CTR => E3: 1,5 * CNT 6 HDP CHAINS / 31 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 2,9 => CTR => F2: 4,5,8 * DIS F2: 4,5,8 # E2: 5 => CTR => E2: 2,9 * DIS F2: 4,5,8 + E2: 2,9 # G3: 4 => CTR => G3: 5,9 * PRF F2: 4,5,8 + E2: 2,9 + G3: 5,9 # I3: 8 => SOL * STA F2: 4,5,8 + E2: 2,9 + G3: 5,9 + I3: 8 * CNT 4 HDP CHAINS / 16 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .84.6.......7...3..........73.1...........6.1......8....6.4.2..1..3...5.......... | initial |
| .84.631.761.7...3..73....6.73.186.4.8.5.3.671461.7.8.33568472191483..756..76..384 | autosolve |
| 984563127612798435573412968739186542825934671461275893356847219148329756297651384 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C2: 2,9 H1: 2,9 C4: 2,9 B5: 2,9 G4: 5,9 I4: 2,5 H6: 2,9 A9: 2,9 B9: 2,9 E8: 2,9 F8: 2,9 E9: 1,5 F9: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 1.. / E3 = 1 => 14 pairs (_) / F3 = 1 => 17 pairs (_) E9,F9: 1.. / E9 = 1 => 17 pairs (_) / F9 = 1 => 14 pairs (_) E3,E9: 1.. / E3 = 1 => 14 pairs (_) / E9 = 1 => 17 pairs (_) F3,F9: 1.. / F3 = 1 => 17 pairs (_) / F9 = 1 => 14 pairs (_) C4,B5: 2.. / C4 = 2 => 19 pairs (_) / B5 = 2 => 19 pairs (_) I4,H6: 2.. / I4 = 2 => 19 pairs (_) / H6 = 2 => 19 pairs (_) A9,B9: 2.. / A9 = 2 => 19 pairs (_) / B9 = 2 => 19 pairs (_) E8,F8: 2.. / E8 = 2 => 15 pairs (_) / F8 = 2 => 15 pairs (_) C4,I4: 2.. / C4 = 2 => 19 pairs (_) / I4 = 2 => 19 pairs (_) B5,B9: 2.. / B5 = 2 => 19 pairs (_) / B9 = 2 => 19 pairs (_) C2,C4: 2.. / C2 = 2 => 19 pairs (_) / C4 = 2 => 19 pairs (_) H1,H6: 2.. / H1 = 2 => 19 pairs (_) / H6 = 2 => 19 pairs (_) G2,G3: 4.. / G2 = 4 => 14 pairs (_) / G3 = 4 => 0 pairs (X) D5,F5: 4.. / D5 = 4 => 20 pairs (_) / F5 = 4 => 15 pairs (_) F2,G2: 4.. / F2 = 4 => 0 pairs (X) / G2 = 4 => 14 pairs (_) D3,D5: 4.. / D3 = 4 => 15 pairs (_) / D5 = 4 => 20 pairs (_) A1,A3: 5.. / A1 = 5 => 15 pairs (_) / A3 = 5 => 19 pairs (_) D6,F6: 5.. / D6 = 5 => 19 pairs (_) / F6 = 5 => 18 pairs (_) G4,I4: 5.. / G4 = 5 => 19 pairs (_) / I4 = 5 => 19 pairs (_) E9,F9: 5.. / E9 = 5 => 14 pairs (_) / F9 = 5 => 17 pairs (_) A1,D1: 5.. / A1 = 5 => 15 pairs (_) / D1 = 5 => 19 pairs (_) F2,F3: 8.. / F2 = 8 => 15 pairs (_) / F3 = 8 => 15 pairs (_) I2,I3: 8.. / I2 = 8 => 15 pairs (_) / I3 = 8 => 15 pairs (_) F2,I2: 8.. / F2 = 8 => 15 pairs (_) / I2 = 8 => 15 pairs (_) F3,I3: 8.. / F3 = 8 => 15 pairs (_) / I3 = 8 => 15 pairs (_) C4,B5: 9.. / C4 = 9 => 19 pairs (_) / B5 = 9 => 19 pairs (_) G4,H6: 9.. / G4 = 9 => 19 pairs (_) / H6 = 9 => 19 pairs (_) A9,B9: 9.. / A9 = 9 => 19 pairs (_) / B9 = 9 => 19 pairs (_) E8,F8: 9.. / E8 = 9 => 15 pairs (_) / F8 = 9 => 15 pairs (_) C4,G4: 9.. / C4 = 9 => 19 pairs (_) / G4 = 9 => 19 pairs (_) B5,B9: 9.. / B5 = 9 => 19 pairs (_) / B9 = 9 => 19 pairs (_) C2,C4: 9.. / C2 = 9 => 19 pairs (_) / C4 = 9 => 19 pairs (_) H1,H6: 9.. / H1 = 9 => 19 pairs (_) / H6 = 9 => 19 pairs (_) * DURATION: 0:01:09.385744 START: 15:46:07.610513 END: 15:47:16.996257 2017-05-04 * CP COUNT: (33) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B5,B9,C2,C4,E8,E9,F8,F9,G4,H1,H6,I4) * .84.631.761.7...3..73....6.73.186.4.8.5.3.671461.7.8.33568472191483..756..76..384 * PAIR C2: 2,9 BLK 1 A1: 2,9,5 # reduction candidate for 2,9 A1: 2,9 # 19 pairs A3: 2,9,5 # reduction candidate for 2,9 A3: 2,9 # 15 pairs * PAIR C2: 2,9 ROW 2 E2: 2,9,5 # reduction candidate for 2,9 E2: 2,9 # 17 pairs F2: 2,9,4,5,8 # reduction candidate for 2,9 F2: 2,9 => CTR * .84.631.761.75.438.73..8.6.73.186.4.8.5.34671461.7.8.33568472191483..756..76.1384 F2: 4,5,8 # 13 pairs * PAIR H1: 2,9 ROW 1 A1: 2,9,5 # reduction candidate for 2,9 A1: 2,9 # 19 pairs D1: 2,9,5 # reduction candidate for 2,9 D1: 2,9 # 15 pairs * PAIR B5: 2,9 ROW 5 D5: 2,9,4 # reduction candidate for 2,9 D5: 2,9 # 15 pairs F5: 2,9,4 # reduction candidate for 2,9 F5: 2,9 # 20 pairs * PAIR G4: 5,9 COL G G2: 5,9,4 # reduction candidate for 5,9 G2: 5,9 => CTR * .84.631.761.7.4538.73.1846273218694589543267146197582335684721914832.756..7651384 G2: 4 # 14 pairs G3: 5,9,4 # reduction candidate for 5,9 G3: 5,9 # 14 pairs * PAIR I4: 2,5 COL I I2: 2,5,8 # reduction candidate for 2,5 I2: 2,5 # 15 pairs I3: 2,5,8 # reduction candidate for 2,5 I3: 2,5 # 15 pairs * PAIR H6: 2,9 ROW 6 D6: 2,9,5 # reduction candidate for 2,9 D6: 2,9 # 18 pairs F6: 2,9,5 # reduction candidate for 2,9 F6: 2,9 # 19 pairs * PAIR A9: 2,9 COL A A1: 2,9,5 # reduction candidate for 2,9 A1: 2,9 # 19 pairs A3: 2,9,5 # reduction candidate for 2,9 A3: 2,9 # 15 pairs * PAIR E8: 2,9 COL E E2: 2,9,5 # reduction candidate for 2,9 E2: 2,9 # 17 pairs E3: 2,9,1,5 # reduction candidate for 2,9 E3: 2,9 => CTR * .84.631.761.758432.734.15687321869458952346714615798233568472191483927569.7615384 E3: 1,5 # 17 pairs * PAIR F8: 2,9 COL F F2: 2,9,4,5,8 # reduction candidate for 2,9 F2: 2,9 => CTR * .84.631.761.75.438.73..8.6.73.186.4.8.5.34671461.7.8.33568472191483..756..76.1384 F2: 4,5,8 # 13 pairs F3: 2,9,1,4,5,8 # reduction candidate for 2,9 F3: 2,9 => SOLVED * 984563127612798435573412968739186542825934671461275893356847219148329756297651384 F3: 1,4,5,8 # 13 pairs F5: 2,9,4 # reduction candidate for 2,9 F5: 2,9 # 20 pairs F6: 2,9,5 # reduction candidate for 2,9 F6: 2,9 # 19 pairs * PAIR E9: 1,5 COL E E3: 1,5,2,9 # reduction candidate for 1,5 E3: 2,9 => CTR * .84.631.761.758432.734.15687321869458952346714615798233568472191483927569.7615384 E3: 1,5 # 17 pairs * PAIR F9: 1,5 COL F F3: 1,5,2,4,8,9 # reduction candidate for 1,5 F3: 1,5 # 20 pairs F3: 2,4,8,9 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-377-base-pr-000.dot * REASONING * DIS # F2: 2,9 => CTR => F2: 4,5,8 * DIS # G2: 5,9 => CTR => G2: 4 * DIS # E3: 2,9 => CTR => E3: 1,5 * DIS # F2: 2,9 => CTR => F2: 4,5,8 * PRF # F3: 2,9 => SOL * DIS # E3: 2,9 => CTR => E3: 1,5 * CNT 6 HDP CHAINS / 31 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B5,B9,C2,C4,E8,E9,F8,F9,G4,H1,H6,I4) * .84.631.761.7...3..73....6.73.186.4.8.5.3.671461.7.8.33568472191483..756..76..384 * PAIR C2: 2,9 BLK 1 A1: 2,9,5 # reduction candidate for 2,9 A1: 2,9 # 19 pairs A3: 2,9,5 # reduction candidate for 2,9 A3: 2,9 # 15 pairs * PAIR C2: 2,9 ROW 2 E2: 2,9,5 # reduction candidate for 2,9 E2: 2,9 # 17 pairs F2: 2,9,4,5,8 # reduction candidate for 2,9 F2: 2,9 => CTR * .84.631.761.75.438.73..8.6.73.186.4.8.5.34671461.7.8.33568472191483..756..76.1384 * RESTART * PAIR C2: 2,9 ROW 2 E2: 2,9,5 # reduction candidate for 2,9 E2: 5 => CTR * 584263197619758432273491568732186945895.3.67146157.8233568472191483..756..7615384 * PAIR RESTART * PAIR C2: 2,9 BLK 1 A1: 2,9,5 # reduction candidate for 2,9 A1: 2,9 # 19 pairs A3: 2,9,5 # reduction candidate for 2,9 A3: 2,9 # 20 pairs * PAIR H1: 2,9 ROW 1 A1: 2,9,5 # reduction candidate for 2,9 A1: 2,9 # 19 pairs D1: 2,9,5 # reduction candidate for 2,9 D1: 2,9 # 20 pairs * PAIR B5: 2,9 ROW 5 D5: 2,9,4 # reduction candidate for 2,9 D5: 2,9 # 19 pairs F5: 2,9,4 # reduction candidate for 2,9 F5: 2,9 # 20 pairs * PAIR G4: 5,9 COL G G3: 5,9,4 # reduction candidate for 5,9 G3: 4 => CTR * .84.6319761.7...3..73...462732186945895432671461.7.8233568472191483297569276..384 * PAIR RESTART * PAIR I4: 2,5 COL I I3: 2,5,8 # reduction candidate for 2,5 I3: 8 => SOLVED * 984563127612798435573412968739186542825934671461275893356847219148329756297651384 * DURATION: 0:00:19.185446 START: 15:47:51.054505 END: 15:48:10.239951 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-377-base-pr-001.dot * REASONING * DIS # F2: 2,9 => CTR => F2: 4,5,8 * DIS F2: 4,5,8 # E2: 5 => CTR => E2: 2,9 * DIS F2: 4,5,8 + E2: 2,9 # G3: 4 => CTR => G3: 5,9 * PRF F2: 4,5,8 + E2: 2,9 + G3: 5,9 # I3: 8 => SOL * STA F2: 4,5,8 + E2: 2,9 + G3: 5,9 + I3: 8 * CNT 4 HDP CHAINS / 16 HYP OPENED
Header Info
Top 500 Minimum 17 377 solution: 984563127612798435573412968739186542825934671461275893356847219148329756297651384 info: 18455 FNBXYK S8.f 39367 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 984563127612798435573412968739186542825934671461275893356847219148329756297651384 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 # A1: 2,9 => UNS * INC # A3: 2,9 => UNS * INC # E2: 2,9 => UNS * DIS # F2: 2,9 => CTR => F2: 4,5,8 * INC # F2: 4,5,8 => UNS * INC # A1: 2,9 => UNS * INC # D1: 2,9 => UNS * INC # D5: 2,9 => UNS * INC # F5: 2,9 => UNS * DIS # G2: 5,9 => CTR => G2: 4 * INC # G2: 4 => UNS * INC # G3: 5,9 => UNS * INC # I2: 2,5 => UNS * INC # I3: 2,5 => UNS * INC # D6: 2,9 => UNS * INC # F6: 2,9 => UNS * INC # A1: 2,9 => UNS * INC # A3: 2,9 => UNS * INC # E2: 2,9 => UNS * DIS # E3: 2,9 => CTR => E3: 1,5 * INC # E3: 1,5 => UNS * DIS # F2: 2,9 => CTR => F2: 4,5,8 * INC # F2: 4,5,8 => UNS * PRF # F3: 2,9 => SOL * INC # F3: 1,4,5,8 => UNS * INC # F5: 2,9 => UNS * INC # F6: 2,9 => UNS * INC # E3: 1,5 => UNS * DIS # E3: 2,9 => CTR => E3: 1,5 * INC # F3: 1,5 => UNS * INC # F3: 2,4,8,9 => UNS * CNT 31 HDP CHAINS / 31 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 2,9 => UNS * INC # A3: 2,9 => UNS * INC # E2: 2,9 => UNS * DIS # F2: 2,9 => CTR => F2: 4,5,8 * INC F2: 4,5,8 # E2: 2,9 => UNS * DIS F2: 4,5,8 # E2: 5 => CTR => E2: 2,9 * INC F2: 4,5,8 + E2: 2,9 # A1: 2,9 => UNS * INC F2: 4,5,8 + E2: 2,9 # A3: 2,9 => UNS * INC F2: 4,5,8 + E2: 2,9 # A1: 2,9 => UNS * INC F2: 4,5,8 + E2: 2,9 # D1: 2,9 => UNS * INC F2: 4,5,8 + E2: 2,9 # D5: 2,9 => UNS * INC F2: 4,5,8 + E2: 2,9 # F5: 2,9 => UNS * INC F2: 4,5,8 + E2: 2,9 # G3: 5,9 => UNS * DIS F2: 4,5,8 + E2: 2,9 # G3: 4 => CTR => G3: 5,9 * INC F2: 4,5,8 + E2: 2,9 + G3: 5,9 # I3: 2,5 => UNS * PRF F2: 4,5,8 + E2: 2,9 + G3: 5,9 # I3: 8 => SOL * STA F2: 4,5,8 + E2: 2,9 + G3: 5,9 + I3: 8 * CNT 16 HDP CHAINS / 16 HYP OPENED