Analysis of xx-top500-149-base.sdk
Contents
Original Sudoku
level: medium
position: .87.4........7..1....6.....3..1.2...5.....7.4......8..1..3......5....4........... initial
Autosolve
position: .875413.24.527..18..16.8547374182.5.5189..724...75483114.3.728575281.4.38.342517. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # A6: 2 => CTR => A6: 6,9 * DIS # B3: 2,9 => CTR => B3: 3 * PRF # B3: 3 => SOL * PRF # A6: 2,9 => SOL * DIS # A6: 6 => CTR => A6: 2,9 * PRF # B2: 3,9 => SOL * DIS # B2: 6 => CTR => B2: 3,9 * DIS # B3: 2 => CTR => B3: 3,9 * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # B6: 6,9 => CTR => B6: 2 * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # B6: 6,9 => CTR => B6: 2 * CNT 16 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B2: 6,9 => SOL * STA B2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .87.4........7..1....6.....3..1.2...5.....7.4......8..1..3......5....4........... | initial |
| .875413.24.527..18..16.8547374182.5.5189..724...75483114.3.728575281.4.38.342517. | autosolve |
| 687541392495273618231698547374182956518936724926754831149367285752819463863425179 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) A1: 6,9 A3: 2,9 F2: 3,9 E3: 3,9 H1: 6,9 G2: 6,9 C6: 6,9 E5: 3,6 F5: 3,6 G4: 6,9 I4: 6,9 C7: 6,9 B9: 6,9 E7: 6,9 F8: 6,9 H8: 6,9 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 2.. / A3 = 2 => 18 pairs (_) / B3 = 2 => 0 pairs (X) A6,B6: 2.. / A6 = 2 => 0 pairs (X) / B6 = 2 => 18 pairs (_) A3,A6: 2.. / A3 = 2 => 18 pairs (_) / A6 = 2 => 0 pairs (X) B3,B6: 2.. / B3 = 2 => 0 pairs (X) / B6 = 2 => 18 pairs (_) B2,B3: 3.. / B2 = 3 => 0 pairs (X) / B3 = 3 => 0 pairs (_) F2,E3: 3.. / F2 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) E5,F5: 3.. / E5 = 3 => 0 pairs (*) / F5 = 3 => 0 pairs (X) B2,F2: 3.. / B2 = 3 => 0 pairs (X) / F2 = 3 => 0 pairs (_) B3,E3: 3.. / B3 = 3 => 0 pairs (*) / E3 = 3 => 0 pairs (X) E3,E5: 3.. / E3 = 3 => 0 pairs (X) / E5 = 3 => 0 pairs (_) F2,F5: 3.. / F2 = 3 => 0 pairs (*) / F5 = 3 => 0 pairs (X) A1,B2: 6.. / A1 = 6 => 0 pairs (*) / B2 = 6 => 0 pairs (X) H1,G2: 6.. / H1 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) E5,F5: 6.. / E5 = 6 => 0 pairs (X) / F5 = 6 => 0 pairs (_) G4,I4: 6.. / G4 = 6 => 0 pairs (X) / I4 = 6 => 0 pairs (_) C7,B9: 6.. / C7 = 6 => 0 pairs (X) / B9 = 6 => 0 pairs (_) E7,F8: 6.. / E7 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) H8,I9: 6.. / H8 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A1,H1: 6.. / A1 = 6 => 0 pairs (*) / H1 = 6 => 0 pairs (X) B2,G2: 6.. / B2 = 6 => 0 pairs (X) / G2 = 6 => 0 pairs (_) C7,E7: 6.. / C7 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) F8,H8: 6.. / F8 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) B9,I9: 6.. / B9 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) A1,A6: 6.. / A1 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) C6,C7: 6.. / C6 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) E5,E7: 6.. / E5 = 6 => 0 pairs (X) / E7 = 6 => 0 pairs (_) F5,F8: 6.. / F5 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) G2,G4: 6.. / G2 = 6 => 0 pairs (*) / G4 = 6 => 0 pairs (X) H1,H8: 6.. / H1 = 6 => 0 pairs (X) / H8 = 6 => 0 pairs (_) I4,I9: 6.. / I4 = 6 => 0 pairs (*) / I9 = 6 => 0 pairs (X) F2,E3: 9.. / F2 = 9 => 0 pairs (X) / E3 = 9 => 0 pairs (_) H1,G2: 9.. / H1 = 9 => 0 pairs (*) / G2 = 9 => 0 pairs (X) G4,I4: 9.. / G4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) C7,B9: 9.. / C7 = 9 => 0 pairs (*) / B9 = 9 => 0 pairs (X) E7,F8: 9.. / E7 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) H8,I9: 9.. / H8 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) A1,H1: 9.. / A1 = 9 => 0 pairs (X) / H1 = 9 => 0 pairs (_) C7,E7: 9.. / C7 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) F8,H8: 9.. / F8 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) B9,I9: 9.. / B9 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) C6,C7: 9.. / C6 = 9 => 0 pairs (X) / C7 = 9 => 0 pairs (_) E3,E7: 9.. / E3 = 9 => 0 pairs (*) / E7 = 9 => 0 pairs (X) F2,F8: 9.. / F2 = 9 => 0 pairs (X) / F8 = 9 => 0 pairs (_) G2,G4: 9.. / G2 = 9 => 0 pairs (X) / G4 = 9 => 0 pairs (_) H1,H8: 9.. / H1 = 9 => 0 pairs (*) / H8 = 9 => 0 pairs (X) I4,I9: 9.. / I4 = 9 => 0 pairs (X) / I9 = 9 => 0 pairs (_) * DURATION: 0:01:22.476165 START: 07:50:13.809595 END: 07:51:36.285760 2017-05-04 * CP COUNT: (46) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B9,C6,C7,E3,E5,E7,F2,F5,F8,G2,G4,H1,H8,I4,I9) * .875413.24.527..18..16.8547374182.5.5189..724...75483114.3.728575281.4.38.342517. * PAIR A1: 6,9 BLK 1 B2: 6,9,3 # reduction candidate for 6,9 B2: 6,9 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 B2: 3 => CTR * 687541392435279618..1638547374182956518963724...7548311463972857528164.38.342517. * PAIR A1: 6,9 COL A A6: 6,9,2 # reduction candidate for 6,9 A6: 2 => CTR * 6875413924.527.618921638547374182956518963724...75483114.3.728575281.4.38.342517. A6: 6,9 # 18 pairs * PAIR A3: 2,9 BLK 1 B3: 2,9,3 # reduction candidate for 2,9 B3: 2,9 => CTR * .875413.2435279618..1638547374182956518963724...7548311463972857528164.38.342517. B3: 3 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 * PAIR A3: 2,9 COL A A6: 2,9,6 # reduction candidate for 2,9 A6: 2,9 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 A6: 6 => CTR * .875413.24.527..182.16.8547374182.5.5189..724629754831146397285752816493893425176 * PAIR F2: 3,9 ROW 2 B2: 3,9,6 # reduction candidate for 3,9 B2: 3,9 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 B2: 6 => CTR * .875413.2465273918.3169854737418265951893672462975483114.3.728575281.4.38.342517. * PAIR E3: 3,9 ROW 3 B3: 3,9,2 # reduction candidate for 3,9 B3: 2 => CTR * .875413.24352796189216385473741829565189637242..7548311463972857528164.38.342517. B3: 3,9 # 18 pairs * PAIR G2: 6,9 ROW 2 B2: 6,9,3 # reduction candidate for 6,9 B2: 6,9 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 B2: 3 => CTR * 687541392435279618..1638547374182956518963724...7548311463972857528164.38.342517. * PAIR C6: 6,9 BLK 4 A6: 6,9,2 # reduction candidate for 6,9 A6: 6,9 # 18 pairs B6: 6,9,2 # reduction candidate for 6,9 B6: 6,9 => CTR * .875413.24.527..18.21638547374182.5.5189637242..754831146397285752816493893425176 B6: 2 # 18 pairs * PAIR B9: 6,9 COL B B2: 6,9,3 # reduction candidate for 6,9 B2: 6,9 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 B2: 3 => CTR * 687541392435279618..1638547374182956518963724...7548311463972857528164.38.342517. B6: 6,9,2 # reduction candidate for 6,9 B6: 6,9 => CTR * .875413.24.527..18.21638547374182.5.5189637242..754831146397285752816493893425176 B6: 2 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-149-base-pr-000.dot * REASONING * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # A6: 2 => CTR => A6: 6,9 * DIS # B3: 2,9 => CTR => B3: 3 * PRF # B3: 3 => SOL * PRF # A6: 2,9 => SOL * DIS # A6: 6 => CTR => A6: 2,9 * PRF # B2: 3,9 => SOL * DIS # B2: 6 => CTR => B2: 3,9 * DIS # B3: 2 => CTR => B3: 3,9 * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # B6: 6,9 => CTR => B6: 2 * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # B6: 6,9 => CTR => B6: 2 * CNT 16 HDP CHAINS / 21 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B9,C6,C7,E3,E5,E7,F2,F5,F8,G2,G4,H1,H8,I4,I9) * .875413.24.527..18..16.8547374182.5.5189..724...75483114.3.728575281.4.38.342517. * PAIR A1: 6,9 BLK 1 B2: 6,9,3 # reduction candidate for 6,9 B2: 6,9 => SOLVED * 687541392495273618231698547374182956518936724926754831149367285752819463863425179 * DURATION: 0:00:01.962699 START: 07:52:03.857667 END: 07:52:05.820366 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-149-base-pr-001.dot * REASONING * PRF # B2: 6,9 => SOL * STA B2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 149 solution: 687541392495273618231698547374182956518936724926754831149367285752819463863425179 info: 1816 FNBWX S8.f 24270 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 687541392495273618231698547374182956518936724926754831149367285752819463863425179 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 # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * INC # A6: 6,9 => UNS * DIS # A6: 2 => CTR => A6: 6,9 * DIS # B3: 2,9 => CTR => B3: 3 * PRF # B3: 3 => SOL * PRF # A6: 2,9 => SOL * DIS # A6: 6 => CTR => A6: 2,9 * PRF # B2: 3,9 => SOL * DIS # B2: 6 => CTR => B2: 3,9 * INC # B3: 3,9 => UNS * DIS # B3: 2 => CTR => B3: 3,9 * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * INC # A6: 6,9 => UNS * DIS # B6: 6,9 => CTR => B6: 2 * INC # B6: 2 => UNS * PRF # B2: 6,9 => SOL * DIS # B2: 3 => CTR => B2: 6,9 * DIS # B6: 6,9 => CTR => B6: 2 * INC # B6: 2 => UNS * CNT 21 HDP CHAINS / 21 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B2: 6,9 => SOL * STA B2: 6,9 * CNT 1 HDP CHAINS / 1 HYP OPENED