Analysis of xx-top500-132-base.sdk
Contents
Original Sudoku
level: medium
position: 5...1.....4......8.......3...6...2..7.....1.....8........42.5...3.5.......8....1. initial
Autosolve
position: 58.314.2.3412...58..2.85431896153247723.4.1854158723..1..4285.3.345.1872258.3..14 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 7,9 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # F2: 6,9 => SOL * DIS # F2: 7 => CTR => F2: 6,9 * PRF # F2: 7,9 => SOL * DIS # F2: 6 => CTR => F2: 7,9 * PRF # D9: 6 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 7 => CTR => G1: 6,9 * DIS # G1: 7,9 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # F2: 7,9 => SOL * DIS # F2: 6 => CTR => F2: 7,9 * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * PRF # F2: 6,9 => SOL * DIS # F2: 7 => CTR => F2: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 7 => CTR => G1: 6,9 * CNT 29 HDP CHAINS / 30 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 7,9 => CTR => G1: 6 * PRF G1: 6 => SOL * STA G1: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5...1.....4......8.......3...6...2..7.....1.....8........42.5...3.5.......8....1. | initial |
| 58.314.2.3412...58..2.85431896153247723.4.1854158723..1..4285.3.345.1872258.3..14 | autosolve |
| 587314629341269758962785431896153247723946185415872396179428563634591872258637914 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 7,9 A3: 6,9 B3: 6,7 E2: 6,9 D3: 7,9 I1: 6,9 G2: 7,9 D5: 6,9 F5: 6,9 H6: 6,9 I6: 6,9 B7: 6,7 C7: 7,9 A8: 6,9 E8: 6,9 H7: 6,9 G9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 6.. / A3 = 6 => 0 pairs (X) / B3 = 6 => 0 pairs (_) E2,F2: 6.. / E2 = 6 => 0 pairs (*) / F2 = 6 => 0 pairs (X) G1,I1: 6.. / G1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) D5,F5: 6.. / D5 = 6 => 18 pairs (_) / F5 = 6 => 0 pairs (*) H6,I6: 6.. / H6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) B7,A8: 6.. / B7 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) H7,G9: 6.. / H7 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) B7,H7: 6.. / B7 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) A8,E8: 6.. / A8 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) A3,A8: 6.. / A3 = 6 => 0 pairs (X) / A8 = 6 => 0 pairs (_) B3,B7: 6.. / B3 = 6 => 0 pairs (*) / B7 = 6 => 0 pairs (X) D5,D9: 6.. / D5 = 6 => 18 pairs (_) / D9 = 6 => 0 pairs (*) E2,E8: 6.. / E2 = 6 => 0 pairs (*) / E8 = 6 => 0 pairs (X) G1,G9: 6.. / G1 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) H6,H7: 6.. / H6 = 6 => 0 pairs (X) / H7 = 6 => 0 pairs (_) I1,I6: 6.. / I1 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) C1,B3: 7.. / C1 = 7 => 0 pairs (*) / B3 = 7 => 0 pairs (X) F2,D3: 7.. / F2 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) G1,G2: 7.. / G1 = 7 => 0 pairs (X) / G2 = 7 => 0 pairs (_) B7,C7: 7.. / B7 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) D9,F9: 7.. / D9 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) C1,G1: 7.. / C1 = 7 => 0 pairs (*) / G1 = 7 => 0 pairs (X) F2,G2: 7.. / F2 = 7 => 0 pairs (X) / G2 = 7 => 0 pairs (_) B3,D3: 7.. / B3 = 7 => 0 pairs (X) / D3 = 7 => 0 pairs (_) B3,B7: 7.. / B3 = 7 => 0 pairs (X) / B7 = 7 => 0 pairs (_) C1,C7: 7.. / C1 = 7 => 0 pairs (*) / C7 = 7 => 0 pairs (X) D3,D9: 7.. / D3 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) F2,F9: 7.. / F2 = 7 => 0 pairs (X) / F9 = 7 => 0 pairs (_) C1,A3: 9.. / C1 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) D5,F5: 9.. / D5 = 9 => 0 pairs (*) / F5 = 9 => 0 pairs (X) H6,I6: 9.. / H6 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) C7,A8: 9.. / C7 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) H7,G9: 9.. / H7 = 9 => 0 pairs (X) / G9 = 9 => 0 pairs (_) A3,D3: 9.. / A3 = 9 => 0 pairs (*) / D3 = 9 => 0 pairs (X) C7,H7: 9.. / C7 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) A8,E8: 9.. / A8 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) A3,A8: 9.. / A3 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) C1,C7: 9.. / C1 = 9 => 0 pairs (X) / C7 = 9 => 0 pairs (_) E2,E8: 9.. / E2 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) H6,H7: 9.. / H6 = 9 => 0 pairs (*) / H7 = 9 => 0 pairs (X) I1,I6: 9.. / I1 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) * DURATION: 0:01:10.084220 START: 07:15:52.517059 END: 07:17:02.601279 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B3,B7,C1,C7,D3,D5,E2,E8,F5,G2,G9,H6,H7,I1,I6) * 58.314.2.3412...58..2.85431896153247723.4.1854158723..1..4285.3.345.1872258.3..14 * PAIR C1: 7,9 ROW 1 G1: 7,9,6 # reduction candidate for 7,9 G1: 7,9 => CTR * 58931472634129..58..2.85431896153247723.4.185415872369167428593934561872258.3.614 G1: 6 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 * PAIR E2: 6,9 BLK 2 F2: 6,9,7 # reduction candidate for 6,9 F2: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 F2: 7 => CTR * 58.314.2.341267958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 * PAIR D3: 7,9 BLK 2 F2: 7,9,6 # reduction candidate for 7,9 F2: 7,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 F2: 6 => CTR * 58.314.2.3412.6758..27854318961532477236491854158723..179428563.345.1872258.3..14 * PAIR D3: 7,9 COL D D9: 7,9,6 # reduction candidate for 7,9 D9: 6 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 D9: 7,9 # 18 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,7 # reduction candidate for 6,9 G1: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 G1: 7 => CTR * 58.3147263412.7958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 * PAIR G2: 7,9 BLK 3 G1: 7,9,6 # reduction candidate for 7,9 G1: 7,9 => CTR * 58931472634129..58..2.85431896153247723.4.185415872369167428593934561872258.3.614 G1: 6 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 * PAIR G2: 7,9 ROW 2 F2: 7,9,6 # reduction candidate for 7,9 F2: 7,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 F2: 6 => CTR * 58.314.2.3412.6758..27854318961532477236491854158723..179428563.345.1872258.3..14 * PAIR D5: 6,9 COL D D9: 6,9,7 # reduction candidate for 6,9 D9: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 D9: 7 => CTR * 58.314.2.3412...58..2.854318961532477236491854158723..1..4285.3.34591872258736914 * PAIR F5: 6,9 COL F F2: 6,9,7 # reduction candidate for 6,9 F2: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 F2: 7 => CTR * 58.314.2.341267958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 58.314.2.3412.7958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 F9: 7 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 * PAIR E8: 6,9 BLK 8 D9: 6,9,7 # reduction candidate for 6,9 D9: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 D9: 7 => CTR * 58.314.2.3412...58..2.854318961532477236491854158723..1..4285.3.34591872258736914 F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 58.314.2.3412.7958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 F9: 7 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 * PAIR G9: 6,9 ROW 9 D9: 6,9,7 # reduction candidate for 6,9 D9: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 D9: 7 => CTR * 58.314.2.3412...58..2.854318961532477236491854158723..1..4285.3.34591872258736914 F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 58.314.2.3412.7958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 F9: 7 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 * PAIR G9: 6,9 COL G G1: 6,9,7 # reduction candidate for 6,9 G1: 6,9 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 G1: 7 => CTR * 58.3147263412.7958.729854318961532477236491854158723..1..4285.3.345.1872258.3..14 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-132-base-pr-000.dot * REASONING * DIS # G1: 7,9 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # F2: 6,9 => SOL * DIS # F2: 7 => CTR => F2: 6,9 * PRF # F2: 7,9 => SOL * DIS # F2: 6 => CTR => F2: 7,9 * PRF # D9: 6 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 7 => CTR => G1: 6,9 * DIS # G1: 7,9 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # F2: 7,9 => SOL * DIS # F2: 6 => CTR => F2: 7,9 * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * PRF # F2: 6,9 => SOL * DIS # F2: 7 => CTR => F2: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 7 => CTR => G1: 6,9 * CNT 29 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A8,B3,B7,C1,C7,D3,D5,E2,E8,F5,G2,G9,H6,H7,I1,I6) * 58.314.2.3412...58..2.85431896153247723.4.1854158723..1..4285.3.345.1872258.3..14 * PAIR C1: 7,9 ROW 1 G1: 7,9,6 # reduction candidate for 7,9 G1: 7,9 => CTR * 58931472634129..58..2.85431896153247723.4.185415872369167428593934561872258.3.614 G1: 6 => SOLVED * 587314629341269758962785431896153247723946185415872396179428563634591872258637914 * DURATION: 0:00:02.943312 START: 07:17:37.625049 END: 07:17:40.568361 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-132-base-pr-001.dot * REASONING * DIS # G1: 7,9 => CTR => G1: 6 * PRF G1: 6 => SOL * STA G1: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 132 solution: 587314629341269758962785431896153247723946185415872396179428563634591872258637914 info: 1811 FNBWX S8.f 32304 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 587314629341269758962785431896153247723946185415872396179428563634591872258637914 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 # G1: 7,9 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # F2: 6,9 => SOL * DIS # F2: 7 => CTR => F2: 6,9 * PRF # F2: 7,9 => SOL * DIS # F2: 6 => CTR => F2: 7,9 * INC # D9: 7,9 => UNS * PRF # D9: 6 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 7 => CTR => G1: 6,9 * DIS # G1: 7,9 => CTR => G1: 6 * PRF # G1: 6 => SOL * PRF # F2: 7,9 => SOL * DIS # F2: 6 => CTR => F2: 7,9 * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * PRF # F2: 6,9 => SOL * DIS # F2: 7 => CTR => F2: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # D9: 6,9 => SOL * DIS # D9: 7 => CTR => D9: 6,9 * DIS # F9: 6,9 => CTR => F9: 7 * PRF # F9: 7 => SOL * PRF # G1: 6,9 => SOL * DIS # G1: 7 => CTR => G1: 6,9 * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # G1: 7,9 => CTR => G1: 6 * PRF G1: 6 => SOL * STA G1: 6 * CNT 2 HDP CHAINS / 1 HYP OPENED