Analysis of xx-top500-336-base.sdk
Contents
Original Sudoku
level: medium
position: ...35....4......1.....9....8..6.1.........9.7......3....3...5.4.9.7............2. initial
Autosolve
position: 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # B3: 6,8 => SOL * DIS # B3: 2 => CTR => B3: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,4 * PRF # C9: 6,8 => SOL * DIS # B3: 2,6 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # E2: 2,8 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # E2: 6,8 => SOL * DIS # E2: 2 => CTR => E2: 6,8 * DIS # B3: 2,6 => CTR => B3: 8 * PRF # B3: 8 => SOL * PRF # B7: 2,6 => SOL * DIS # B7: 8 => CTR => B7: 2,6 * DIS # C8: 2,6 => CTR => C8: 4,8 * PRF # C8: 4,8 => SOL * DIS # E2: 2,8 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # E8: 2,8 => SOL * DIS # F7: 2,8 => CTR => F7: 6 * PRF # F7: 6 => SOL * PRF # B7: 2,6 => SOL * DIS # B7: 8 => CTR => B7: 2,6 * DIS # C8: 2,6 => CTR => C8: 4,8 * PRF # C8: 4,8 => SOL * PRF # E8: 2,6 => SOL * DIS # F7: 2,8 => CTR => F7: 6 * PRF # F7: 6 => SOL * PRF # E8: 2,8 => SOL * PRF # B7: 2,8 => SOL * DIS # B7: 6 => CTR => B7: 2,8 * DIS # C8: 6,8 => CTR => C8: 2,4 * DIS # E8: 6,8 => CTR => E8: 2,4 * PRF # C9: 6,8 => SOL * CNT 34 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # B3: 6,8 => SOL * STA B3: 6,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...35....4......1.....9....8..6.1.........9.7......3....3...5.4.9.7............2. | initial |
| 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372. | autosolve |
| 916358472435267819287194653879631245341582967562479381723816594694725138158943726 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) C1: 6,8 A3: 2,6 D2: 2,8 G2: 6,8 B6: 2,6 C6: 2,6 E5: 2,8 F5: 2,8 A8: 2,6 D7: 2,8 I8: 6,8 I9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 2.. / A3 = 2 => 0 pairs (*) / B3 = 2 => 0 pairs (X) D2,E2: 2.. / D2 = 2 => 0 pairs (*) / E2 = 2 => 0 pairs (X) B6,C6: 2.. / B6 = 2 => 0 pairs (X) / C6 = 2 => 0 pairs (_) E5,F5: 2.. / E5 = 2 => 0 pairs (X) / F5 = 2 => 0 pairs (_) A3,A8: 2.. / A3 = 2 => 0 pairs (*) / A8 = 2 => 0 pairs (X) C6,C8: 2.. / C6 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) D2,D7: 2.. / D2 = 2 => 0 pairs (*) / D7 = 2 => 0 pairs (X) F5,F7: 2.. / F5 = 2 => 0 pairs (*) / F7 = 2 => 0 pairs (X) F1,F3: 4.. / F1 = 4 => 14 pairs (_) / F3 = 4 => 14 pairs (_) G1,G3: 4.. / G1 = 4 => 14 pairs (_) / G3 = 4 => 14 pairs (_) C8,C9: 4.. / C8 = 4 => 0 pairs (*) / C9 = 4 => 0 pairs (X) E8,E9: 4.. / E8 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (*) F1,G1: 4.. / F1 = 4 => 14 pairs (_) / G1 = 4 => 14 pairs (_) F3,G3: 4.. / F3 = 4 => 14 pairs (_) / G3 = 4 => 14 pairs (_) C8,E8: 4.. / C8 = 4 => 0 pairs (*) / E8 = 4 => 0 pairs (X) C9,E9: 4.. / C9 = 4 => 14 pairs (_) / E9 = 4 => 0 pairs (*) B6,C6: 6.. / B6 = 6 => 0 pairs (*) / C6 = 6 => 0 pairs (X) I8,I9: 6.. / I8 = 6 => 0 pairs (X) / I9 = 6 => 12 pairs (_) E2,G2: 6.. / E2 = 6 => 0 pairs (*) / G2 = 6 => 0 pairs (X) B7,F7: 6.. / B7 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) A3,A8: 6.. / A3 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) C1,B3: 8.. / C1 = 8 => 0 pairs (X) / B3 = 8 => 0 pairs (_) E5,F5: 8.. / E5 = 8 => 0 pairs (*) / F5 = 8 => 0 pairs (X) I8,I9: 8.. / I8 = 8 => 12 pairs (_) / I9 = 8 => 0 pairs (X) B3,B7: 8.. / B3 = 8 => 0 pairs (*) / B7 = 8 => 0 pairs (X) D2,D7: 8.. / D2 = 8 => 0 pairs (X) / D7 = 8 => 0 pairs (_) * DURATION: 0:00:49.175705 START: 14:14:38.526411 END: 14:15:27.702116 2017-05-04 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B6,C1,C6,D2,D7,E5,F5,G2,I8,I9) * 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372. * PAIR C1: 6,8 BLK 1 B3: 6,8,2 # reduction candidate for 6,8 B3: 6,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 B3: 2 => CTR * 91835..72435..7.1962719..538796312453415..96756247938178321659429.7.513.15.9.372. * PAIR C1: 6,8 ROW 1 F1: 6,8,4 # reduction candidate for 6,8 F1: 6,8 # 14 pairs G1: 6,8,4 # reduction candidate for 6,8 G1: 6,8 # 14 pairs * PAIR C1: 6,8 COL C C8: 6,8,2,4 # reduction candidate for 6,8 C8: 6,8 => CTR * 91.35..72435..7.19..719..538796312453415..9675624793817.3.16594296745138154983726 C8: 2,4 # 13 pairs C9: 6,8,4 # reduction candidate for 6,8 C9: 6,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 C9: 4 # 14 pairs * PAIR A3: 2,6 BLK 1 B3: 2,6,8 # reduction candidate for 2,6 B3: 2,6 => CTR * 91835..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372. B3: 8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 * PAIR D2: 2,8 BLK 2 E2: 2,8,6 # reduction candidate for 2,8 E2: 2,8 => CTR * 91.35..72435..7619..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372. E2: 6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 * PAIR G2: 6,8 BLK 3 G1: 6,8,4 # reduction candidate for 6,8 G1: 6,8 # 14 pairs G3: 6,8,4 # reduction candidate for 6,8 G3: 6,8 # 14 pairs * PAIR G2: 6,8 ROW 2 E2: 6,8,2 # reduction candidate for 6,8 E2: 6,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 E2: 2 => CTR * 91.35..72435827619.8719.4538796312453415829675264793817.3218594.9.7.513.15.9.372. * PAIR B6: 2,6 COL B B3: 2,6,8 # reduction candidate for 2,6 B3: 2,6 => CTR * 91835..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372. B3: 8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 B7: 2,6,8 # reduction candidate for 2,6 B7: 2,6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 B7: 8 => CTR * 91.35..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372. * PAIR C6: 2,6 COL C C8: 2,6,4,8 # reduction candidate for 2,6 C8: 2,6 => CTR * 91835..724358.7.19..719..538796312453415..9675..4793817.3.1.594.9.745138154983726 C8: 4,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 * PAIR E5: 2,8 COL E E2: 2,8,6 # reduction candidate for 2,8 E2: 2,8 => CTR * 91.35..72435..7619..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372. E2: 6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 E8: 2,8,4,6 # reduction candidate for 2,8 E8: 2,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 E8: 4,6 # 14 pairs * PAIR F5: 2,8 COL F F7: 2,8,6 # reduction candidate for 2,8 F7: 2,8 => CTR * 91.35..72435..7.19..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372. F7: 6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 * PAIR A8: 2,6 BLK 7 B7: 2,6,8 # reduction candidate for 2,6 B7: 2,6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 B7: 8 => CTR * 91.35..72435..7.19..719..538796312453415..9675..479381783216594.9.7.513.15.9.372. C8: 2,6,4,8 # reduction candidate for 2,6 C8: 2,6 => CTR * 91835..724358.7.19..719..538796312453415..9675..4793817.3.1.594.9.745138154983726 C8: 4,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 * PAIR A8: 2,6 ROW 8 E8: 2,6,4,8 # reduction candidate for 2,6 E8: 2,6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 E8: 4,8 # 14 pairs * PAIR D7: 2,8 BLK 8 F7: 2,8,6 # reduction candidate for 2,8 F7: 2,8 => CTR * 91.35..72435..7.19..719..538796312453415..9675..479381763.1.59429.7.513.15.9.372. F7: 6 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 E8: 2,8,4,6 # reduction candidate for 2,8 E8: 2,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 E8: 4,6 # 14 pairs * PAIR D7: 2,8 ROW 7 B7: 2,8,6 # reduction candidate for 2,8 B7: 2,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 B7: 6 => CTR * 91.35..72435..7.19.8719..538796312453415..9675264793817.3.1.594.9.7.513.15.9.372. * PAIR I8: 6,8 ROW 8 C8: 6,8,2,4 # reduction candidate for 6,8 C8: 6,8 => CTR * 91.35..72435..7.19..719..538796312453415..9675624793817.3.16594296745138154983726 C8: 2,4 # 13 pairs E8: 6,8,2,4 # reduction candidate for 6,8 E8: 6,8 => CTR * 91.35..72435..7.1962719..538796312453415..96756247938178321659429478513.15.94372. E8: 2,4 # 13 pairs * PAIR I9: 6,8 ROW 9 C9: 6,8,4 # reduction candidate for 6,8 C9: 6,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 C9: 4 # 14 pairs E9: 6,8,4 # reduction candidate for 6,8 E9: 6,8 # 14 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-336-base-pr-000.dot * REASONING * PRF # B3: 6,8 => SOL * DIS # B3: 2 => CTR => B3: 6,8 * DIS # C8: 6,8 => CTR => C8: 2,4 * PRF # C9: 6,8 => SOL * DIS # B3: 2,6 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # E2: 2,8 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # E2: 6,8 => SOL * DIS # E2: 2 => CTR => E2: 6,8 * DIS # B3: 2,6 => CTR => B3: 8 * PRF # B3: 8 => SOL * PRF # B7: 2,6 => SOL * DIS # B7: 8 => CTR => B7: 2,6 * DIS # C8: 2,6 => CTR => C8: 4,8 * PRF # C8: 4,8 => SOL * DIS # E2: 2,8 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # E8: 2,8 => SOL * DIS # F7: 2,8 => CTR => F7: 6 * PRF # F7: 6 => SOL * PRF # B7: 2,6 => SOL * DIS # B7: 8 => CTR => B7: 2,6 * DIS # C8: 2,6 => CTR => C8: 4,8 * PRF # C8: 4,8 => SOL * PRF # E8: 2,6 => SOL * DIS # F7: 2,8 => CTR => F7: 6 * PRF # F7: 6 => SOL * PRF # E8: 2,8 => SOL * PRF # B7: 2,8 => SOL * DIS # B7: 6 => CTR => B7: 2,8 * DIS # C8: 6,8 => CTR => C8: 2,4 * DIS # E8: 6,8 => CTR => E8: 2,4 * PRF # C9: 6,8 => SOL * CNT 34 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B6,C1,C6,D2,D7,E5,F5,G2,I8,I9) * 91.35..72435..7.19..719..538796312453415..9675..4793817.3.1.594.9.7.513.15.9.372. * PAIR C1: 6,8 BLK 1 B3: 6,8,2 # reduction candidate for 6,8 B3: 6,8 => SOLVED * 916358472435267819287194653879631245341582967562479381723816594694725138158943726 * DURATION: 0:00:02.077595 START: 14:16:25.588286 END: 14:16:27.665881 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-336-base-pr-001.dot * REASONING * PRF # B3: 6,8 => SOL * STA B3: 6,8 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 336 solution: 916358472435267819287194653879631245341582967562479381723816594694725138158943726 info: 3103 FNBWXY S8.f 8757 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 916358472435267819287194653879631245341582967562479381723816594694725138158943726 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 # B3: 6,8 => SOL * DIS # B3: 2 => CTR => B3: 6,8 * INC # F1: 6,8 => UNS * INC # G1: 6,8 => UNS * DIS # C8: 6,8 => CTR => C8: 2,4 * INC # C8: 2,4 => UNS * PRF # C9: 6,8 => SOL * INC # C9: 4 => UNS * DIS # B3: 2,6 => CTR => B3: 8 * PRF # B3: 8 => SOL * DIS # E2: 2,8 => CTR => E2: 6 * PRF # E2: 6 => SOL * INC # G1: 6,8 => UNS * INC # G3: 6,8 => UNS * PRF # E2: 6,8 => SOL * DIS # E2: 2 => CTR => E2: 6,8 * DIS # B3: 2,6 => CTR => B3: 8 * PRF # B3: 8 => SOL * PRF # B7: 2,6 => SOL * DIS # B7: 8 => CTR => B7: 2,6 * DIS # C8: 2,6 => CTR => C8: 4,8 * PRF # C8: 4,8 => SOL * DIS # E2: 2,8 => CTR => E2: 6 * PRF # E2: 6 => SOL * PRF # E8: 2,8 => SOL * INC # E8: 4,6 => UNS * DIS # F7: 2,8 => CTR => F7: 6 * PRF # F7: 6 => SOL * PRF # B7: 2,6 => SOL * DIS # B7: 8 => CTR => B7: 2,6 * DIS # C8: 2,6 => CTR => C8: 4,8 * PRF # C8: 4,8 => SOL * PRF # E8: 2,6 => SOL * INC # E8: 4,8 => UNS * DIS # F7: 2,8 => CTR => F7: 6 * PRF # F7: 6 => SOL * PRF # E8: 2,8 => SOL * INC # E8: 4,6 => UNS * PRF # B7: 2,8 => SOL * DIS # B7: 6 => CTR => B7: 2,8 * DIS # C8: 6,8 => CTR => C8: 2,4 * INC # C8: 2,4 => UNS * DIS # E8: 6,8 => CTR => E8: 2,4 * INC # E8: 2,4 => UNS * PRF # C9: 6,8 => SOL * INC # C9: 4 => UNS * INC # E9: 6,8 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # B3: 6,8 => SOL * STA B3: 6,8 * CNT 1 HDP CHAINS / 1 HYP OPENED