Analysis of xx-top500-114-base.sdk
Contents
Original Sudoku
level: medium
position: .316.........4..5...........7.1.6..........28...3.....4.2.5....5.....6........1.. initial
Autosolve
position: .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF # B6: 2,8,9 => SOL * DIS # H9: 7,8 => CTR => H9: 4 * PRF # A4: 3,8 => SOL * DIS # A4: 2 => CTR => A4: 3,8 * DIS # C9: 7,9 => CTR => C9: 3,8 * DIS # B6: 4,9 => CTR => B6: 2,5,8 * DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF # B6: 2,8,9 => SOL * PRF # E6: 2,8 => SOL * DIS # E6: 9 => CTR => E6: 2,8 * DIS # F6: 2,8 => CTR => F6: 4,9 * PRF # F6: 4,9 => SOL * DIS # A4: 2,8 => CTR => A4: 3 * PRF # A4: 3 => SOL * DIS # E1: 2,8 => CTR => E1: 9 * PRF # E1: 9 => SOL * PRF # F6: 4,9 => SOL * DIS # F6: 2,8 => CTR => F6: 4,9 * DIS # A9: 8,9 => CTR => A9: 3,7 * DIS # C9: 8,9 => CTR => C9: 3,7 * PRF # D9: 8,9 => SOL * DIS # F9: 8,9 => CTR => F9: 2,7 * PRF # B2: 8,9 => SOL * DIS # B2: 2 => CTR => B2: 8,9 * DIS # B6: 8,9 => CTR => B6: 2,4,5 * DIS # D8: 7,8 => CTR => D8: 4,9 * DIS # D9: 7,8 => CTR => D9: 2,4,9 * DIS # F9: 7,8 => CTR => F9: 2,9 * DIS # D3: 7,8 => CTR => D3: 2,9 * PRF # G3: 8,9 => SOL * CNT 31 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF B6: 2,8,9 => SOL * STA B6: 2,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .316.........4..5...........7.1.6..........28...3.....4.2.5....5.....6........1.. | initial |
| .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5 | autosolve |
| 231695487697843251854217963378126594146579328925384716462751839519438672783962145 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) B3: 4,5 C3: 4,5 H1: 7,8 I1: 7,9 C4: 3,8 B5: 4,9 C6: 4,5 E4: 2,8 F5: 4,9 B9: 8,9 D7: 7,8 G7: 8,9 I7: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,G3: 2.. / G2 = 2 => 0 pairs (*) / G3 = 2 => 0 pairs (X) D9,F9: 2.. / D9 = 2 => 0 pairs (X) / F9 = 2 => 0 pairs (_) A1,E1: 2.. / A1 = 2 => 0 pairs (*) / E1 = 2 => 0 pairs (X) A4,E4: 2.. / A4 = 2 => 0 pairs (X) / E4 = 2 => 0 pairs (_) B2,B6: 2.. / B2 = 2 => 0 pairs (X) / B6 = 2 => 0 pairs (_) A4,C4: 3.. / A4 = 3 => 0 pairs (*) / C4 = 3 => 0 pairs (X) A9,C9: 3.. / A9 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) A4,A9: 3.. / A4 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) C4,C9: 3.. / C4 = 3 => 0 pairs (X) / C9 = 3 => 0 pairs (_) B3,C3: 4.. / B3 = 4 => 0 pairs (X) / C3 = 4 => 10 pairs (_) F5,F6: 4.. / F5 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) D8,D9: 4.. / D8 = 4 => 14 pairs (_) / D9 = 4 => 0 pairs (X) H8,H9: 4.. / H8 = 4 => 0 pairs (X) / H9 = 4 => 14 pairs (_) B5,F5: 4.. / B5 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) D8,H8: 4.. / D8 = 4 => 14 pairs (_) / H8 = 4 => 0 pairs (X) D9,H9: 4.. / D9 = 4 => 0 pairs (X) / H9 = 4 => 14 pairs (_) C3,C6: 4.. / C3 = 4 => 10 pairs (_) / C6 = 4 => 0 pairs (X) B3,C3: 5.. / B3 = 5 => 10 pairs (_) / C3 = 5 => 0 pairs (X) B6,C6: 5.. / B6 = 5 => 0 pairs (X) / C6 = 5 => 10 pairs (_) B3,B6: 5.. / B3 = 5 => 10 pairs (_) / B6 = 5 => 0 pairs (X) C3,C6: 5.. / C3 = 5 => 0 pairs (X) / C6 = 5 => 10 pairs (_) C2,A3: 7.. / C2 = 7 => 0 pairs (*) / A3 = 7 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) C2,D2: 7.. / C2 = 7 => 0 pairs (*) / D2 = 7 => 0 pairs (X) D7,I7: 7.. / D7 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) A3,A9: 7.. / A3 = 7 => 0 pairs (X) / A9 = 7 => 0 pairs (_) I1,I7: 7.. / I1 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) D7,G7: 8.. / D7 = 8 => 0 pairs (X) / G7 = 8 => 0 pairs (_) G7,I7: 9.. / G7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) B5,F5: 9.. / B5 = 9 => 0 pairs (X) / F5 = 9 => 0 pairs (_) E1,E6: 9.. / E1 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) I1,I7: 9.. / I1 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) * DURATION: 0:01:05.800193 START: 06:39:20.540253 END: 06:40:26.340446 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C3,C4,C6,D7,E4,F5,G7,H1,I1,I7) * .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5 * PAIR B3: 4,5 COL B B6: 4,5,2,8,9 # reduction candidate for 4,5 B6: 4,5 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 B6: 2,8,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 * PAIR H1: 7,8 COL H H8: 7,8,4 # reduction candidate for 7,8 H8: 7,8 # 14 pairs H9: 7,8,4 # reduction candidate for 7,8 H9: 7,8 => CTR * 2316954876...43.51.54.1.963.7.126594146579328925384716462751839517938642...462175 H9: 4 # 14 pairs * PAIR C4: 3,8 BLK 4 A4: 3,8,2 # reduction candidate for 3,8 A4: 3,8 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 A4: 2 => CTR * 9316254876287439517...1.2632731865941965743288..392716462851.3.51..3.6.23..26.145 * PAIR C4: 3,8 COL C C9: 3,8,7,9 # reduction candidate for 3,8 C9: 7,9 => CTR * .316.54796..743.517...1..63.731.65941.657.3289..3..71646285193751..3.6.23...6.1.5 C9: 3,8 # 17 pairs * PAIR B5: 4,9 BLK 4 B6: 4,9,2,5,8 # reduction candidate for 4,9 B6: 4,9 => CTR * 931625487628743951754918263273186594196574328845392716462851.3.51.43.6.238.26.145 B6: 2,5,8 # 13 pairs * PAIR C6: 4,5 BLK 4 B6: 4,5,2,8,9 # reduction candidate for 4,5 B6: 4,5 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 B6: 2,8,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 * PAIR E4: 2,8 BLK 5 E6: 2,8,9 # reduction candidate for 2,8 E6: 2,8 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 E6: 9 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 F6: 2,8,4,9 # reduction candidate for 2,8 F6: 2,8 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 F6: 4,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 * PAIR E4: 2,8 ROW 4 A4: 2,8,3 # reduction candidate for 2,8 A4: 2,8 => CTR * .316.54796..743.517...1..63.731.65941.657.3289..3..71646285193751..3.6.23...6.1.5 A4: 3 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 * PAIR E4: 2,8 COL E E1: 2,8,9 # reduction candidate for 2,8 E1: 2,8 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 E1: 9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 * PAIR F5: 4,9 BLK 5 F6: 4,9,2,8 # reduction candidate for 4,9 F6: 4,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 F6: 2,8 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 * PAIR B9: 8,9 BLK 7 C8: 8,9,7 # reduction candidate for 8,9 C8: 8,9 # 17 pairs A9: 8,9,3,7 # reduction candidate for 8,9 A9: 8,9 => CTR * 2316.54..6897432517...1..633781265941.657.328925384716462851937517.396.2..3.6.1.5 A9: 3,7 # 14 pairs C9: 8,9,3,7 # reduction candidate for 8,9 C9: 8,9 => CTR * .316.54796..743.517...1..63.731.65941.657.3289..3..716462851937517.396823..267145 C9: 3,7 # 14 pairs * PAIR B9: 8,9 ROW 9 D9: 8,9,2,4,7 # reduction candidate for 8,9 D9: 8,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 D9: 2,4,7 # 13 pairs F9: 8,9,2,7 # reduction candidate for 8,9 F9: 8,9 => CTR * 9316254876287439517..9182632731865941965743288..392716462.51.3.51943.6.2387269145 F9: 2,7 # 14 pairs * PAIR B9: 8,9 COL B B2: 8,9,2 # reduction candidate for 8,9 B2: 8,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 B2: 2 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 B6: 8,9,2,4,5 # reduction candidate for 8,9 B6: 8,9 => CTR * .316.54..62..43.51.54.1.263.7.1.6594146579328..53.4716462.51.3.51..3.6.2...26.145 B6: 2,4,5 # 13 pairs * PAIR D7: 7,8 BLK 8 D8: 7,8,4,9 # reduction candidate for 7,8 D8: 7,8 => CTR * .316.54..6...43.51....17.63.7.1.6594196574328...398716462.51.3.51..3964278.4621.5 D8: 4,9 # 14 pairs F8: 7,8,9 # reduction candidate for 7,8 F8: 7,8 # 16 pairs D9: 7,8,2,4,9 # reduction candidate for 7,8 D9: 7,8 => CTR * .316.54..6...43.51....17.63.7.1.6594196574328...398716462.51.3.51.4396.278..62145 D9: 2,4,9 # 13 pairs F9: 7,8,2,9 # reduction candidate for 7,8 F9: 7,8 => CTR * .316254796297438517..91826327.1.6594196574328...392716462851937517439682.8.267145 F9: 2,9 # 14 pairs * PAIR D7: 7,8 COL D D2: 7,8,2,9 # reduction candidate for 7,8 D2: 7,8 # 16 pairs D3: 7,8,2,9 # reduction candidate for 7,8 D3: 7,8 => CTR * 2316.54..6972438518..71926337812659414657.328...3..716462.51.3.51943.6.2783.6.145 D3: 2,9 # 14 pairs * PAIR G7: 8,9 COL G G2: 8,9,2 # reduction candidate for 8,9 G2: 8,9 # 14 pairs G3: 8,9,2 # reduction candidate for 8,9 G3: 8,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 G3: 2 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-114-base-pr-000.dot * REASONING * DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF # B6: 2,8,9 => SOL * DIS # H9: 7,8 => CTR => H9: 4 * PRF # A4: 3,8 => SOL * DIS # A4: 2 => CTR => A4: 3,8 * DIS # C9: 7,9 => CTR => C9: 3,8 * DIS # B6: 4,9 => CTR => B6: 2,5,8 * DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF # B6: 2,8,9 => SOL * PRF # E6: 2,8 => SOL * DIS # E6: 9 => CTR => E6: 2,8 * DIS # F6: 2,8 => CTR => F6: 4,9 * PRF # F6: 4,9 => SOL * DIS # A4: 2,8 => CTR => A4: 3 * PRF # A4: 3 => SOL * DIS # E1: 2,8 => CTR => E1: 9 * PRF # E1: 9 => SOL * PRF # F6: 4,9 => SOL * DIS # F6: 2,8 => CTR => F6: 4,9 * DIS # A9: 8,9 => CTR => A9: 3,7 * DIS # C9: 8,9 => CTR => C9: 3,7 * PRF # D9: 8,9 => SOL * DIS # F9: 8,9 => CTR => F9: 2,7 * PRF # B2: 8,9 => SOL * DIS # B2: 2 => CTR => B2: 8,9 * DIS # B6: 8,9 => CTR => B6: 2,4,5 * DIS # D8: 7,8 => CTR => D8: 4,9 * DIS # D9: 7,8 => CTR => D9: 2,4,9 * DIS # F9: 7,8 => CTR => F9: 2,9 * DIS # D3: 7,8 => CTR => D3: 2,9 * PRF # G3: 8,9 => SOL * CNT 31 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B5,B9,C3,C4,C6,D7,E4,F5,G7,H1,I1,I7) * .316.54..6...43.51....1..63.7.1.65941.657.328...3..716462.51.3.51..3.6.2....6.1.5 * PAIR B3: 4,5 COL B B6: 4,5,2,8,9 # reduction candidate for 4,5 B6: 4,5 => CTR * 9316254876287439517..9182632731865941965743288..392716462851.3.51.43.6.238.26.145 B6: 2,8,9 => SOLVED * 231695487697843251854217963378126594146579328925384716462751839519438672783962145 * DURATION: 0:00:03.513379 START: 06:41:22.942058 END: 06:41:26.455437 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-114-base-pr-001.dot * REASONING * DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF B6: 2,8,9 => SOL * STA B6: 2,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 114 solution: 231695487697843251854217963378126594146579328925384716462751839519438672783962145 info: 1702 FNBTHWXY S8.f 18249 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 231695487697843251854217963378126594146579328925384716462751839519438672783962145 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 # B6: 4,5 => CTR => B6: 2,8,9 * PRF # B6: 2,8,9 => SOL * INC # H8: 7,8 => UNS * DIS # H9: 7,8 => CTR => H9: 4 * INC # H9: 4 => UNS * PRF # A4: 3,8 => SOL * DIS # A4: 2 => CTR => A4: 3,8 * INC # C9: 3,8 => UNS * DIS # C9: 7,9 => CTR => C9: 3,8 * DIS # B6: 4,9 => CTR => B6: 2,5,8 * INC # B6: 2,5,8 => UNS * DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF # B6: 2,8,9 => SOL * PRF # E6: 2,8 => SOL * DIS # E6: 9 => CTR => E6: 2,8 * DIS # F6: 2,8 => CTR => F6: 4,9 * PRF # F6: 4,9 => SOL * DIS # A4: 2,8 => CTR => A4: 3 * PRF # A4: 3 => SOL * DIS # E1: 2,8 => CTR => E1: 9 * PRF # E1: 9 => SOL * PRF # F6: 4,9 => SOL * DIS # F6: 2,8 => CTR => F6: 4,9 * INC # C8: 8,9 => UNS * DIS # A9: 8,9 => CTR => A9: 3,7 * INC # A9: 3,7 => UNS * DIS # C9: 8,9 => CTR => C9: 3,7 * INC # C9: 3,7 => UNS * PRF # D9: 8,9 => SOL * INC # D9: 2,4,7 => UNS * DIS # F9: 8,9 => CTR => F9: 2,7 * INC # F9: 2,7 => UNS * PRF # B2: 8,9 => SOL * DIS # B2: 2 => CTR => B2: 8,9 * DIS # B6: 8,9 => CTR => B6: 2,4,5 * INC # B6: 2,4,5 => UNS * DIS # D8: 7,8 => CTR => D8: 4,9 * INC # D8: 4,9 => UNS * INC # F8: 7,8 => UNS * DIS # D9: 7,8 => CTR => D9: 2,4,9 * INC # D9: 2,4,9 => UNS * DIS # F9: 7,8 => CTR => F9: 2,9 * INC # F9: 2,9 => UNS * INC # D2: 7,8 => UNS * DIS # D3: 7,8 => CTR => D3: 2,9 * INC # D3: 2,9 => UNS * INC # G2: 8,9 => UNS * PRF # G3: 8,9 => SOL * INC # G3: 2 => UNS * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B6: 4,5 => CTR => B6: 2,8,9 * PRF B6: 2,8,9 => SOL * STA B6: 2,8,9 * CNT 2 HDP CHAINS / 1 HYP OPENED