Analysis of xx-top500-070-base.sdk
Contents
Original Sudoku
level: medium
position: .61..........3...9.......2.9......3....6..8.....5..7...5.1....63...2..........4.. initial
Autosolve
position: 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76..521.93.631..2695.6..35.412 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # H1: 7,8 => SOL * DIS # H1: 4 => CTR => H1: 7,8 * DIS # H2: 7,8 => CTR => H2: 4 * PRF # H2: 4 => SOL * DIS # A3: 7,8 => CTR => A3: 4 * PRF # A3: 4 => SOL * PRF # D3: 7,8 => SOL * DIS # D3: 4 => CTR => D3: 7,8 * DIS # B5: 4,7 => CTR => B5: 2,3 * PRF # D4: 4,7 => SOL * PRF # D4: 4,7 => SOL * DIS # B5: 4,7 => CTR => B5: 2,3 * DIS # E1: 4,7 => CTR => E1: 8 * DIS # B5: 4,7 => CTR => B5: 2,3 * DIS # E7: 7,8 => CTR => E7: 4 * PRF # F4: 7,8 => SOL * DIS # E7: 7,8 => CTR => E7: 4 * PRF # H1: 7,8 => SOL * DIS # H1: 4 => CTR => H1: 7,8 * DIS # H2: 7,8 => CTR => H2: 4 * PRF # H2: 4 => SOL * DIS # C8: 7,8 => CTR => C8: 4 * CNT 22 HDP CHAINS / 53 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # H1: 7,8 => SOL * STA H1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .61..........3...9.......2.9......3....6..8.....5..7...5.1....63...2..........4.. | initial |
| 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76..521.93.631..2695.6..35.412 | autosolve |
| 261984573587231649439765128976418235125673894843592761752149386314826957698357412 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B3: 3,9 C3: 3,9 I3: 7,8 B4: 4,7 E5: 4,7 F5: 2,3 F6: 2,3 I5: 1,4 I6: 1,4 F9: 7,8 H7: 7,8 I8: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,A6: 1.. / A5 = 1 => 16 pairs (_) / A6 = 1 => 11 pairs (_) I5,I6: 1.. / I5 = 1 => 11 pairs (_) / I6 = 1 => 16 pairs (_) A5,I5: 1.. / A5 = 1 => 16 pairs (_) / I5 = 1 => 11 pairs (_) A6,I6: 1.. / A6 = 1 => 11 pairs (_) / I6 = 1 => 16 pairs (_) B5,B6: 2.. / B5 = 2 => 10 pairs (_) / B6 = 2 => 11 pairs (_) F5,F6: 2.. / F5 = 2 => 11 pairs (_) / F6 = 2 => 10 pairs (_) B5,F5: 2.. / B5 = 2 => 10 pairs (_) / F5 = 2 => 11 pairs (_) B6,F6: 2.. / B6 = 2 => 11 pairs (_) / F6 = 2 => 10 pairs (_) B3,C3: 3.. / B3 = 3 => 11 pairs (_) / C3 = 3 => 14 pairs (_) F5,F6: 3.. / F5 = 3 => 10 pairs (_) / F6 = 3 => 11 pairs (_) H1,H2: 4.. / H1 = 4 => 0 pairs (X) / H2 = 4 => 0 pairs (_) I5,I6: 4.. / I5 = 4 => 16 pairs (_) / I6 = 4 => 11 pairs (_) A7,C8: 4.. / A7 = 4 => 0 pairs (X) / C8 = 4 => 21 pairs (_) E7,D8: 4.. / E7 = 4 => 21 pairs (_) / D8 = 4 => 0 pairs (X) A3,D3: 4.. / A3 = 4 => 0 pairs (*) / D3 = 4 => 0 pairs (X) A7,E7: 4.. / A7 = 4 => 0 pairs (X) / E7 = 4 => 21 pairs (_) C8,D8: 4.. / C8 = 4 => 21 pairs (_) / D8 = 4 => 0 pairs (X) F1,F4: 4.. / F1 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) A2,C2: 5.. / A2 = 5 => 13 pairs (_) / C2 = 5 => 11 pairs (_) A5,C5: 5.. / A5 = 5 => 11 pairs (_) / C5 = 5 => 13 pairs (_) A2,A5: 5.. / A2 = 5 => 13 pairs (_) / A5 = 5 => 11 pairs (_) C2,C5: 5.. / C2 = 5 => 11 pairs (_) / C5 = 5 => 13 pairs (_) H7,I8: 7.. / H7 = 7 => 18 pairs (_) / I8 = 7 => 21 pairs (_) I3,I8: 7.. / I3 = 7 => 18 pairs (_) / I8 = 7 => 21 pairs (_) D4,F4: 8.. / D4 = 8 => 16 pairs (_) / F4 = 8 => 0 pairs (*) H7,I8: 8.. / H7 = 8 => 21 pairs (_) / I8 = 8 => 18 pairs (_) E1,E7: 8.. / E1 = 8 => 16 pairs (_) / E7 = 8 => 0 pairs (X) I3,I8: 8.. / I3 = 8 => 21 pairs (_) / I8 = 8 => 18 pairs (_) B3,C3: 9.. / B3 = 9 => 14 pairs (_) / C3 = 9 => 11 pairs (_) B9,C9: 9.. / B9 = 9 => 11 pairs (_) / C9 = 9 => 14 pairs (_) B3,B9: 9.. / B3 = 9 => 14 pairs (_) / B9 = 9 => 11 pairs (_) C3,C9: 9.. / C3 = 9 => 11 pairs (_) / C9 = 9 => 14 pairs (_) * DURATION: 0:00:59.168753 START: 05:04:22.590095 END: 05:05:21.758848 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,C3,E5,F5,F6,F9,H7,I3,I5,I6,I8) * 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76..521.93.631..2695.6..35.412 * PAIR I3: 7,8 BLK 3 H1: 7,8,4 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 H1: 4 => CTR * 261987543...2316898..465127976814235...67.89..8359276.7521493.63147269586..358412 H2: 7,8,4 # reduction candidate for 7,8 H2: 7,8 => CTR * 261987543...2316898..465127976814235...67.89..8359276.7521493.63147269586..358412 H2: 4 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 * PAIR I3: 7,8 ROW 3 A3: 7,8,4 # reduction candidate for 7,8 A3: 7,8 => CTR * 261987543...2316898..465127976814235...67.89..8359276.7521493.63147269586..358412 A3: 4 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 D3: 7,8,4 # reduction candidate for 7,8 D3: 7,8 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 D3: 4 => CTR * 261987543...2316898..465127976814235...67.89..8359276.7521493.63147269586..358412 * PAIR B4: 4,7 BLK 4 A5: 4,7,1,5 # reduction candidate for 4,7 A5: 4,7 # 13 pairs B5: 4,7,2,3 # reduction candidate for 4,7 B5: 4,7 => CTR * 261987543.852316.9.39.6512.9.6.1.2355.36.2891128593764852149376314726958697358412 B5: 2,3 # 13 pairs C5: 4,7,3,5 # reduction candidate for 4,7 C5: 4,7 # 13 pairs * PAIR B4: 4,7 ROW 4 D4: 4,7,8 # reduction candidate for 4,7 D4: 4,7 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 D4: 8 # 16 pairs F4: 4,7,8 # reduction candidate for 4,7 F4: 4,7 # 16 pairs * PAIR B4: 4,7 COL B B2: 4,7,8 # reduction candidate for 4,7 B2: 8 # 17 pairs B2: 4,7 # 15 pairs * PAIR E5: 4,7 BLK 5 D4: 4,7,8 # reduction candidate for 4,7 D4: 4,7 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 D4: 8 # 16 pairs F4: 4,7,8 # reduction candidate for 4,7 F4: 4,7 # 16 pairs * PAIR E5: 4,7 ROW 5 A5: 4,7,1,5 # reduction candidate for 4,7 A5: 4,7 # 13 pairs B5: 4,7,2,3 # reduction candidate for 4,7 B5: 4,7 => CTR * 261987543.852316.9.39.6512.9.6.1.2355.36.2891128593764852149376314726958697358412 B5: 2,3 # 13 pairs C5: 4,7,3,5 # reduction candidate for 4,7 C5: 4,7 # 13 pairs * PAIR E5: 4,7 COL E E1: 4,7,8 # reduction candidate for 4,7 E1: 4,7 => CTR * 261974583...2316494...6512.9.6.1.235...6..89....59.76..5218937631.4269586..357412 E1: 8 # 16 pairs E7: 4,7,8 # reduction candidate for 4,7 E7: 4,7 # 16 pairs * PAIR F5: 2,3 ROW 5 B5: 2,3,4,7 # reduction candidate for 2,3 B5: 4,7 => CTR * 261987543.852316.9.39.6512.9.6.1.2355.36.2891128593764852149376314726958697358412 B5: 2,3 # 13 pairs * PAIR F6: 2,3 ROW 6 B6: 2,3,4,8 # reduction candidate for 2,3 B6: 2,3 # 14 pairs B6: 4,8 # 10 pairs * PAIR I5: 1,4 ROW 5 A5: 1,4,5,7 # reduction candidate for 1,4 A5: 1,4 # 18 pairs A5: 5,7 # 12 pairs * PAIR I6: 1,4 ROW 6 A6: 1,4,8 # reduction candidate for 1,4 A6: 8 # 19 pairs A6: 1,4 # 14 pairs * PAIR F9: 7,8 BLK 8 E7: 7,8,4 # reduction candidate for 7,8 E7: 7,8 => CTR * 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76.4521.93.631.42695.6..35.412 E7: 4 # 21 pairs D8: 7,8,4 # reduction candidate for 7,8 D8: 7,8 # 21 pairs * PAIR F9: 7,8 ROW 9 B9: 7,8,9 # reduction candidate for 7,8 B9: 7,8 # 14 pairs C9: 7,8,9 # reduction candidate for 7,8 C9: 7,8 # 11 pairs * PAIR F9: 7,8 COL F F1: 7,8,4 # reduction candidate for 7,8 F1: 7,8 # 18 pairs F4: 7,8,4 # reduction candidate for 7,8 F4: 7,8 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 F4: 4 # 18 pairs * PAIR H7: 7,8 ROW 7 A7: 7,8,4 # reduction candidate for 7,8 A7: 7,8 # 21 pairs E7: 7,8,4 # reduction candidate for 7,8 E7: 7,8 => CTR * 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76.4521.93.631.42695.6..35.412 E7: 4 # 21 pairs * PAIR H7: 7,8 COL H H1: 7,8,4 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 H1: 4 => CTR * 261987543...2316898..465127976814235...67.89..8359276.7521493.63147269586..358412 H2: 7,8,4 # reduction candidate for 7,8 H2: 7,8 => CTR * 261987543...2316898..465127976814235...67.89..8359276.7521493.63147269586..358412 H2: 4 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 * PAIR I8: 7,8 ROW 8 C8: 7,8,4 # reduction candidate for 7,8 C8: 7,8 => CTR * 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76.4521.93.631.42695.6..35.412 C8: 4 # 21 pairs D8: 7,8,4 # reduction candidate for 7,8 D8: 7,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-070-base-pr-000.dot * REASONING * PRF # H1: 7,8 => SOL * DIS # H1: 4 => CTR => H1: 7,8 * DIS # H2: 7,8 => CTR => H2: 4 * PRF # H2: 4 => SOL * DIS # A3: 7,8 => CTR => A3: 4 * PRF # A3: 4 => SOL * PRF # D3: 7,8 => SOL * DIS # D3: 4 => CTR => D3: 7,8 * DIS # B5: 4,7 => CTR => B5: 2,3 * PRF # D4: 4,7 => SOL * PRF # D4: 4,7 => SOL * DIS # B5: 4,7 => CTR => B5: 2,3 * DIS # E1: 4,7 => CTR => E1: 8 * DIS # B5: 4,7 => CTR => B5: 2,3 * DIS # E7: 7,8 => CTR => E7: 4 * PRF # F4: 7,8 => SOL * DIS # E7: 7,8 => CTR => E7: 4 * PRF # H1: 7,8 => SOL * DIS # H1: 4 => CTR => H1: 7,8 * DIS # H2: 7,8 => CTR => H2: 4 * PRF # H2: 4 => SOL * DIS # C8: 7,8 => CTR => C8: 4 * CNT 22 HDP CHAINS / 53 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B4,C3,E5,F5,F6,F9,H7,I3,I5,I6,I8) * 2619..5.3...2316.9....6512.9.6.1.235...6..89....59.76..521.93.631..2695.6..35.412 * PAIR I3: 7,8 BLK 3 H1: 7,8,4 # reduction candidate for 7,8 H1: 7,8 => SOLVED * 261984573587231649439765128976418235125673894843592761752149386314826957698357412 * DURATION: 0:00:02.404396 START: 05:06:20.174829 END: 05:06:22.579225 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-070-base-pr-001.dot * REASONING * PRF # H1: 7,8 => SOL * STA H1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 070 solution: 261984573587231649439765128976418235125673894843592761752149386314826957698357412 info: 1453 FNBTHWX S8.f 21683 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 261984573587231649439765128976418235125673894843592761752149386314826957698357412 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:
* PRF # H1: 7,8 => SOL * DIS # H1: 4 => CTR => H1: 7,8 * DIS # H2: 7,8 => CTR => H2: 4 * PRF # H2: 4 => SOL * DIS # A3: 7,8 => CTR => A3: 4 * PRF # A3: 4 => SOL * PRF # D3: 7,8 => SOL * DIS # D3: 4 => CTR => D3: 7,8 * INC # A5: 4,7 => UNS * DIS # B5: 4,7 => CTR => B5: 2,3 * INC # B5: 2,3 => UNS * INC # C5: 4,7 => UNS * PRF # D4: 4,7 => SOL * INC # D4: 8 => UNS * INC # F4: 4,7 => UNS * INC # B2: 4,7 => UNS * INC # B2: 8 => UNS * PRF # D4: 4,7 => SOL * INC # D4: 8 => UNS * INC # F4: 4,7 => UNS * INC # A5: 4,7 => UNS * DIS # B5: 4,7 => CTR => B5: 2,3 * INC # B5: 2,3 => UNS * INC # C5: 4,7 => UNS * DIS # E1: 4,7 => CTR => E1: 8 * INC # E1: 8 => UNS * INC # E7: 4,7 => UNS * INC # B5: 2,3 => UNS * DIS # B5: 4,7 => CTR => B5: 2,3 * INC # B6: 2,3 => UNS * INC # B6: 4,8 => UNS * INC # A5: 1,4 => UNS * INC # A5: 5,7 => UNS * INC # A6: 1,4 => UNS * INC # A6: 8 => UNS * DIS # E7: 7,8 => CTR => E7: 4 * INC # E7: 4 => UNS * INC # D8: 7,8 => UNS * INC # B9: 7,8 => UNS * INC # C9: 7,8 => UNS * INC # F1: 7,8 => UNS * PRF # F4: 7,8 => SOL * INC # F4: 4 => UNS * INC # A7: 7,8 => UNS * DIS # E7: 7,8 => CTR => E7: 4 * INC # E7: 4 => UNS * PRF # H1: 7,8 => SOL * DIS # H1: 4 => CTR => H1: 7,8 * DIS # H2: 7,8 => CTR => H2: 4 * PRF # H2: 4 => SOL * DIS # C8: 7,8 => CTR => C8: 4 * INC # C8: 4 => UNS * INC # D8: 7,8 => UNS * CNT 53 HDP CHAINS / 53 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # H1: 7,8 => SOL * STA H1: 7,8 * CNT 1 HDP CHAINS / 1 HYP OPENED