Analysis of xx-top500-141-base.sdk
Contents
Original Sudoku
level: medium
position: .....48.....5.1...2............3.2...1....4...5.6.....3.1.4.......7...5.........6 initial
Autosolve
position: 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # C2: 7,9 => SOL * DIS # C2: 8 => CTR => C2: 7,9 * DIS # B4: 7,9 => CTR => B4: 8 * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # C2: 7,9 => SOL * DIS # C2: 8 => CTR => C2: 7,9 * DIS # B4: 7,9 => CTR => B4: 8 * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * DIS # B4: 7,9 => CTR => B4: 8 * PRF # B8: 2 => SOL * PRF # A2: 8,9 => SOL * DIS # A2: 7 => CTR => A2: 8,9 * PRF # B9: 7,8 => SOL * PRF # C2: 7,8 => SOL * DIS # C2: 9 => CTR => C2: 7,8 * DIS # C4: 7,8 => CTR => C4: 9 * PRF # C4: 9 => SOL * PRF # B8: 2,8 => SOL * DIS # B8: 9 => CTR => B8: 2,8 * PRF # B9: 7 => SOL * CNT 24 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A2: 7,9 => CTR => A2: 8 * PRF A2: 8 => SOL * STA A2: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....48.....5.1...2............3.2...1....4...5.6.....3.1.4.......7...5.........6 | initial |
| 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946 | autosolve |
| 195264837837591624246378591689437215713852469452619378361945782924786153578123946 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) B1: 7,9 E2: 7,9 E3: 7,9 I1: 7,9 H3: 7,9 A5: 7,9 F4: 7,9 F6: 7,9 I5: 7,9 H6: 7,9 A8: 8,9 C9: 7,8 E8: 2,8 E9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B8,B9: 2.. / B8 = 2 => 0 pairs (*) / B9 = 2 => 0 pairs (X) E8,E9: 2.. / E8 = 2 => 14 pairs (_) / E9 = 2 => 0 pairs (*) B8,E8: 2.. / B8 = 2 => 0 pairs (*) / E8 = 2 => 0 pairs (X) B9,E9: 2.. / B9 = 2 => 14 pairs (_) / E9 = 2 => 0 pairs (*) E2,E3: 7.. / E2 = 7 => 0 pairs (X) / E3 = 7 => 0 pairs (_) I1,H3: 7.. / I1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) F4,F6: 7.. / F4 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) I5,H6: 7.. / I5 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) B9,C9: 7.. / B9 = 7 => 0 pairs (*) / C9 = 7 => 0 pairs (X) B1,I1: 7.. / B1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) E3,H3: 7.. / E3 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) A5,I5: 7.. / A5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) F6,H6: 7.. / F6 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) A2,A5: 7.. / A2 = 7 => 0 pairs (X) / A5 = 7 => 0 pairs (_) H3,H6: 7.. / H3 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) I1,I5: 7.. / I1 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) A2,C2: 8.. / A2 = 8 => 0 pairs (*) / C2 = 8 => 0 pairs (X) B4,C4: 8.. / B4 = 8 => 17 pairs (_) / C4 = 8 => 0 pairs (X) E8,E9: 8.. / E8 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A2,A8: 8.. / A2 = 8 => 0 pairs (*) / A8 = 8 => 0 pairs (X) E2,E3: 9.. / E2 = 9 => 0 pairs (*) / E3 = 9 => 0 pairs (X) I1,H3: 9.. / I1 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) F4,F6: 9.. / F4 = 9 => 0 pairs (X) / F6 = 9 => 0 pairs (_) I5,H6: 9.. / I5 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) A8,B8: 9.. / A8 = 9 => 0 pairs (*) / B8 = 9 => 0 pairs (X) B1,I1: 9.. / B1 = 9 => 0 pairs (*) / I1 = 9 => 0 pairs (X) E3,H3: 9.. / E3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) A5,I5: 9.. / A5 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) F6,H6: 9.. / F6 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) C2,C4: 9.. / C2 = 9 => 0 pairs (X) / C4 = 9 => 0 pairs (_) H3,H6: 9.. / H3 = 9 => 0 pairs (*) / H6 = 9 => 0 pairs (X) I1,I5: 9.. / I1 = 9 => 0 pairs (X) / I5 = 9 => 0 pairs (_) * DURATION: 0:00:56.259761 START: 07:33:49.147680 END: 07:34:45.407441 2017-05-04 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,E2,E3,E8,E9,F4,F6,H3,H6,I1,I5) * 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946 * PAIR B1: 7,9 BLK 1 A2: 7,9,8 # reduction candidate for 7,9 A2: 7,9 => CTR * 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946 A2: 8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 C2: 7,9,8 # reduction candidate for 7,9 C2: 7,9 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 C2: 8 => CTR * 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946 * PAIR B1: 7,9 COL B B4: 7,9,8 # reduction candidate for 7,9 B4: 7,9 => CTR * 1.526483.8395716242463985716.843.21571385246945261.3.8361945782..47.61535.71.3946 B4: 8 # 17 pairs * PAIR E2: 7,9 ROW 2 A2: 7,9,8 # reduction candidate for 7,9 A2: 7,9 => CTR * 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946 A2: 8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 C2: 7,9,8 # reduction candidate for 7,9 C2: 7,9 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 C2: 8 => CTR * 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946 * PAIR A5: 7,9 BLK 4 B4: 7,9,8 # reduction candidate for 7,9 B4: 7,9 => CTR * 1.526483.8395716242463985716.843.21571385246945261.3.8361945782..47.61535.71.3946 B4: 8 # 17 pairs C4: 7,9,8 # reduction candidate for 7,9 C4: 7,9 # 17 pairs * PAIR A5: 7,9 COL A A2: 7,9,8 # reduction candidate for 7,9 A2: 7,9 => CTR * 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946 A2: 8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 * PAIR F4: 7,9 ROW 4 B4: 7,9,8 # reduction candidate for 7,9 B4: 7,9 => CTR * 1.526483.8395716242463985716.843.21571385246945261.3.8361945782..47.61535.71.3946 B4: 8 # 17 pairs C4: 7,9,8 # reduction candidate for 7,9 C4: 7,9 # 17 pairs * PAIR A8: 8,9 BLK 7 B8: 8,9,2 # reduction candidate for 8,9 B8: 2 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 B8: 8,9 # 14 pairs * PAIR A8: 8,9 COL A A2: 8,9,7 # reduction candidate for 8,9 A2: 8,9 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 A2: 7 => CTR * 1.526483.73859162424637859168.43.215.1385246.45261.3.8361945782..47.61535..1.3946 * PAIR C9: 7,8 BLK 7 B9: 7,8,2 # reduction candidate for 7,8 B9: 7,8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 B9: 2 # 14 pairs * PAIR C9: 7,8 COL C C2: 7,8,9 # reduction candidate for 7,8 C2: 7,8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 C2: 9 => CTR * 1.526483.8395716242463985716..43.21571385246945261.3.8361945782..47.61535..1.3946 C4: 7,8,9 # reduction candidate for 7,8 C4: 7,8 => CTR * 1.526483..395716242463985716..43.21571385246945261.3.8361945782..47.61535..1.3946 C4: 9 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 * PAIR E8: 2,8 ROW 8 B8: 2,8,9 # reduction candidate for 2,8 B8: 2,8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 B8: 9 => CTR * 175264839.3.57162424639857168.43.215.1385246.45261.3.8361945782.94726153527183946 * PAIR E9: 2,8 ROW 9 B9: 2,8,7 # reduction candidate for 2,8 B9: 7 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 B9: 2,8 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-141-base-pr-000.dot * REASONING * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # C2: 7,9 => SOL * DIS # C2: 8 => CTR => C2: 7,9 * DIS # B4: 7,9 => CTR => B4: 8 * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # C2: 7,9 => SOL * DIS # C2: 8 => CTR => C2: 7,9 * DIS # B4: 7,9 => CTR => B4: 8 * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * DIS # B4: 7,9 => CTR => B4: 8 * PRF # B8: 2 => SOL * PRF # A2: 8,9 => SOL * DIS # A2: 7 => CTR => A2: 8,9 * PRF # B9: 7,8 => SOL * PRF # C2: 7,8 => SOL * DIS # C2: 9 => CTR => C2: 7,8 * DIS # C4: 7,8 => CTR => C4: 9 * PRF # C4: 9 => SOL * PRF # B8: 2,8 => SOL * DIS # B8: 9 => CTR => B8: 2,8 * PRF # B9: 7 => SOL * CNT 24 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A8,B1,C9,E2,E3,E8,E9,F4,F6,H3,H6,I1,I5) * 1.526483..3.5.16242463.85.16..43.215.1385246.45261.3.8361945782..47.61535..1.3946 * PAIR B1: 7,9 BLK 1 A2: 7,9,8 # reduction candidate for 7,9 A2: 7,9 => CTR * 1.526483..385.16242463.85.16894372157138524694526193783619457828947.61535..1.3946 A2: 8 => SOLVED * 195264837837591624246378591689437215713852469452619378361945782924786153578123946 * DURATION: 0:00:01.678434 START: 07:35:24.446127 END: 07:35:26.124561 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-141-base-pr-001.dot * REASONING * DIS # A2: 7,9 => CTR => A2: 8 * PRF A2: 8 => SOL * STA A2: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 141 solution: 195264837837591624246378591689437215713852469452619378361945782924786153578123946 info: 1813 FNBWX S8.f 49017 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 195264837837591624246378591689437215713852469452619378361945782924786153578123946 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 # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # C2: 7,9 => SOL * DIS # C2: 8 => CTR => C2: 7,9 * DIS # B4: 7,9 => CTR => B4: 8 * INC # B4: 8 => UNS * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * PRF # C2: 7,9 => SOL * DIS # C2: 8 => CTR => C2: 7,9 * DIS # B4: 7,9 => CTR => B4: 8 * INC # B4: 8 => UNS * INC # C4: 7,9 => UNS * DIS # A2: 7,9 => CTR => A2: 8 * PRF # A2: 8 => SOL * DIS # B4: 7,9 => CTR => B4: 8 * INC # B4: 8 => UNS * INC # C4: 7,9 => UNS * INC # B8: 8,9 => UNS * PRF # B8: 2 => SOL * PRF # A2: 8,9 => SOL * DIS # A2: 7 => CTR => A2: 8,9 * PRF # B9: 7,8 => SOL * INC # B9: 2 => UNS * PRF # C2: 7,8 => SOL * DIS # C2: 9 => CTR => C2: 7,8 * DIS # C4: 7,8 => CTR => C4: 9 * PRF # C4: 9 => SOL * PRF # B8: 2,8 => SOL * DIS # B8: 9 => CTR => B8: 2,8 * INC # B9: 2,8 => UNS * PRF # B9: 7 => SOL * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A2: 7,9 => CTR => A2: 8 * PRF A2: 8 => SOL * STA A2: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED