Analysis of xx-top500-367-base.sdk
Contents
Original Sudoku
level: medium
position: 3.41.....5....76.....2.....6...3.....8......7.......1.72...........8.3...1....... initial
Autosolve
position: 3741682..5923476811682..7436.173.82.28..16437.3782..1672.4.31.8....81372813.72..4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * DIS # F4: 9 => CTR => F4: 4,5 * DIS # F6: 5 => CTR => F6: 4,9 * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * CNT 14 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:
* PRF # F4: 5,9 => SOL * STA F4: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.41.....5....76.....2.....6...3.....8......7.......1.72...........8.3...1....... | initial |
| 3741682..5923476811682..7436.173.82.28..16437.3782..1672.4.31.8....81372813.72..4 | autosolve |
| 374168295592347681168259743641735829285916437937824516726493158459681372813572964 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (14) E3: 5,9 F3: 5,9 H1: 5,9 I1: 5,9 B4: 4,5 C5: 5,9 A6: 4,9 D5: 5,9 I4: 5,9 G6: 5,9 A8: 4,9 B8: 4,5 E7: 5,9 G9: 5,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B4,A6: 4.. / B4 = 4 => 0 pairs (*) / A6 = 4 => 0 pairs (X) F4,F6: 4.. / F4 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) A8,B8: 4.. / A8 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) B4,F4: 4.. / B4 = 4 => 0 pairs (*) / F4 = 4 => 0 pairs (X) A6,F6: 4.. / A6 = 4 => 0 pairs (X) / F6 = 4 => 0 pairs (_) A6,A8: 4.. / A6 = 4 => 0 pairs (X) / A8 = 4 => 0 pairs (_) B4,B8: 4.. / B4 = 4 => 0 pairs (*) / B8 = 4 => 0 pairs (X) E3,F3: 5.. / E3 = 5 => 0 pairs (*) / F3 = 5 => 0 pairs (X) H1,I1: 5.. / H1 = 5 => 0 pairs (X) / I1 = 5 => 14 pairs (_) B4,C5: 5.. / B4 = 5 => 0 pairs (X) / C5 = 5 => 0 pairs (_) I4,G6: 5.. / I4 = 5 => 0 pairs (X) / G6 = 5 => 14 pairs (_) C5,D5: 5.. / C5 = 5 => 0 pairs (*) / D5 = 5 => 0 pairs (X) F6,G6: 5.. / F6 = 5 => 0 pairs (X) / G6 = 5 => 14 pairs (_) B4,B8: 5.. / B4 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) E3,E7: 5.. / E3 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) G6,G9: 5.. / G6 = 5 => 14 pairs (_) / G9 = 5 => 0 pairs (X) I1,I4: 5.. / I1 = 5 => 14 pairs (_) / I4 = 5 => 0 pairs (X) C7,C8: 6.. / C7 = 6 => 17 pairs (_) / C8 = 6 => 17 pairs (_) D8,D9: 6.. / D8 = 6 => 17 pairs (_) / D9 = 6 => 17 pairs (_) H7,H9: 6.. / H7 = 6 => 17 pairs (_) / H9 = 6 => 17 pairs (_) C7,H7: 6.. / C7 = 6 => 17 pairs (_) / H7 = 6 => 17 pairs (_) C8,D8: 6.. / C8 = 6 => 17 pairs (_) / D8 = 6 => 17 pairs (_) D9,H9: 6.. / D9 = 6 => 17 pairs (_) / H9 = 6 => 17 pairs (_) E3,F3: 9.. / E3 = 9 => 0 pairs (X) / F3 = 9 => 0 pairs (_) H1,I1: 9.. / H1 = 9 => 14 pairs (_) / I1 = 9 => 0 pairs (X) C5,A6: 9.. / C5 = 9 => 0 pairs (X) / A6 = 9 => 0 pairs (_) I4,G6: 9.. / I4 = 9 => 14 pairs (_) / G6 = 9 => 0 pairs (X) F4,I4: 9.. / F4 = 9 => 0 pairs (X) / I4 = 9 => 14 pairs (_) C5,D5: 9.. / C5 = 9 => 0 pairs (X) / D5 = 9 => 0 pairs (_) A6,A8: 9.. / A6 = 9 => 0 pairs (*) / A8 = 9 => 0 pairs (X) E3,E7: 9.. / E3 = 9 => 0 pairs (X) / E7 = 9 => 0 pairs (_) G6,G9: 9.. / G6 = 9 => 0 pairs (X) / G9 = 9 => 14 pairs (_) I1,I4: 9.. / I1 = 9 => 0 pairs (X) / I4 = 9 => 14 pairs (_) * DURATION: 0:00:55.276558 START: 15:23:32.074147 END: 15:24:27.350705 2017-05-04 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B4,B8,C5,D5,E3,E7,F3,G6,G9,H1,I1,I4) * 3741682..5923476811682..7436.173.82.28..16437.3782..1672.4.31.8....81372813.72..4 * PAIR F3: 5,9 COL F F4: 5,9,4 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 F4: 4 => CTR * 3741682..5923476811682..7436.173482928..1643743782951672.4.31.894..81372813972..4 F6: 5,9,4 # reduction candidate for 5,9 F6: 5,9 => CTR * 3741682..5923476811682..7436.173482928..1643743782951672.4.31.894..81372813972..4 F6: 4 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 * PAIR H1: 5,9 COL H H7: 5,9,6 # reduction candidate for 5,9 H7: 5,9 # 17 pairs H9: 5,9,6 # reduction candidate for 5,9 H9: 5,9 # 17 pairs * PAIR B4: 4,5 ROW 4 F4: 4,5,9 # reduction candidate for 4,5 F4: 9 => CTR * 3741682..5923476811682..74364173982528..16437.3782..1672.4.31.8....81372813.72..4 F4: 4,5 # 14 pairs * PAIR C5: 5,9 COL C C7: 5,9,6 # reduction candidate for 5,9 C7: 5,9 # 17 pairs C8: 5,9,6 # reduction candidate for 5,9 C8: 5,9 # 17 pairs * PAIR A6: 4,9 ROW 6 F6: 4,9,5 # reduction candidate for 4,9 F6: 5 => CTR * 3741682..5923476811682..7436.173482928.916437.3782..1672.4.31.8....81372813.72..4 F6: 4,9 # 14 pairs * PAIR D5: 5,9 BLK 5 F4: 5,9,4 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 F4: 4 => CTR * 3741682..5923476811682..7436.173482928..1643743782951672.4.31.894..81372813972..4 F6: 5,9,4 # reduction candidate for 5,9 F6: 5,9 => CTR * 3741682..5923476811682..7436.173482928..1643743782951672.4.31.894..81372813972..4 F6: 4 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 * PAIR D5: 5,9 COL D D8: 5,9,6 # reduction candidate for 5,9 D8: 5,9 # 17 pairs D9: 5,9,6 # reduction candidate for 5,9 D9: 5,9 # 17 pairs * PAIR I4: 5,9 ROW 4 F4: 5,9,4 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 F4: 4 => CTR * 3741682..5923476811682..7436.173482928..1643743782951672.4.31.894..81372813972..4 * PAIR G6: 5,9 ROW 6 F6: 5,9,4 # reduction candidate for 5,9 F6: 5,9 => CTR * 3741682..5923476811682..7436.173482928..1643743782951672.4.31.894..81372813972..4 F6: 4 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 * PAIR E7: 5,9 BLK 8 D8: 5,9,6 # reduction candidate for 5,9 D8: 5,9 # 17 pairs D9: 5,9,6 # reduction candidate for 5,9 D9: 5,9 # 17 pairs * PAIR E7: 5,9 ROW 7 C7: 5,9,6 # reduction candidate for 5,9 C7: 5,9 # 17 pairs H7: 5,9,6 # reduction candidate for 5,9 H7: 5,9 # 17 pairs * PAIR G9: 5,9 BLK 9 H7: 5,9,6 # reduction candidate for 5,9 H7: 5,9 # 17 pairs H9: 5,9,6 # reduction candidate for 5,9 H9: 5,9 # 17 pairs * PAIR G9: 5,9 ROW 9 D9: 5,9,6 # reduction candidate for 5,9 D9: 6 # 17 pairs D9: 5,9 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-367-base-pr-000.dot * REASONING * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * DIS # F4: 9 => CTR => F4: 4,5 * DIS # F6: 5 => CTR => F6: 4,9 * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * CNT 14 HDP CHAINS / 30 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A6,A8,B4,B8,C5,D5,E3,E7,F3,G6,G9,H1,I1,I4) * 3741682..5923476811682..7436.173.82.28..16437.3782..1672.4.31.8....81372813.72..4 * PAIR F3: 5,9 COL F F4: 5,9,4 # reduction candidate for 5,9 F4: 5,9 => SOLVED * 374168295592347681168259743641735829285916437937824516726493158459681372813572964 * DURATION: 0:00:01.947626 START: 15:24:57.434816 END: 15:24:59.382442 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-367-base-pr-001.dot * REASONING * PRF # F4: 5,9 => SOL * STA F4: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 367 solution: 374168295592347681168259743641735829285916437937824516726493158459681372813572964 info: 5144 FNWX S8.f 45272 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 374168295592347681168259743641735829285916437937824516726493158459681372813572964 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 # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * INC # H7: 5,9 => UNS * INC # H9: 5,9 => UNS * INC # F4: 4,5 => UNS * DIS # F4: 9 => CTR => F4: 4,5 * INC # C7: 5,9 => UNS * INC # C8: 5,9 => UNS * INC # F6: 4,9 => UNS * DIS # F6: 5 => CTR => F6: 4,9 * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * INC # D8: 5,9 => UNS * INC # D9: 5,9 => UNS * PRF # F4: 5,9 => SOL * DIS # F4: 4 => CTR => F4: 5,9 * DIS # F6: 5,9 => CTR => F6: 4 * PRF # F6: 4 => SOL * INC # D8: 5,9 => UNS * INC # D9: 5,9 => UNS * INC # C7: 5,9 => UNS * INC # H7: 5,9 => UNS * INC # H7: 5,9 => UNS * INC # H9: 5,9 => UNS * INC # D9: 5,9 => UNS * INC # D9: 6 => UNS * CNT 30 HDP CHAINS / 30 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # F4: 5,9 => SOL * STA F4: 5,9 * CNT 1 HDP CHAINS / 1 HYP OPENED