Analysis of xx-top500-150-base.sdk
Contents
Original Sudoku
level: medium
position: 3...6.......1..8..........5....3.96...5...4...1..........5.2..79......3....8..... initial
Autosolve
position: 35..6.719..615.8.31..3..6.58...35961.359..47..19...35.4635921879.....534571843296 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C3: 2,7 => SOL * DIS # C3: 4,8 => CTR => C3: 2,7 * DIS # A6: 6 => CTR => A6: 2,7 * PRF # C1: 8 => SOL * PRF # D6: 2,4 => SOL * DIS # D6: 6,7 => CTR => D6: 2,4 * DIS # F3: 4,8 => CTR => F3: 7,9 * PRF # C1: 4,8 => SOL * DIS # C1: 2 => CTR => C1: 4,8 * PRF # F6: 6,7 => SOL * DIS # B2: 2,4 => CTR => B2: 9 * PRF # B3: 2,4 => SOL * DIS # C3: 2,4 => CTR => C3: 7,8 * PRF # C4: 2,4 => SOL * DIS # C4: 7 => CTR => C4: 2,4 * DIS # B2: 2,4 => CTR => B2: 9 * PRF # B3: 2,4 => SOL * DIS # A6: 2,6 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # D6: 2,7 => CTR => D6: 4,6 * PRF # C4: 4 => SOL * DIS # E6: 7 => CTR => E6: 2,8 * PRF # B3: 4,9 => SOL * DIS # C3: 2,8 => CTR => C3: 4,7 * DIS # D6: 6,7 => CTR => D6: 2,4 * PRF # D6: 2,4 => SOL * DIS # F8: 6 => CTR => F8: 1,7 * CNT 27 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 # C3: 2,7 => SOL * STA C3: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3...6.......1..8..........5....3.96...5...4...1..........5.2..79......3....8..... | initial |
| 35..6.719..615.8.31..3..6.58...35961.359..47..19...35.4635921879.....534571843296 | autosolve |
| 358264719296157843147389625824735961635918472719426358463592187982671534571843296 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) A2: 2,7 D1: 2,4 F1: 4,8 H2: 2,4 H3: 2,4 B4: 2,4 A5: 2,6 D4: 2,7 I5: 2,8 I6: 2,8 B8: 2,8 C8: 2,8 D8: 6,7 E8: 1,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E5,F5: 1.. / E5 = 1 => 23 pairs (_) / F5 = 1 => 18 pairs (_) E8,F8: 1.. / E8 = 1 => 18 pairs (_) / F8 = 1 => 23 pairs (_) E5,E8: 1.. / E5 = 1 => 23 pairs (_) / E8 = 1 => 18 pairs (_) F5,F8: 1.. / F5 = 1 => 18 pairs (_) / F8 = 1 => 23 pairs (_) D1,E3: 2.. / D1 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) H2,H3: 2.. / H2 = 2 => 0 pairs (X) / H3 = 2 => 0 pairs (_) I5,I6: 2.. / I5 = 2 => 17 pairs (_) / I6 = 2 => 16 pairs (_) B8,C8: 2.. / B8 = 2 => 15 pairs (_) / C8 = 2 => 0 pairs (*) C1,D1: 2.. / C1 = 2 => 0 pairs (X) / D1 = 2 => 0 pairs (_) H2,H3: 4.. / H2 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) B4,C4: 4.. / B4 = 4 => 15 pairs (_) / C4 = 4 => 0 pairs (*) D6,F6: 4.. / D6 = 4 => 0 pairs (*) / F6 = 4 => 0 pairs (X) D1,D6: 4.. / D1 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) A5,A6: 6.. / A5 = 6 => 17 pairs (_) / A6 = 6 => 0 pairs (X) D8,F8: 6.. / D8 = 6 => 18 pairs (_) / F8 = 6 => 0 pairs (X) A5,F5: 6.. / A5 = 6 => 17 pairs (_) / F5 = 6 => 0 pairs (X) D6,D8: 6.. / D6 = 6 => 0 pairs (X) / D8 = 6 => 18 pairs (_) A2,C3: 7.. / A2 = 7 => 0 pairs (X) / C3 = 7 => 0 pairs (_) C4,A6: 7.. / C4 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) A2,F2: 7.. / A2 = 7 => 0 pairs (X) / F2 = 7 => 0 pairs (_) C4,D4: 7.. / C4 = 7 => 0 pairs (X) / D4 = 7 => 0 pairs (_) A2,A6: 7.. / A2 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) C3,C4: 7.. / C3 = 7 => 0 pairs (*) / C4 = 7 => 0 pairs (X) I5,I6: 8.. / I5 = 8 => 16 pairs (_) / I6 = 8 => 17 pairs (_) B8,C8: 8.. / B8 = 8 => 0 pairs (*) / C8 = 8 => 0 pairs (X) C1,F1: 8.. / C1 = 8 => 0 pairs (*) / F1 = 8 => 0 pairs (X) B3,B8: 8.. / B3 = 8 => 15 pairs (_) / B8 = 8 => 0 pairs (*) B2,B3: 9.. / B2 = 9 => 15 pairs (_) / B3 = 9 => 0 pairs (X) F2,F3: 9.. / F2 = 9 => 0 pairs (X) / F3 = 9 => 15 pairs (_) B2,F2: 9.. / B2 = 9 => 15 pairs (_) / F2 = 9 => 0 pairs (X) B3,F3: 9.. / B3 = 9 => 0 pairs (X) / F3 = 9 => 15 pairs (_) * DURATION: 0:01:02.352701 START: 07:52:37.114049 END: 07:53:39.466750 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B4,B8,C8,D1,D4,D8,E8,F1,H2,H3,I5,I6) * 35..6.719..615.8.31..3..6.58...35961.359..47..19...35.4635921879.....534571843296 * PAIR A2: 2,7 BLK 1 C3: 2,7,4,8 # reduction candidate for 2,7 C3: 2,7 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 C3: 4,8 => CTR * 3524687197.615982319.3..6.58.7235961.359..47..19...35.4635921879.....534571843296 * PAIR A2: 2,7 COL A A6: 2,7,6 # reduction candidate for 2,7 A6: 6 => CTR * 3524687197.615982319.3..6.58.72359612359.6478619...3524635921879..6.1534571843296 A6: 2,7 # 17 pairs * PAIR D1: 2,4 ROW 1 C1: 2,4,8 # reduction candidate for 2,4 C1: 8 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 C1: 2,4 # 16 pairs * PAIR D1: 2,4 COL D D6: 2,4,6,7 # reduction candidate for 2,4 D6: 2,4 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 D6: 6,7 => CTR * 35.468719..615.8.31..32.6458.4.35961.359..47..19...35.4635921879.....534571843296 * PAIR F1: 4,8 BLK 2 F3: 4,8,7,9 # reduction candidate for 4,8 F3: 4,8 => CTR * 35..6.719..61598.319.37.6.58.7235961.359..47..19.8.352463592187982.1.534571843296 F3: 7,9 # 15 pairs * PAIR F1: 4,8 ROW 1 C1: 4,8,2 # reduction candidate for 4,8 C1: 4,8 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 C1: 2 => CTR * 3524687197.61598231983..6.58...35961.359..47..19...35.4635921879.....534571843296 * PAIR F1: 4,8 COL F F6: 4,8,6,7 # reduction candidate for 4,8 F6: 6,7 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 F6: 4,8 # 23 pairs * PAIR H2: 2,4 ROW 2 B2: 2,4,9 # reduction candidate for 2,4 B2: 2,4 => CTR * 35.26.71972615984319.3..625847.35961.359..47..19...35.463592187982...534571843296 B2: 9 # 15 pairs * PAIR H3: 2,4 ROW 3 B3: 2,4,8,9 # reduction candidate for 2,4 B3: 2,4 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 B3: 8,9 # 15 pairs C3: 2,4,7,8 # reduction candidate for 2,4 C3: 2,4 => CTR * 3524687197.61598231..3..6.58.7235961.359..47..19...35.4635921879.....534571843296 C3: 7,8 # 15 pairs * PAIR B4: 2,4 BLK 4 C4: 2,4,7 # reduction candidate for 2,4 C4: 2,4 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 C4: 7 => CTR * 3524687197.615.8.31..3..6.5847235961.359..47..19...35.4635921879.....534571843296 * PAIR B4: 2,4 COL B B2: 2,4,9 # reduction candidate for 2,4 B2: 2,4 => CTR * 35.26.71972615984319.3..625847.35961.359..47..19...35.463592187982...534571843296 B2: 9 # 15 pairs B3: 2,4,8,9 # reduction candidate for 2,4 B3: 2,4 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 B3: 8,9 # 15 pairs * PAIR A5: 2,6 BLK 4 A6: 2,6,7 # reduction candidate for 2,6 A6: 2,6 => CTR * 3524687197.615982319.3..6.58.7235961.359..47..19...35.4635921879.....534571843296 A6: 7 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 * PAIR D4: 2,7 BLK 5 D6: 2,7,4,6 # reduction candidate for 2,7 D6: 2,7 => CTR * 35.468719..615.8.31..32.6458.4735961.359..47.7192..35.4635921879.....534571843296 D6: 4,6 # 15 pairs E6: 2,7,8 # reduction candidate for 2,7 E6: 2,7 # 17 pairs * PAIR D4: 2,7 ROW 4 C4: 2,7,4 # reduction candidate for 2,7 C4: 4 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 C4: 2,7 # 15 pairs * PAIR I5: 2,8 ROW 5 E5: 2,8,1 # reduction candidate for 2,8 E5: 1 # 23 pairs E5: 2,8 # 18 pairs * PAIR I6: 2,8 ROW 6 E6: 2,8,7 # reduction candidate for 2,8 E6: 7 => CTR * 3524687197.615982319.3.76.58.72359616359814722196743584635921879..716534571843296 E6: 2,8 # 16 pairs * PAIR B8: 2,8 COL B B3: 2,8,4,9 # reduction candidate for 2,8 B3: 4,9 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 B3: 2,8 # 16 pairs * PAIR C8: 2,8 COL C C1: 2,8,4 # reduction candidate for 2,8 C1: 2,8 # 18 pairs C3: 2,8,4,7 # reduction candidate for 2,8 C3: 2,8 => CTR * 35..6.7197.615.8.31..3..6.58.7235961.359..47..19...35.4635921879.....534571843296 C3: 4,7 # 15 pairs * PAIR D8: 6,7 BLK 8 F8: 6,7,1 # reduction candidate for 6,7 F8: 1 # 23 pairs F8: 6,7 # 18 pairs * PAIR D8: 6,7 COL D D6: 6,7,2,4 # reduction candidate for 6,7 D6: 6,7 => CTR * 35.468719..615.8.31..32.6458.4.35961.359..47..19...35.4635921879.....534571843296 D6: 2,4 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 * PAIR E8: 1,7 BLK 8 F8: 1,7,6 # reduction candidate for 1,7 F8: 6 => CTR * 35.468719..615.8.31..32.6458...359616359.147..196.435.4635921879..716534571843296 F8: 1,7 # 18 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-150-base-pr-000.dot * REASONING * PRF # C3: 2,7 => SOL * DIS # C3: 4,8 => CTR => C3: 2,7 * DIS # A6: 6 => CTR => A6: 2,7 * PRF # C1: 8 => SOL * PRF # D6: 2,4 => SOL * DIS # D6: 6,7 => CTR => D6: 2,4 * DIS # F3: 4,8 => CTR => F3: 7,9 * PRF # C1: 4,8 => SOL * DIS # C1: 2 => CTR => C1: 4,8 * PRF # F6: 6,7 => SOL * DIS # B2: 2,4 => CTR => B2: 9 * PRF # B3: 2,4 => SOL * DIS # C3: 2,4 => CTR => C3: 7,8 * PRF # C4: 2,4 => SOL * DIS # C4: 7 => CTR => C4: 2,4 * DIS # B2: 2,4 => CTR => B2: 9 * PRF # B3: 2,4 => SOL * DIS # A6: 2,6 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # D6: 2,7 => CTR => D6: 4,6 * PRF # C4: 4 => SOL * DIS # E6: 7 => CTR => E6: 2,8 * PRF # B3: 4,9 => SOL * DIS # C3: 2,8 => CTR => C3: 4,7 * DIS # D6: 6,7 => CTR => D6: 2,4 * PRF # D6: 2,4 => SOL * DIS # F8: 6 => CTR => F8: 1,7 * CNT 27 HDP CHAINS / 48 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A5,B4,B8,C8,D1,D4,D8,E8,F1,H2,H3,I5,I6) * 35..6.719..615.8.31..3..6.58...35961.359..47..19...35.4635921879.....534571843296 * PAIR A2: 2,7 BLK 1 C3: 2,7,4,8 # reduction candidate for 2,7 C3: 2,7 => SOLVED * 358264719296157843147389625824735961635918472719426358463592187982671534571843296 * DURATION: 0:00:02.319601 START: 07:54:36.226936 END: 07:54:38.546537 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-150-base-pr-001.dot * REASONING * PRF # C3: 2,7 => SOL * STA C3: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 150 solution: 358264719296157843147389625824735961635918472719426358463592187982671534571843296 info: 1816 FNBWY S8.f 29206 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 358264719296157843147389625824735961635918472719426358463592187982671534571843296 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 # C3: 2,7 => SOL * DIS # C3: 4,8 => CTR => C3: 2,7 * INC # A6: 2,7 => UNS * DIS # A6: 6 => CTR => A6: 2,7 * INC # C1: 2,4 => UNS * PRF # C1: 8 => SOL * PRF # D6: 2,4 => SOL * DIS # D6: 6,7 => CTR => D6: 2,4 * DIS # F3: 4,8 => CTR => F3: 7,9 * INC # F3: 7,9 => UNS * PRF # C1: 4,8 => SOL * DIS # C1: 2 => CTR => C1: 4,8 * INC # F6: 4,8 => UNS * PRF # F6: 6,7 => SOL * DIS # B2: 2,4 => CTR => B2: 9 * INC # B2: 9 => UNS * PRF # B3: 2,4 => SOL * INC # B3: 8,9 => UNS * DIS # C3: 2,4 => CTR => C3: 7,8 * INC # C3: 7,8 => UNS * PRF # C4: 2,4 => SOL * DIS # C4: 7 => CTR => C4: 2,4 * DIS # B2: 2,4 => CTR => B2: 9 * INC # B2: 9 => UNS * PRF # B3: 2,4 => SOL * INC # B3: 8,9 => UNS * DIS # A6: 2,6 => CTR => A6: 7 * PRF # A6: 7 => SOL * DIS # D6: 2,7 => CTR => D6: 4,6 * INC # D6: 4,6 => UNS * INC # E6: 2,7 => UNS * INC # C4: 2,7 => UNS * PRF # C4: 4 => SOL * INC # E5: 2,8 => UNS * INC # E5: 1 => UNS * INC # E6: 2,8 => UNS * DIS # E6: 7 => CTR => E6: 2,8 * INC # B3: 2,8 => UNS * PRF # B3: 4,9 => SOL * INC # C1: 2,8 => UNS * DIS # C3: 2,8 => CTR => C3: 4,7 * INC # C3: 4,7 => UNS * INC # F8: 6,7 => UNS * INC # F8: 1 => UNS * DIS # D6: 6,7 => CTR => D6: 2,4 * PRF # D6: 2,4 => SOL * INC # F8: 1,7 => UNS * DIS # F8: 6 => CTR => F8: 1,7 * CNT 48 HDP CHAINS / 48 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C3: 2,7 => SOL * STA C3: 2,7 * CNT 1 HDP CHAINS / 1 HYP OPENED