Analysis of xx-top500-143-base.sdk
Contents
Original Sudoku
level: medium
position: 46..3..........1...3.......2..1.5......8....6.4.....3.7.1...5.....2............4. initial
Autosolve
position: 462.31.858754.61.31395..6.42831654..917843256546...8317213.456.69425.31.35861..42 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E6: 2,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # E3: 2,8 => SOL * DIS # E3: 7 => CTR => E3: 2,8 * PRF # E3: 2,7 => SOL * DIS # E3: 8 => CTR => E3: 2,7 * PRF # E6: 7,9 => SOL * DIS # E6: 2 => CTR => E6: 7,9 * DIS # E6: 2,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * CNT 10 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E6: 2,9 => CTR => E6: 7 * PRF E6: 7 => SOL * STA E6: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 46..3..........1...3.......2..1.5......8....6.4.....3.7.1...5.....2............4. | initial |
| 462.31.858754.61.31395..6.42831654..917843256546...8317213.456.69425.31.35861..42 | autosolve |
| 462731985875496123139528674283165497917843256546972831721384569694257318358619742 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) D1: 7,9 E2: 2,9 F3: 2,8 G1: 7,9 H2: 2,9 H3: 2,7 D6: 7,9 F6: 2,9 H4: 7,9 I4: 7,9 E7: 8,9 F8: 7,8 F9: 7,9 I7: 8,9 I8: 7,8 G9: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 2.. / H2 = 2 => 0 pairs (*) / H3 = 2 => 0 pairs (X) E6,F6: 2.. / E6 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) E2,H2: 2.. / E2 = 2 => 0 pairs (X) / H2 = 2 => 0 pairs (_) F3,F6: 2.. / F3 = 2 => 0 pairs (X) / F6 = 2 => 0 pairs (_) D1,E3: 7.. / D1 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) G1,H3: 7.. / G1 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) D6,E6: 7.. / D6 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) H4,I4: 7.. / H4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) F8,F9: 7.. / F8 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) I8,G9: 7.. / I8 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) D1,G1: 7.. / D1 = 7 => 0 pairs (*) / G1 = 7 => 0 pairs (X) E3,H3: 7.. / E3 = 7 => 0 pairs (X) / H3 = 7 => 0 pairs (_) F8,I8: 7.. / F8 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) F9,G9: 7.. / F9 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) D1,D6: 7.. / D1 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) E3,E6: 7.. / E3 = 7 => 0 pairs (X) / E6 = 7 => 0 pairs (_) G1,G9: 7.. / G1 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) H3,H4: 7.. / H3 = 7 => 0 pairs (*) / H4 = 7 => 0 pairs (X) I4,I8: 7.. / I4 = 7 => 0 pairs (*) / I8 = 7 => 0 pairs (X) E3,F3: 8.. / E3 = 8 => 0 pairs (X) / F3 = 8 => 0 pairs (_) E7,F8: 8.. / E7 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) I7,I8: 8.. / I7 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) E7,I7: 8.. / E7 = 8 => 0 pairs (*) / I7 = 8 => 0 pairs (X) F8,I8: 8.. / F8 = 8 => 0 pairs (X) / I8 = 8 => 0 pairs (_) E3,E7: 8.. / E3 = 8 => 0 pairs (X) / E7 = 8 => 0 pairs (_) F3,F8: 8.. / F3 = 8 => 0 pairs (*) / F8 = 8 => 0 pairs (X) D1,E2: 9.. / D1 = 9 => 0 pairs (X) / E2 = 9 => 0 pairs (_) G1,H2: 9.. / G1 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) H4,I4: 9.. / H4 = 9 => 0 pairs (*) / I4 = 9 => 0 pairs (X) E7,F9: 9.. / E7 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) I7,G9: 9.. / I7 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) D1,G1: 9.. / D1 = 9 => 0 pairs (X) / G1 = 9 => 0 pairs (_) E2,H2: 9.. / E2 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) E7,I7: 9.. / E7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) F9,G9: 9.. / F9 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) D1,D6: 9.. / D1 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) F6,F9: 9.. / F6 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) G1,G9: 9.. / G1 = 9 => 0 pairs (*) / G9 = 9 => 0 pairs (X) H2,H4: 9.. / H2 = 9 => 0 pairs (X) / H4 = 9 => 0 pairs (_) I4,I7: 9.. / I4 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) * DURATION: 0:01:11.719093 START: 07:37:34.232649 END: 07:38:45.951742 2017-05-04 * CP COUNT: (40) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D6,E2,E7,F3,F6,F8,F9,G1,G9,H2,H3,H4,I4,I7,I8) * 462.31.858754.61.31395..6.42831654..917843256546...8317213.456.69425.31.35861..42 * PAIR E2: 2,9 COL E E6: 2,9,7 # reduction candidate for 2,9 E6: 2,9 => CTR * 462.31.858754.61.3139578624283165479917843256546...8317213.456.69425.31.35861..42 E6: 7 => SOLVED * 462731985875496123139528674283165497917843256546972831721384569694257318358619742 * PAIR F3: 2,8 BLK 2 E3: 2,8,7 # reduction candidate for 2,8 E3: 2,8 => SOLVED * 462731985875496123139528674283165497917843256546972831721384569694257318358619742 E3: 7 => CTR * 462.31.858754.61.3139578624283165479917843256546...8317213.456.69425.31.35861..42 * PAIR H3: 2,7 ROW 3 E3: 2,7,8 # reduction candidate for 2,7 E3: 2,7 => SOLVED * 462731985875496123139528674283165497917843256546972831721384569694257318358619742 E3: 8 => CTR * 46273198587549612313958.6.42831654..917843256546...8317213.456.69425.31.35861..42 * PAIR D6: 7,9 BLK 5 E6: 7,9,2 # reduction candidate for 7,9 E6: 7,9 => SOLVED * 462731985875496123139528674283165497917843256546972831721384569694257318358619742 E6: 2 => CTR * 462.31.858754.61.3139578624283165479917843256546...8317213.456.69425.31.35861..42 * PAIR F6: 2,9 BLK 5 E6: 2,9,7 # reduction candidate for 2,9 E6: 2,9 => CTR * 462.31.858754.61.3139578624283165479917843256546...8317213.456.69425.31.35861..42 E6: 7 => SOLVED * 462731985875496123139528674283165497917843256546972831721384569694257318358619742 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-143-base-pr-000.dot * REASONING * DIS # E6: 2,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # E3: 2,8 => SOL * DIS # E3: 7 => CTR => E3: 2,8 * PRF # E3: 2,7 => SOL * DIS # E3: 8 => CTR => E3: 2,7 * PRF # E6: 7,9 => SOL * DIS # E6: 2 => CTR => E6: 7,9 * DIS # E6: 2,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * CNT 10 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,D6,E2,E7,F3,F6,F8,F9,G1,G9,H2,H3,H4,I4,I7,I8) * 462.31.858754.61.31395..6.42831654..917843256546...8317213.456.69425.31.35861..42 * PAIR E2: 2,9 COL E E6: 2,9,7 # reduction candidate for 2,9 E6: 2,9 => CTR * 462.31.858754.61.3139578624283165479917843256546...8317213.456.69425.31.35861..42 E6: 7 => SOLVED * 462731985875496123139528674283165497917843256546972831721384569694257318358619742 * DURATION: 0:00:02.973158 START: 07:38:59.049698 END: 07:39:02.022856 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-143-base-pr-001.dot * REASONING * DIS # E6: 2,9 => CTR => E6: 7 * PRF E6: 7 => SOL * STA E6: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 143 solution: 462731985875496123139528674283165497917843256546972831721384569694257318358619742 info: 1814 FNBWY S8.f 31740 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 462731985875496123139528674283165497917843256546972831721384569694257318358619742 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 # E6: 2,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * PRF # E3: 2,8 => SOL * DIS # E3: 7 => CTR => E3: 2,8 * PRF # E3: 2,7 => SOL * DIS # E3: 8 => CTR => E3: 2,7 * PRF # E6: 7,9 => SOL * DIS # E6: 2 => CTR => E6: 7,9 * DIS # E6: 2,9 => CTR => E6: 7 * PRF # E6: 7 => SOL * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E6: 2,9 => CTR => E6: 7 * PRF E6: 7 => SOL * STA E6: 7 * CNT 2 HDP CHAINS / 1 HYP OPENED