Analysis of xx-top500-153-base.sdk
Contents
Original Sudoku
level: medium
position: .6.3.2.....7...41........8..3.5..6......1..2.............6..3..8...2....1........ initial
Autosolve
position: 461382...2879..4133..1..286.325.86.16...13.2..1.2...3..2.6.13.88.3.2.16.1.683...2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B5: 5,9 => CTR => B5: 4,7 * DIS # B9: 5,9 => CTR => B9: 4,7 * PRF # C5: 5,9 => SOL * DIS # C6: 5,9 => CTR => C6: 4,8 * DIS # E6: 4,7 => CTR => E6: 6,9 * DIS # E7: 4,7 => CTR => E7: 5,9 * DIS # F6: 4,7 => CTR => F6: 6,9 * PRF # F8: 4,7 => SOL * DIS # E4: 7,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H4: 7,9 => SOL * DIS # H4: 4 => CTR => H4: 7,9 * DIS # E6: 4,7 => CTR => E6: 6,9 * DIS # F6: 4,7 => CTR => F6: 6,9 * DIS # I5: 4,7 => CTR => I5: 5,9 * DIS # E7: 4,7 => CTR => E7: 5,9 * PRF # F8: 4,7 => SOL * DIS # B8: 4,7 => CTR => B8: 5,9 * CNT 18 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B5: 5,9 => CTR => B5: 4,7 * DIS B5: 4,7 # B9: 5,9 => CTR => B9: 4,7 * PRF B5: 4,7 + B9: 4,7 # C5: 5,9 => SOL * STA B5: 4,7 + B9: 4,7 + C5: 5,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .6.3.2.....7...41........8..3.5..6......1..2.............6..3..8...2....1........ | initial |
| 461382...2879..4133..1..286.325.86.16...13.2..1.2...3..2.6.13.88.3.2.16.1.683...2 | autosolve |
| 461382957287965413395174286732548691649713825518296734924651378853427169176839542 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) B3: 5,9 C3: 5,9 E2: 5,6 F2: 5,6 E3: 4,7 F3: 4,7 A4: 7,9 D5: 4,7 D8: 4,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E3,F3: 4.. / E3 = 4 => 0 pairs (X) / F3 = 4 => 8 pairs (_) E4,H4: 4.. / E4 = 4 => 0 pairs (*) / H4 = 4 => 0 pairs (X) D5,D8: 4.. / D5 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) B3,C3: 5.. / B3 = 5 => 6 pairs (_) / C3 = 5 => 8 pairs (_) E2,F2: 5.. / E2 = 5 => 7 pairs (_) / F2 = 5 => 11 pairs (_) A6,A7: 5.. / A6 = 5 => 10 pairs (_) / A7 = 5 => 11 pairs (_) E2,E7: 5.. / E2 = 5 => 7 pairs (_) / E7 = 5 => 11 pairs (_) E2,F2: 6.. / E2 = 6 => 11 pairs (_) / F2 = 6 => 7 pairs (_) E6,F6: 6.. / E6 = 6 => 7 pairs (_) / F6 = 6 => 11 pairs (_) E2,E6: 6.. / E2 = 6 => 11 pairs (_) / E6 = 6 => 7 pairs (_) F2,F6: 6.. / F2 = 6 => 7 pairs (_) / F6 = 6 => 11 pairs (_) E3,F3: 7.. / E3 = 7 => 8 pairs (_) / F3 = 7 => 0 pairs (X) D5,D8: 7.. / D5 = 7 => 0 pairs (*) / D8 = 7 => 0 pairs (X) C5,C6: 8.. / C5 = 8 => 9 pairs (_) / C6 = 8 => 0 pairs (*) G5,G6: 8.. / G5 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) C5,G5: 8.. / C5 = 8 => 9 pairs (_) / G5 = 8 => 0 pairs (*) C6,G6: 8.. / C6 = 8 => 0 pairs (*) / G6 = 8 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 8 pairs (_) / C3 = 9 => 6 pairs (_) * DURATION: 0:00:31.259269 START: 07:58:59.841519 END: 07:59:31.100788 2017-05-04 * CP COUNT: (18) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,C3,D5,D8,E2,E3,F2,F3) * 461382...2879..4133..1..286.325.86.16...13.2..1.2...3..2.6.13.88.3.2.16.1.683...2 * PAIR B3: 5,9 COL B B5: 5,9,4,7 # reduction candidate for 5,9 B5: 5,9 => CTR * 461382...2879564133..1..286.325986416...13.2..1.26..3..2.64137884372.16.17683...2 B5: 4,7 # 11 pairs B8: 5,9,4,7 # reduction candidate for 5,9 B8: 5,9 # 13 pairs B9: 5,9,4,7 # reduction candidate for 5,9 B9: 5,9 => CTR * 461382.572879..4133..1742867325486916497138255182..73492465137887342.16.1.6837.42 B9: 4,7 # 10 pairs * PAIR C3: 5,9 COL C C5: 5,9,4,8 # reduction candidate for 5,9 C5: 5,9 => SOLVED * 461382957287965413395174286732548691649713825518296734924651378853427169176839542 C5: 4,8 # 10 pairs C6: 5,9,4,8 # reduction candidate for 5,9 C6: 5,9 => CTR * 461382...2879..4133..174286.32548671648713.2.7152..8345246913.88.342.16.1.683..42 C6: 4,8 # 10 pairs C7: 5,9,4 # reduction candidate for 5,9 C7: 5,9 # 12 pairs * PAIR E3: 4,7 COL E E4: 4,7,9 # reduction candidate for 4,7 E4: 4,7 # 14 pairs E6: 4,7,6,9 # reduction candidate for 4,7 E6: 4,7 => CTR * 461382...2879654133.514728673259864164.713.2.51.2.6.3.9246513788.3.2.1641.6834..2 E6: 6,9 # 10 pairs E7: 4,7,5,9 # reduction candidate for 4,7 E7: 4,7 => CTR * 461382...2879564133..1..2867325986416..413.2..1426783..2.6413788.372.1641.683...2 E7: 5,9 # 10 pairs * PAIR F3: 4,7 COL F F6: 4,7,6,9 # reduction candidate for 4,7 F6: 4,7 => CTR * 461382...2879564133..1..2867325986416..413.2..1426783..2.6413788.372.1641.683...2 F6: 6,9 # 10 pairs F8: 4,7,5,9 # reduction candidate for 4,7 F8: 4,7 => SOLVED * 461382957287965413395174286732548691649713825518296734924651378853427169176839542 F8: 5,9 # 10 pairs F9: 4,7,5,9 # reduction candidate for 4,7 F9: 4,7 # 13 pairs * PAIR A4: 7,9 BLK 4 B5: 7,9,4,5 # reduction candidate for 7,9 B5: 7,9 # 14 pairs A6: 7,9,5 # reduction candidate for 7,9 A6: 7,9 # 11 pairs * PAIR A4: 7,9 ROW 4 E4: 7,9,4 # reduction candidate for 7,9 E4: 7,9 => CTR * 461382...2879564133..1742867325986416.8413.2..1426783..2.6413788.372.16414683...2 E4: 4 => SOLVED * 461382957287965413395174286732548691649713825518296734924651378853427169176839542 H4: 7,9,4 # reduction candidate for 7,9 H4: 7,9 => SOLVED * 461382957287965413395174286732548691649713825518296734924651378853427169176839542 H4: 4 => CTR * 461382...2879564133..1742867325986416.8413.2..1426783..2.6413788.372.16414683...2 * PAIR A4: 7,9 COL A A7: 7,9,5 # reduction candidate for 7,9 A7: 5 # 11 pairs A7: 7,9 # 10 pairs * PAIR D5: 4,7 BLK 5 E4: 4,7,9 # reduction candidate for 4,7 E4: 4,7 # 14 pairs E6: 4,7,6,9 # reduction candidate for 4,7 E6: 4,7 => CTR * 461382...2879654133.514728673259864164.713.2.51.2.6.3.9246513788.3.2.1641.6834..2 E6: 6,9 # 10 pairs F6: 4,7,6,9 # reduction candidate for 4,7 F6: 4,7 => CTR * 461382...2879564133..1..2867325986416..413.2..1426783..2.6413788.372.1641.683...2 F6: 6,9 # 10 pairs * PAIR D5: 4,7 ROW 5 B5: 4,7,5,9 # reduction candidate for 4,7 B5: 4,7 # 11 pairs I5: 4,7,5,9 # reduction candidate for 4,7 I5: 4,7 => CTR * 4613827..2879564133..1742867325986416.8413.27.1426783..2.64137884372.16.17683...2 I5: 5,9 # 10 pairs * PAIR D8: 4,7 BLK 8 E7: 4,7,5,9 # reduction candidate for 4,7 E7: 4,7 => CTR * 461382...2879564133..1..2867325986416..413.2..1426783..2.6413788.372.1641.683...2 E7: 5,9 # 10 pairs F8: 4,7,5,9 # reduction candidate for 4,7 F8: 4,7 => SOLVED * 461382957287965413395174286732548691649713825518296734924651378853427169176839542 F8: 5,9 # 10 pairs F9: 4,7,5,9 # reduction candidate for 4,7 F9: 4,7 # 13 pairs * PAIR D8: 4,7 ROW 8 B8: 4,7,5,9 # reduction candidate for 4,7 B8: 4,7 => CTR * 461382.5.2879..4133..1742867325486916497138255182..73492465137887342.16.1.6837.42 B8: 5,9 # 13 pairs I8: 4,7,5,9 # reduction candidate for 4,7 I8: 4,7 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-153-base-pr-000.dot * REASONING * DIS # B5: 5,9 => CTR => B5: 4,7 * DIS # B9: 5,9 => CTR => B9: 4,7 * PRF # C5: 5,9 => SOL * DIS # C6: 5,9 => CTR => C6: 4,8 * DIS # E6: 4,7 => CTR => E6: 6,9 * DIS # E7: 4,7 => CTR => E7: 5,9 * DIS # F6: 4,7 => CTR => F6: 6,9 * PRF # F8: 4,7 => SOL * DIS # E4: 7,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H4: 7,9 => SOL * DIS # H4: 4 => CTR => H4: 7,9 * DIS # E6: 4,7 => CTR => E6: 6,9 * DIS # F6: 4,7 => CTR => F6: 6,9 * DIS # I5: 4,7 => CTR => I5: 5,9 * DIS # E7: 4,7 => CTR => E7: 5,9 * PRF # F8: 4,7 => SOL * DIS # B8: 4,7 => CTR => B8: 5,9 * CNT 18 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,B3,C3,D5,D8,E2,E3,F2,F3) * 461382...2879..4133..1..286.325.86.16...13.2..1.2...3..2.6.13.88.3.2.16.1.683...2 * PAIR B3: 5,9 COL B B5: 5,9,4,7 # reduction candidate for 5,9 B5: 5,9 => CTR * 461382...2879564133..1..286.325986416...13.2..1.26..3..2.64137884372.16.17683...2 B8: 5,9,4,7 # reduction candidate for 5,9 B8: 5,9 # 13 pairs B9: 5,9,4,7 # reduction candidate for 5,9 B9: 5,9 => CTR * 461382.572879..4133..1742867325486916497138255182..73492465137887342.16.1.6837.42 * RESTART * PAIR RESTART * PAIR C3: 5,9 COL C C5: 5,9,8 # reduction candidate for 5,9 C5: 5,9 => SOLVED * 461382957287965413395174286732548691649713825518296734924651378853427169176839542 * DURATION: 0:00:05.781023 START: 08:00:13.692181 END: 08:00:19.473204 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-153-base-pr-001.dot * REASONING * DIS # B5: 5,9 => CTR => B5: 4,7 * DIS B5: 4,7 # B9: 5,9 => CTR => B9: 4,7 * PRF B5: 4,7 + B9: 4,7 # C5: 5,9 => SOL * STA B5: 4,7 + B9: 4,7 + C5: 5,9 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 153 solution: 461382957287965413395174286732548691649713825518296734924651378853427169176839542 info: 1817 FNBWXY S8.f 21418 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 461382957287965413395174286732548691649713825518296734924651378853427169176839542 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 # B5: 5,9 => CTR => B5: 4,7 * INC # B5: 4,7 => UNS * INC # B8: 5,9 => UNS * DIS # B9: 5,9 => CTR => B9: 4,7 * INC # B9: 4,7 => UNS * PRF # C5: 5,9 => SOL * INC # C5: 4,8 => UNS * DIS # C6: 5,9 => CTR => C6: 4,8 * INC # C6: 4,8 => UNS * INC # C7: 5,9 => UNS * INC # E4: 4,7 => UNS * DIS # E6: 4,7 => CTR => E6: 6,9 * INC # E6: 6,9 => UNS * DIS # E7: 4,7 => CTR => E7: 5,9 * INC # E7: 5,9 => UNS * DIS # F6: 4,7 => CTR => F6: 6,9 * INC # F6: 6,9 => UNS * PRF # F8: 4,7 => SOL * INC # F8: 5,9 => UNS * INC # F9: 4,7 => UNS * INC # B5: 7,9 => UNS * INC # A6: 7,9 => UNS * DIS # E4: 7,9 => CTR => E4: 4 * PRF # E4: 4 => SOL * PRF # H4: 7,9 => SOL * DIS # H4: 4 => CTR => H4: 7,9 * INC # A7: 7,9 => UNS * INC # A7: 5 => UNS * INC # E4: 4,7 => UNS * DIS # E6: 4,7 => CTR => E6: 6,9 * INC # E6: 6,9 => UNS * DIS # F6: 4,7 => CTR => F6: 6,9 * INC # F6: 6,9 => UNS * INC # B5: 4,7 => UNS * DIS # I5: 4,7 => CTR => I5: 5,9 * INC # I5: 5,9 => UNS * DIS # E7: 4,7 => CTR => E7: 5,9 * INC # E7: 5,9 => UNS * PRF # F8: 4,7 => SOL * INC # F8: 5,9 => UNS * INC # F9: 4,7 => UNS * DIS # B8: 4,7 => CTR => B8: 5,9 * INC # B8: 5,9 => UNS * INC # I8: 4,7 => UNS * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B5: 5,9 => CTR => B5: 4,7 * INC B5: 4,7 # B8: 5,9 => UNS * DIS B5: 4,7 # B9: 5,9 => CTR => B9: 4,7 * PRF B5: 4,7 + B9: 4,7 # C5: 5,9 => SOL * STA B5: 4,7 + B9: 4,7 + C5: 5,9 * CNT 4 HDP CHAINS / 4 HYP OPENED