Analysis of xx-top500-186-base.sdk
Contents
Original Sudoku
level: medium
position: ...4.5...7.....3........1..3..7.........8..6.....3...5.65..8......2..7...4....... initial
Autosolve
position: ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E1: 2 => SOL * DIS # B2: 2 => CTR => B2: 1,9 * PRF # E1: 2,9 => SOL * PRF # B2: 2,9 => SOL * DIS # I4: 2,9 => CTR => I4: 1 * DIS # C5: 2,9 => CTR => C5: 1 * DIS # I4: 2,9 => CTR => I4: 1 * DIS # I4: 2,9 => CTR => I4: 1 * DIS # C5: 2,9 => CTR => C5: 1 * DIS # A7: 2 => CTR => A7: 1,9 * DIS # A9: 1,9 => CTR => A9: 2,8 * PRF # E1: 2 => SOL * PRF # A7: 1 => SOL * CNT 13 HDP CHAINS / 48 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E1: 2 => SOL * STA E1: 2 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...4.5...7.....3........1..3..7.........8..6.....3...5.65..8......2..7...4....... | initial |
| ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35.. | autosolve |
| 813425697794861352526397148359746821471582963682139475165978234938254716247613589 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) F2: 1,9 E3: 2,9 I2: 2,9 C4: 2,9 D6: 1,9 G5: 2,9 D7: 1,9 E9: 1,9 G7: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F2: 1.. / E1 = 1 => 16 pairs (_) / F2 = 1 => 0 pairs (*) H4,I4: 1.. / H4 = 1 => 0 pairs (X) / I4 = 1 => 10 pairs (_) D7,E9: 1.. / D7 = 1 => 16 pairs (_) / E9 = 1 => 0 pairs (*) B2,F2: 1.. / B2 = 1 => 16 pairs (_) / F2 = 1 => 0 pairs (*) C5,F5: 1.. / C5 = 1 => 10 pairs (_) / F5 = 1 => 0 pairs (X) A7,D7: 1.. / A7 = 1 => 0 pairs (*) / D7 = 1 => 0 pairs (X) D6,D7: 1.. / D6 = 1 => 0 pairs (*) / D7 = 1 => 0 pairs (X) E1,E9: 1.. / E1 = 1 => 16 pairs (_) / E9 = 1 => 0 pairs (*) I4,I9: 1.. / I4 = 1 => 10 pairs (_) / I9 = 1 => 0 pairs (X) E1,E3: 2.. / E1 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) F5,F6: 2.. / F5 = 2 => 14 pairs (_) / F6 = 2 => 10 pairs (_) A7,A9: 2.. / A7 = 2 => 0 pairs (X) / A9 = 2 => 12 pairs (_) B2,I2: 2.. / B2 = 2 => 0 pairs (X) / I2 = 2 => 12 pairs (_) A7,G7: 2.. / A7 = 2 => 0 pairs (X) / G7 = 2 => 12 pairs (_) G5,G7: 2.. / G5 = 2 => 0 pairs (X) / G7 = 2 => 12 pairs (_) B1,C1: 3.. / B1 = 3 => 9 pairs (_) / C1 = 3 => 9 pairs (_) B8,C8: 3.. / B8 = 3 => 9 pairs (_) / C8 = 3 => 9 pairs (_) B1,B8: 3.. / B1 = 3 => 9 pairs (_) / B8 = 3 => 9 pairs (_) C1,C8: 3.. / C1 = 3 => 9 pairs (_) / C8 = 3 => 9 pairs (_) H1,I3: 8.. / H1 = 8 => 13 pairs (_) / I3 = 8 => 11 pairs (_) B6,C6: 8.. / B6 = 8 => 13 pairs (_) / C6 = 8 => 9 pairs (_) B3,I3: 8.. / B3 = 8 => 13 pairs (_) / I3 = 8 => 11 pairs (_) I3,I9: 8.. / I3 = 8 => 11 pairs (_) / I9 = 8 => 13 pairs (_) D7,E9: 9.. / D7 = 9 => 0 pairs (*) / E9 = 9 => 0 pairs (X) D6,D7: 9.. / D6 = 9 => 16 pairs (_) / D7 = 9 => 0 pairs (*) G5,G7: 9.. / G5 = 9 => 12 pairs (_) / G7 = 9 => 0 pairs (X) * DURATION: 0:00:43.046360 START: 09:02:41.825250 END: 09:03:24.871610 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,D6,D7,E3,E9,F2,G5,G7,I2) * ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35.. * PAIR F2: 1,9 BLK 2 E1: 1,9,2 # reduction candidate for 1,9 E1: 2 => SOLVED * 813425697794861352526397148359746821471582963682139475165978234938254716247613589 E1: 1,9 # 11 pairs * PAIR F2: 1,9 ROW 2 B2: 1,9,2 # reduction candidate for 1,9 B2: 2 => CTR * .134.56877248613595863971423597468..47158..636..13.475165978234...254716247613598 B2: 1,9 # 12 pairs * PAIR F2: 1,9 COL F F5: 1,9,2 # reduction candidate for 1,9 F5: 1,9 # 10 pairs F6: 1,9,2 # reduction candidate for 1,9 F6: 1,9 # 14 pairs * PAIR E3: 2,9 BLK 2 E1: 2,9,1 # reduction candidate for 2,9 E1: 2,9 => SOLVED * 813425697794861352526397148359746821471582963682139475165978234938254716247613589 E1: 1 # 16 pairs * PAIR E3: 2,9 ROW 3 B3: 2,9,8 # reduction candidate for 2,9 B3: 2,9 # 11 pairs I3: 2,9,8 # reduction candidate for 2,9 I3: 2,9 # 13 pairs * PAIR I2: 2,9 BLK 3 H1: 2,9,8 # reduction candidate for 2,9 H1: 2,9 # 11 pairs I3: 2,9,8 # reduction candidate for 2,9 I3: 2,9 # 13 pairs * PAIR I2: 2,9 ROW 2 B2: 2,9,1 # reduction candidate for 2,9 B2: 2,9 => SOLVED * 813425697794861352526397148359746821471582963682139475165978234938254716247613589 B2: 1 # 16 pairs * PAIR I2: 2,9 COL I I4: 2,9,1 # reduction candidate for 2,9 I4: 2,9 => CTR * ...4156.77148693525.632714835274681947958126368193247526517893419.2547.6.476.35.1 I4: 1 # 10 pairs I9: 2,9,1,8 # reduction candidate for 2,9 I9: 2,9 # 16 pairs * PAIR C4: 2,9 BLK 4 C5: 2,9,1 # reduction candidate for 2,9 C5: 2,9 => CTR * .234156.771486935259632714835.7468.9479581263681932475265178934938254716.476935.. C5: 1 # 10 pairs B6: 2,9,1,8 # reduction candidate for 2,9 B6: 2,9 # 12 pairs C6: 2,9,1,8 # reduction candidate for 2,9 C6: 2,9 # 15 pairs * PAIR C4: 2,9 ROW 4 H4: 2,9,1 # reduction candidate for 2,9 H4: 2,9 # 10 pairs I4: 2,9,1 # reduction candidate for 2,9 I4: 2,9 => CTR * ...4156.77148693525.632714835274681947958126368193247526517893419.2547.6.476.35.1 I4: 1 # 10 pairs * PAIR C4: 2,9 COL C C1: 2,9,1,3,8 # reduction candidate for 2,9 C1: 2,9 # 12 pairs C1: 1,3,8 # 9 pairs * PAIR D6: 1,9 BLK 5 F5: 1,9,2 # reduction candidate for 1,9 F5: 1,9 # 10 pairs F6: 1,9,2 # reduction candidate for 1,9 F6: 1,9 # 14 pairs * PAIR D6: 1,9 ROW 6 B6: 1,9,2,8 # reduction candidate for 1,9 B6: 1,9 # 11 pairs C6: 1,9,2,8 # reduction candidate for 1,9 C6: 1,9 # 15 pairs * PAIR G5: 2,9 BLK 6 H4: 2,9,1 # reduction candidate for 2,9 H4: 2,9 # 10 pairs I4: 2,9,1 # reduction candidate for 2,9 I4: 2,9 => CTR * ...4156.77148693525.632714835274681947958126368193247526517893419.2547.6.476.35.1 I4: 1 # 10 pairs * PAIR G5: 2,9 ROW 5 C5: 2,9,1 # reduction candidate for 2,9 C5: 2,9 => CTR * .234156.771486935259632714835.7468.9479581263681932475265178934938254716.476935.. C5: 1 # 10 pairs F5: 2,9,1 # reduction candidate for 2,9 F5: 2,9 # 10 pairs * PAIR D7: 1,9 ROW 7 A7: 1,9,2 # reduction candidate for 1,9 A7: 2 => CTR * .234156.77148693525.632714.3527468..479581263681932475265178934.38254716147693528 A7: 1,9 # 12 pairs * PAIR E9: 1,9 ROW 9 A9: 1,9,2,8 # reduction candidate for 1,9 A9: 1,9 => CTR * .2341568771486935258632714.35.7468..4795812636.1932475265178934...2547.6147693528 A9: 2,8 # 10 pairs H9: 1,9,2,8 # reduction candidate for 1,9 H9: 1,9 # 14 pairs I9: 1,9,2,8 # reduction candidate for 1,9 I9: 1,9 # 14 pairs * PAIR E9: 1,9 COL E E1: 1,9,2 # reduction candidate for 1,9 E1: 2 => SOLVED * 813425697794861352526397148359746821471582963682139475165978234938254716247613589 E1: 1,9 # 11 pairs * PAIR G7: 2,9 BLK 9 H9: 2,9,1,8 # reduction candidate for 2,9 H9: 2,9 # 13 pairs I9: 2,9,1,8 # reduction candidate for 2,9 I9: 2,9 # 16 pairs * PAIR G7: 2,9 ROW 7 A7: 2,9,1 # reduction candidate for 2,9 A7: 1 => SOLVED * 813425697794861352526397148359746821471582963682139475165978234938254716247613589 A7: 2,9 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-186-base-pr-000.dot * REASONING * PRF # E1: 2 => SOL * DIS # B2: 2 => CTR => B2: 1,9 * PRF # E1: 2,9 => SOL * PRF # B2: 2,9 => SOL * DIS # I4: 2,9 => CTR => I4: 1 * DIS # C5: 2,9 => CTR => C5: 1 * DIS # I4: 2,9 => CTR => I4: 1 * DIS # I4: 2,9 => CTR => I4: 1 * DIS # C5: 2,9 => CTR => C5: 1 * DIS # A7: 2 => CTR => A7: 1,9 * DIS # A9: 1,9 => CTR => A9: 2,8 * PRF # E1: 2 => SOL * PRF # A7: 1 => SOL * CNT 13 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C4,D6,D7,E3,E9,F2,G5,G7,I2) * ...4.56.77.486.35.5.63.714.35.7468..47.58..636...3.475.65.78.34...2547.6.476.35.. * PAIR F2: 1,9 BLK 2 E1: 1,9,2 # reduction candidate for 1,9 E1: 2 => SOLVED * 813425697794861352526397148359746821471582963682139475165978234938254716247613589 * DURATION: 0:00:02.765281 START: 09:04:08.569984 END: 09:04:11.335265 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-186-base-pr-001.dot * REASONING * PRF # E1: 2 => SOL * STA E1: 2 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 186 solution: 813425697794861352526397148359746821471582963682139475165978234938254716247613589 info: 1835 FNBTWXY S8.f 9305 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 813425697794861352526397148359746821471582963682139475165978234938254716247613589 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 # E1: 1,9 => UNS * PRF # E1: 2 => SOL * INC # B2: 1,9 => UNS * DIS # B2: 2 => CTR => B2: 1,9 * INC # F5: 1,9 => UNS * INC # F6: 1,9 => UNS * PRF # E1: 2,9 => SOL * INC # E1: 1 => UNS * INC # B3: 2,9 => UNS * INC # I3: 2,9 => UNS * INC # H1: 2,9 => UNS * INC # I3: 2,9 => UNS * PRF # B2: 2,9 => SOL * INC # B2: 1 => UNS * DIS # I4: 2,9 => CTR => I4: 1 * INC # I4: 1 => UNS * INC # I9: 2,9 => UNS * DIS # C5: 2,9 => CTR => C5: 1 * INC # C5: 1 => UNS * INC # B6: 2,9 => UNS * INC # C6: 2,9 => UNS * INC # H4: 2,9 => UNS * DIS # I4: 2,9 => CTR => I4: 1 * INC # I4: 1 => UNS * INC # C1: 2,9 => UNS * INC # C1: 1,3,8 => UNS * INC # F5: 1,9 => UNS * INC # F6: 1,9 => UNS * INC # B6: 1,9 => UNS * INC # C6: 1,9 => UNS * INC # H4: 2,9 => UNS * DIS # I4: 2,9 => CTR => I4: 1 * INC # I4: 1 => UNS * DIS # C5: 2,9 => CTR => C5: 1 * INC # C5: 1 => UNS * INC # F5: 2,9 => UNS * INC # A7: 1,9 => UNS * DIS # A7: 2 => CTR => A7: 1,9 * DIS # A9: 1,9 => CTR => A9: 2,8 * INC # A9: 2,8 => UNS * INC # H9: 1,9 => UNS * INC # I9: 1,9 => UNS * INC # E1: 1,9 => UNS * PRF # E1: 2 => SOL * INC # H9: 2,9 => UNS * INC # I9: 2,9 => UNS * INC # A7: 2,9 => UNS * PRF # A7: 1 => SOL * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 1,9 => UNS * PRF # E1: 2 => SOL * STA E1: 2 * CNT 2 HDP CHAINS / 2 HYP OPENED