Analysis of xx-top500-467-base.sdk
Contents
Original Sudoku
level: medium
position: ....68.7.52....9.............1.7.......5..2...4.......8.......69..2.......6....3. initial
Autosolve
position: .93.68572528...96..67925...351.72.9.6895..2.7742......8.5....269.42.6...2.6.5..39 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I3: 1,4 => SOL * DIS # D2: 1,4 => CTR => D2: 3,7 * DIS # D7: 1,4 => CTR => D7: 3,7 * DIS # D9: 1,4 => CTR => D9: 7,8 * PRF # I3: 1,4 => SOL * DIS # D2: 1,4 => CTR => D2: 3,7 * DIS # E6: 1,9 => CTR => E6: 8 * DIS # G6: 6,8 => CTR => G6: 1,3 * DIS # D4: 6,8 => CTR => D4: 4 * PRF # D4: 4 => SOL * DIS # D4: 6 => CTR => D4: 4,8 * PRF # H3: 8 => SOL * DIS # D9: 1,7 => CTR => D9: 4,8 * CNT 13 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:
* PRF # I3: 1,4 => SOL * STA I3: 1,4 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....68.7.52....9.............1.7.......5..2...4.......8.......69..2.......6....3. | initial |
| .93.68572528...96..67925...351.72.9.6895..2.7742......8.5....269.42.6...2.6.5..39 | autosolve |
| 493168572528347961167925384351472698689513247742689153835791426974236815216854739 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A1: 1,4 A3: 1,4 D1: 1,4 I2: 1,4 F6: 1,9 G4: 6,8 I4: 4,8 H5: 1,4 B9: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 1.. / A1 = 1 => 0 pairs (X) / A3 = 1 => 10 pairs (_) A1,D1: 1.. / A1 = 1 => 0 pairs (X) / D1 = 1 => 10 pairs (_) G3,I3: 3.. / G3 = 3 => 11 pairs (_) / I3 = 3 => 10 pairs (_) E5,F5: 3.. / E5 = 3 => 16 pairs (_) / F5 = 3 => 10 pairs (_) G6,I6: 3.. / G6 = 3 => 10 pairs (_) / I6 = 3 => 11 pairs (_) B7,B8: 3.. / B7 = 3 => 17 pairs (_) / B8 = 3 => 12 pairs (_) B8,E8: 3.. / B8 = 3 => 12 pairs (_) / E8 = 3 => 17 pairs (_) D2,D7: 3.. / D2 = 3 => 11 pairs (_) / D7 = 3 => 12 pairs (_) G3,G6: 3.. / G3 = 3 => 11 pairs (_) / G6 = 3 => 10 pairs (_) I3,I6: 3.. / I3 = 3 => 10 pairs (_) / I6 = 3 => 11 pairs (_) A1,A3: 4.. / A1 = 4 => 10 pairs (_) / A3 = 4 => 0 pairs (X) I4,H5: 4.. / I4 = 4 => 0 pairs (X) / H5 = 4 => 0 pairs (_) G7,G9: 4.. / G7 = 4 => 9 pairs (_) / G9 = 4 => 17 pairs (_) A1,D1: 4.. / A1 = 4 => 10 pairs (_) / D1 = 4 => 0 pairs (X) D4,I4: 4.. / D4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) H3,H5: 4.. / H3 = 4 => 0 pairs (X) / H5 = 4 => 0 pairs (_) H6,I6: 5.. / H6 = 5 => 10 pairs (_) / I6 = 5 => 13 pairs (_) H8,I8: 5.. / H8 = 5 => 13 pairs (_) / I8 = 5 => 10 pairs (_) H6,H8: 5.. / H6 = 5 => 10 pairs (_) / H8 = 5 => 13 pairs (_) I6,I8: 5.. / I6 = 5 => 13 pairs (_) / I8 = 5 => 10 pairs (_) D4,D6: 6.. / D4 = 6 => 0 pairs (X) / D6 = 6 => 9 pairs (_) G4,G6: 6.. / G4 = 6 => 9 pairs (_) / G6 = 6 => 0 pairs (X) D4,G4: 6.. / D4 = 6 => 0 pairs (X) / G4 = 6 => 9 pairs (_) D6,G6: 6.. / D6 = 6 => 9 pairs (_) / G6 = 6 => 0 pairs (X) D2,F2: 7.. / D2 = 7 => 12 pairs (_) / F2 = 7 => 10 pairs (_) B8,G8: 7.. / B8 = 7 => 13 pairs (_) / G8 = 7 => 11 pairs (_) E8,D9: 8.. / E8 = 8 => 0 pairs (X) / D9 = 8 => 15 pairs (_) D9,G9: 8.. / D9 = 8 => 15 pairs (_) / G9 = 8 => 0 pairs (X) E6,E8: 8.. / E6 = 8 => 15 pairs (_) / E8 = 8 => 0 pairs (X) E6,F6: 9.. / E6 = 9 => 0 pairs (X) / F6 = 9 => 9 pairs (_) E7,F7: 9.. / E7 = 9 => 9 pairs (_) / F7 = 9 => 0 pairs (X) E6,E7: 9.. / E6 = 9 => 0 pairs (X) / E7 = 9 => 9 pairs (_) F6,F7: 9.. / F6 = 9 => 9 pairs (_) / F7 = 9 => 0 pairs (X) * DURATION: 0:01:07.767745 START: 18:39:51.557943 END: 18:40:59.325688 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B9,D1,F6,G4,H5,I2,I4) * .93.68572528...96..67925...351.72.9.6895..2.7742......8.5....269.42.6...2.6.5..39 * PAIR A3: 1,4 ROW 3 H3: 1,4,8 # reduction candidate for 1,4 H3: 1,4 # 14 pairs I3: 1,4,3,8 # reduction candidate for 1,4 I3: 1,4 => SOLVED * 493168572528347961167925384351472698689513247742689153835791426974236815216854739 I3: 3,8 # 10 pairs * PAIR D1: 1,4 BLK 2 D2: 1,4,3,7 # reduction candidate for 1,4 D2: 1,4 => CTR * .93.68572528.3796..67925...3518726946895432177426..3..8753..426934286751216754839 D2: 3,7 # 10 pairs E2: 1,4,3 # reduction candidate for 1,4 E2: 1,4 # 12 pairs F2: 1,4,3,7 # reduction candidate for 1,4 F2: 1,4 # 14 pairs * PAIR D1: 1,4 COL D D7: 1,4,3,7 # reduction candidate for 1,4 D7: 1,4 => CTR * .93.685725283.796..67925...3518726946895432177426..3..875139426934286751216754839 D7: 3,7 # 10 pairs D9: 1,4,7,8 # reduction candidate for 1,4 D9: 1,4 => CTR * .93.68572528...96..67925...3518726946895..2177426..3..8.5...4269342867512.6.5.839 D9: 7,8 # 10 pairs * PAIR I2: 1,4 BLK 3 H3: 1,4,8 # reduction candidate for 1,4 H3: 1,4 # 14 pairs I3: 1,4,3,8 # reduction candidate for 1,4 I3: 1,4 => SOLVED * 493168572528347961167925384351472698689513247742689153835791426974236815216854739 I3: 3,8 # 10 pairs * PAIR I2: 1,4 ROW 2 D2: 1,4,3,7 # reduction candidate for 1,4 D2: 1,4 => CTR * .93.68572528.3796..67925...3518726946895432177426..3..8753..426934286751216754839 D2: 3,7 # 10 pairs E2: 1,4,3 # reduction candidate for 1,4 E2: 1,4 # 12 pairs F2: 1,4,3,7 # reduction candidate for 1,4 F2: 1,4 # 14 pairs * PAIR F6: 1,9 BLK 5 E6: 1,9,8 # reduction candidate for 1,9 E6: 1,9 => CTR * .93.68572528...96..67925...3518726946895..2177426..3..8.5...4269342867512.6.5.839 E6: 8 # 15 pairs * PAIR F6: 1,9 COL F F7: 1,9,3,4,7 # reduction candidate for 1,9 F7: 1,9 # 12 pairs F7: 3,4,7 # 9 pairs * PAIR G4: 6,8 BLK 6 G6: 6,8,1,3 # reduction candidate for 6,8 G6: 6,8 => CTR * 493168572528...96..67925348351.728946895..217742.896538.5.9..269.42.6.852.685..39 G6: 1,3 # 10 pairs * PAIR G4: 6,8 ROW 4 D4: 6,8,4 # reduction candidate for 6,8 D4: 6,8 => CTR * 493168572528...961167925.4.351.72.946895..217742......8.5....269.42.6...2.6.5..39 D4: 4 => SOLVED * 493168572528347961167925384351472698689513247742689153835791426974236815216854739 * PAIR I4: 4,8 ROW 4 D4: 4,8,6 # reduction candidate for 4,8 D4: 6 => CTR * .93.68572528...9611679253483516728946895..2177421896538.5.9..269.42167852.685..39 D4: 4,8 # 9 pairs * PAIR I4: 4,8 COL I I3: 4,8,1,3 # reduction candidate for 4,8 I3: 4,8 # 10 pairs I3: 1,3 # 10 pairs * PAIR H5: 1,4 ROW 5 E5: 1,4,3 # reduction candidate for 1,4 E5: 1,4 # 10 pairs F5: 1,4,3 # reduction candidate for 1,4 F5: 1,4 # 16 pairs * PAIR H5: 1,4 COL H H3: 1,4,8 # reduction candidate for 1,4 H3: 8 => SOLVED * 493168572528347961167925384351472698689513247742689153835791426974236815216854739 H3: 1,4 # 14 pairs * PAIR B9: 1,7 BLK 7 B7: 1,7,3 # reduction candidate for 1,7 B7: 1,7 # 12 pairs B8: 1,7,3 # reduction candidate for 1,7 B8: 1,7 # 17 pairs * PAIR B9: 1,7 ROW 9 D9: 1,7,4,8 # reduction candidate for 1,7 D9: 1,7 => CTR * .93.68572528...96..67925...3518726946895432177426..3..8.5...4269342867512.6.54839 D9: 4,8 # 12 pairs F9: 1,7,4 # reduction candidate for 1,7 F9: 1,7 # 14 pairs G9: 1,7,4,8 # reduction candidate for 1,7 G9: 1,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-467-base-pr-000.dot * REASONING * PRF # I3: 1,4 => SOL * DIS # D2: 1,4 => CTR => D2: 3,7 * DIS # D7: 1,4 => CTR => D7: 3,7 * DIS # D9: 1,4 => CTR => D9: 7,8 * PRF # I3: 1,4 => SOL * DIS # D2: 1,4 => CTR => D2: 3,7 * DIS # E6: 1,9 => CTR => E6: 8 * DIS # G6: 6,8 => CTR => G6: 1,3 * DIS # D4: 6,8 => CTR => D4: 4 * PRF # D4: 4 => SOL * DIS # D4: 6 => CTR => D4: 4,8 * PRF # H3: 8 => SOL * DIS # D9: 1,7 => CTR => D9: 4,8 * CNT 13 HDP CHAINS / 40 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B9,D1,F6,G4,H5,I2,I4) * .93.68572528...96..67925...351.72.9.6895..2.7742......8.5....269.42.6...2.6.5..39 * PAIR A3: 1,4 ROW 3 H3: 1,4,8 # reduction candidate for 1,4 H3: 1,4 # 14 pairs I3: 1,4,3,8 # reduction candidate for 1,4 I3: 1,4 => SOLVED * 493168572528347961167925384351472698689513247742689153835791426974236815216854739 * DURATION: 0:00:03.456191 START: 18:41:44.224276 END: 18:41:47.680467 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-467-base-pr-001.dot * REASONING * PRF # I3: 1,4 => SOL * STA I3: 1,4 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 467 solution: 493168572528347961167925384351472698689513247742689153835791426974236815216854739 info: 95591 FNBXYK S8.f 5535 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 493168572528347961167925384351472698689513247742689153835791426974236815216854739 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 # H3: 1,4 => UNS * PRF # I3: 1,4 => SOL * INC # I3: 3,8 => UNS * DIS # D2: 1,4 => CTR => D2: 3,7 * INC # D2: 3,7 => UNS * INC # E2: 1,4 => UNS * INC # F2: 1,4 => UNS * DIS # D7: 1,4 => CTR => D7: 3,7 * INC # D7: 3,7 => UNS * DIS # D9: 1,4 => CTR => D9: 7,8 * INC # D9: 7,8 => UNS * INC # H3: 1,4 => UNS * PRF # I3: 1,4 => SOL * INC # I3: 3,8 => UNS * DIS # D2: 1,4 => CTR => D2: 3,7 * INC # D2: 3,7 => UNS * INC # E2: 1,4 => UNS * INC # F2: 1,4 => UNS * DIS # E6: 1,9 => CTR => E6: 8 * INC # E6: 8 => UNS * INC # F7: 1,9 => UNS * INC # F7: 3,4,7 => UNS * DIS # G6: 6,8 => CTR => G6: 1,3 * INC # G6: 1,3 => UNS * DIS # D4: 6,8 => CTR => D4: 4 * PRF # D4: 4 => SOL * INC # D4: 4,8 => UNS * DIS # D4: 6 => CTR => D4: 4,8 * INC # I3: 4,8 => UNS * INC # I3: 1,3 => UNS * INC # E5: 1,4 => UNS * INC # F5: 1,4 => UNS * INC # H3: 1,4 => UNS * PRF # H3: 8 => SOL * INC # B7: 1,7 => UNS * INC # B8: 1,7 => UNS * DIS # D9: 1,7 => CTR => D9: 4,8 * INC # D9: 4,8 => UNS * INC # F9: 1,7 => UNS * INC # G9: 1,7 => UNS * CNT 40 HDP CHAINS / 40 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # H3: 1,4 => UNS * PRF # I3: 1,4 => SOL * STA I3: 1,4 * CNT 2 HDP CHAINS / 2 HYP OPENED