Analysis of xx-top500-020-base.sdk
Contents
Original Sudoku
level: medium
position: .13...5.....9...4..............13..862...........5....4......637..2...........1.. initial
Autosolve
position: .13...5..5..981342...3.5.1.9..6132586258...31138.52...4521...637.123...53..5..12. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # E1: 4,7 => SOL * DIS # F1: 4,7 => CTR => F1: 6 * DIS # I1: 6,7 => CTR => I1: 9 * PRF # G3: 6,7 => SOL * PRF # E3: 2 => SOL * PRF # I6: 6,7 => SOL * DIS # F5: 4,7 => CTR => F5: 9 * DIS # G6: 4,7 => CTR => G6: 6,9 * DIS # I6: 4,7 => CTR => I6: 6,9 * PRF # I6: 6,9 => SOL * DIS # G6: 4,7 => CTR => G6: 6,9 * DIS # I6: 4,7 => CTR => I6: 6,9 * PRF # I6: 6,9 => SOL * DIS # F5: 4,7 => CTR => F5: 9 * PRF # G6: 7,9 => SOL * DIS # I6: 7,9 => CTR => I6: 4,6 * PRF # H1: 8 => SOL * DIS # B9: 6,9 => CTR => B9: 8 * DIS # F9: 6,9 => CTR => F9: 4,7,8 * DIS # F7: 7,9 => CTR => F7: 8 * DIS # E9: 7,9 => CTR => E9: 4,6 * DIS # G7: 8 => CTR => G7: 7,9 * PRF # E5: 7,9 => SOL * DIS # E5: 4 => CTR => E5: 7,9 * DIS # G7: 8,9 => CTR => G7: 7 * PRF # G7: 7 => SOL * PRF # G8: 8,9 => SOL * DIS # G8: 4 => CTR => G8: 8,9 * DIS # B8: 8,9 => CTR => B8: 6 * DIS # F8: 8,9 => CTR => F8: 4,6 * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * CNT 32 HDP CHAINS / 57 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # E1: 4,7 => SOL * STA E1: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .13...5.....9...4..............13..862...........5....4......637..2...........1.. | initial |
| .13...5..5..981342...3.5.1.9..6132586258...31138.52...4521...637.123...53..5..12. | autosolve |
| 213746589576981342894325617947613258625879431138452976452198763761234895389567124 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (16) A1: 2,8 B2: 6,7 C2: 6,7 A3: 2,8 B3: 4,9 C3: 4,9 D1: 4,7 I3: 6,7 B4: 4,7 C4: 4,7 D6: 4,7 G5: 4,7 H6: 7,9 C9: 6,9 E7: 7,9 H8: 8,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A1,A3: 2.. / A1 = 2 => 0 pairs (*) / A3 = 2 => 0 pairs (X) E1,E3: 2.. / E1 = 2 => 19 pairs (_) / E3 = 2 => 0 pairs (*) A1,E1: 2.. / A1 = 2 => 0 pairs (*) / E1 = 2 => 0 pairs (X) A3,E3: 2.. / A3 = 2 => 19 pairs (_) / E3 = 2 => 0 pairs (*) B3,C3: 4.. / B3 = 4 => 0 pairs (X) / C3 = 4 => 12 pairs (_) B4,C4: 4.. / B4 = 4 => 12 pairs (_) / C4 = 4 => 0 pairs (X) G8,I9: 4.. / G8 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) F8,G8: 4.. / F8 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) B3,B4: 4.. / B3 = 4 => 0 pairs (X) / B4 = 4 => 12 pairs (_) C3,C4: 4.. / C3 = 4 => 12 pairs (_) / C4 = 4 => 0 pairs (X) D1,D6: 4.. / D1 = 4 => 0 pairs (X) / D6 = 4 => 0 pairs (_) I6,I9: 4.. / I6 = 4 => 0 pairs (X) / I9 = 4 => 0 pairs (_) B2,C2: 6.. / B2 = 6 => 0 pairs (X) / C2 = 6 => 12 pairs (_) G6,I6: 6.. / G6 = 6 => 19 pairs (_) / I6 = 6 => 0 pairs (*) B8,F8: 6.. / B8 = 6 => 10 pairs (_) / F8 = 6 => 0 pairs (X) C2,C9: 6.. / C2 = 6 => 12 pairs (_) / C9 = 6 => 0 pairs (X) G3,G6: 6.. / G3 = 6 => 0 pairs (*) / G6 = 6 => 0 pairs (X) B2,C2: 7.. / B2 = 7 => 12 pairs (_) / C2 = 7 => 0 pairs (X) B4,C4: 7.. / B4 = 7 => 0 pairs (X) / C4 = 7 => 12 pairs (_) G7,I9: 7.. / G7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) B2,B4: 7.. / B2 = 7 => 12 pairs (_) / B4 = 7 => 0 pairs (X) C2,C4: 7.. / C2 = 7 => 0 pairs (X) / C4 = 7 => 12 pairs (_) D1,D6: 7.. / D1 = 7 => 0 pairs (*) / D6 = 7 => 0 pairs (X) H1,H6: 7.. / H1 = 7 => 0 pairs (X) / H6 = 7 => 0 pairs (_) A1,A3: 8.. / A1 = 8 => 19 pairs (_) / A3 = 8 => 0 pairs (*) H1,G3: 8.. / H1 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) B8,B9: 8.. / B8 = 8 => 0 pairs (X) / B9 = 8 => 17 pairs (_) A1,H1: 8.. / A1 = 8 => 19 pairs (_) / H1 = 8 => 0 pairs (*) A3,G3: 8.. / A3 = 8 => 0 pairs (*) / G3 = 8 => 0 pairs (X) F7,G7: 8.. / F7 = 8 => 18 pairs (_) / G7 = 8 => 0 pairs (X) B9,F9: 8.. / B9 = 8 => 17 pairs (_) / F9 = 8 => 0 pairs (X) H1,H8: 8.. / H1 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) B3,C3: 9.. / B3 = 9 => 12 pairs (_) / C3 = 9 => 0 pairs (X) H1,I1: 9.. / H1 = 9 => 0 pairs (X) / I1 = 9 => 19 pairs (_) E5,F5: 9.. / E5 = 9 => 0 pairs (X) / F5 = 9 => 18 pairs (_) C3,C9: 9.. / C3 = 9 => 0 pairs (X) / C9 = 9 => 12 pairs (_) * DURATION: 0:01:06.126649 START: 03:15:28.554362 END: 03:16:34.681011 2017-05-04 * CP COUNT: (36) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,B4,C2,C3,C4,C9,D1,D6,E7,G5,H6,H8,I3) * .13...5..5..981342...3.5.1.9..6132586258...31138.52...4521...637.123...53..5..12. * PAIR D1: 4,7 BLK 2 E1: 4,7,2,6 # reduction candidate for 4,7 E1: 4,7 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 E1: 2,6 # 17 pairs F1: 4,7,6 # reduction candidate for 4,7 F1: 4,7 => CTR * .137.45..5..981342...3.5.1.9..6132586258..431138452.7.4521...637.123...53..54.12. F1: 6 # 14 pairs * PAIR I3: 6,7 BLK 3 I1: 6,7,9 # reduction candidate for 6,7 I1: 6,7 => CTR * 8137245965.698134229436581794761325862584..31138.526794521.87637.123.9853895..124 I1: 9 # 19 pairs G3: 6,7,8 # reduction candidate for 6,7 G3: 6,7 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 G3: 8 # 19 pairs * PAIR I3: 6,7 ROW 3 E3: 6,7,2 # reduction candidate for 6,7 E3: 2 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 E3: 6,7 # 19 pairs * PAIR I3: 6,7 COL I I6: 6,7,4,9 # reduction candidate for 6,7 I6: 6,7 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 I6: 4,9 # 20 pairs * PAIR D6: 4,7 BLK 5 E5: 4,7,9 # reduction candidate for 4,7 E5: 4,7 # 18 pairs F5: 4,7,9 # reduction candidate for 4,7 F5: 4,7 => CTR * .13...5..5..981342...3.57169..61325862589743113845267945217..637.123...53..5..127 F5: 9 # 18 pairs * PAIR D6: 4,7 ROW 6 G6: 4,7,6,9 # reduction candidate for 4,7 G6: 4,7 => CTR * .13...5..5..981342...3.56179..6132586258...31138.52.7.4521...637.123...53..5..12. G6: 6,9 # 17 pairs I6: 4,7,6,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 813.2.5795..9813422..3758169..6132586258...311387526944521987637.123..8538.5..12. I6: 6,9 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 * PAIR G5: 4,7 BLK 6 G6: 4,7,6,9 # reduction candidate for 4,7 G6: 4,7 => CTR * .13...5..5..981342...3.56179..6132586258...31138.52.7.4521...637.123...53..5..12. G6: 6,9 # 17 pairs I6: 4,7,6,9 # reduction candidate for 4,7 I6: 4,7 => CTR * 813.2.5795..9813422..3758169..6132586258...311387526944521987637.123..8538.5..12. I6: 6,9 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 * PAIR G5: 4,7 ROW 5 E5: 4,7,9 # reduction candidate for 4,7 E5: 4,7 # 18 pairs F5: 4,7,9 # reduction candidate for 4,7 F5: 4,7 => CTR * .13...5..5..981342...3.57169..61325862589743113845267945217..637.123...53..5..127 F5: 9 # 18 pairs * PAIR H6: 7,9 BLK 6 G6: 7,9,4,6 # reduction candidate for 7,9 G6: 7,9 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 G6: 4,6 # 19 pairs I6: 7,9,4,6 # reduction candidate for 7,9 I6: 7,9 => CTR * 8137..5..5..981342...3.5.1.9..6132586258..4311384526..4521..7637.12349853895..124 I6: 4,6 # 17 pairs * PAIR H6: 7,9 COL H H1: 7,9,8 # reduction candidate for 7,9 H1: 8 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 H1: 7,9 # 19 pairs * PAIR C9: 6,9 BLK 7 B8: 6,9,8 # reduction candidate for 6,9 B8: 6,9 # 17 pairs B9: 6,9,8 # reduction candidate for 6,9 B9: 6,9 => CTR * .13...5..5..981342...3.5.1.9..6132586258...31138.52...4521...637812364953..5.8127 B9: 8 # 17 pairs * PAIR C9: 6,9 ROW 9 E9: 6,9,4,7 # reduction candidate for 6,9 E9: 6,9 # 22 pairs F9: 6,9,4,7,8 # reduction candidate for 6,9 F9: 6,9 => CTR * .13...5..5..981342...3.5.1.9..6132586258..431138452.7.4521...637.1234..538.576124 F9: 4,7,8 # 16 pairs * PAIR E7: 7,9 BLK 8 F7: 7,9,8 # reduction candidate for 7,9 F7: 7,9 => CTR * .13...5895..9813428..3257169..6132586258..431138.52...4521..8637.123..953..5..127 F7: 8 # 18 pairs E9: 7,9,4,6 # reduction candidate for 7,9 E9: 7,9 => CTR * .13..75..5..981342...3.5.1.9..6132586258.9.31138752.9.4521.8.637.123..853..5..12. E9: 4,6 # 17 pairs F9: 7,9,4,6,8 # reduction candidate for 7,9 F9: 7,9 # 21 pairs * PAIR E7: 7,9 ROW 7 G7: 7,9,8 # reduction candidate for 7,9 G7: 8 => CTR * .13...5895..9813428..3257169..6132586258..431138.52...4521..8637.123..953..5..127 G7: 7,9 # 18 pairs * PAIR E7: 7,9 COL E E5: 7,9,4 # reduction candidate for 7,9 E5: 7,9 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 E5: 4 => CTR * 81342.5795..9813422..3758169..61325862584973113875269445219..637.123..8538.5..127 * PAIR H8: 8,9 BLK 9 G7: 8,9,7 # reduction candidate for 8,9 G7: 8,9 => CTR * 8134265795..9813422..375.169..6132586258..7311387526944521..9637.123.48538.5..127 G7: 7 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 G8: 8,9,4 # reduction candidate for 8,9 G8: 8,9 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 G8: 4 => CTR * 81342.5795..9813422..375.1.9..6132586258..731138752.944521..9637.123.48538.5..127 * PAIR H8: 8,9 ROW 8 B8: 8,9,6 # reduction candidate for 8,9 B8: 8,9 => CTR * 8134275..5..981342...3.5.1.9..6132586258..731138752.944521..9637912364853865..127 B8: 6 # 10 pairs F8: 8,9,4,6 # reduction candidate for 8,9 F8: 8,9 => CTR * 813426579576981342294375.169476132586258..7311387526944521..9637612394853895..127 F8: 4,6 # 17 pairs * PAIR H8: 8,9 COL H H1: 8,9,7 # reduction candidate for 8,9 H1: 8,9 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 H1: 7 => CTR * 813.2.5795..9813422..3758169..6132586258...311387526944521987637.123...53..5..12. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-020-base-pr-000.dot * REASONING * PRF # E1: 4,7 => SOL * DIS # F1: 4,7 => CTR => F1: 6 * DIS # I1: 6,7 => CTR => I1: 9 * PRF # G3: 6,7 => SOL * PRF # E3: 2 => SOL * PRF # I6: 6,7 => SOL * DIS # F5: 4,7 => CTR => F5: 9 * DIS # G6: 4,7 => CTR => G6: 6,9 * DIS # I6: 4,7 => CTR => I6: 6,9 * PRF # I6: 6,9 => SOL * DIS # G6: 4,7 => CTR => G6: 6,9 * DIS # I6: 4,7 => CTR => I6: 6,9 * PRF # I6: 6,9 => SOL * DIS # F5: 4,7 => CTR => F5: 9 * PRF # G6: 7,9 => SOL * DIS # I6: 7,9 => CTR => I6: 4,6 * PRF # H1: 8 => SOL * DIS # B9: 6,9 => CTR => B9: 8 * DIS # F9: 6,9 => CTR => F9: 4,7,8 * DIS # F7: 7,9 => CTR => F7: 8 * DIS # E9: 7,9 => CTR => E9: 4,6 * DIS # G7: 8 => CTR => G7: 7,9 * PRF # E5: 7,9 => SOL * DIS # E5: 4 => CTR => E5: 7,9 * DIS # G7: 8,9 => CTR => G7: 7 * PRF # G7: 7 => SOL * PRF # G8: 8,9 => SOL * DIS # G8: 4 => CTR => G8: 8,9 * DIS # B8: 8,9 => CTR => B8: 6 * DIS # F8: 8,9 => CTR => F8: 4,6 * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * CNT 32 HDP CHAINS / 57 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A3,B2,B3,B4,C2,C3,C4,C9,D1,D6,E7,G5,H6,H8,I3) * .13...5..5..981342...3.5.1.9..6132586258...31138.52...4521...637.123...53..5..12. * PAIR D1: 4,7 BLK 2 E1: 4,7,2,6 # reduction candidate for 4,7 E1: 4,7 => SOLVED * 213746589576981342894325617947613258625879431138452976452198763761234895389567124 * DURATION: 0:00:02.461539 START: 03:17:33.584426 END: 03:17:36.045965 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-020-base-pr-001.dot * REASONING * PRF # E1: 4,7 => SOL * STA E1: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 020 solution: 213746589576981342894325617947613258625879431138452976452198763761234895389567124 info: 1312 FNBWXY S8.f 15843 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 213746589576981342894325617947613258625879431138452976452198763761234895389567124 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 # E1: 4,7 => SOL * INC # E1: 2,6 => UNS * DIS # F1: 4,7 => CTR => F1: 6 * INC # F1: 6 => UNS * DIS # I1: 6,7 => CTR => I1: 9 * INC # I1: 9 => UNS * PRF # G3: 6,7 => SOL * INC # G3: 8 => UNS * INC # E3: 6,7 => UNS * PRF # E3: 2 => SOL * PRF # I6: 6,7 => SOL * INC # I6: 4,9 => UNS * INC # E5: 4,7 => UNS * DIS # F5: 4,7 => CTR => F5: 9 * INC # F5: 9 => UNS * DIS # G6: 4,7 => CTR => G6: 6,9 * INC # G6: 6,9 => UNS * DIS # I6: 4,7 => CTR => I6: 6,9 * PRF # I6: 6,9 => SOL * DIS # G6: 4,7 => CTR => G6: 6,9 * INC # G6: 6,9 => UNS * DIS # I6: 4,7 => CTR => I6: 6,9 * PRF # I6: 6,9 => SOL * INC # E5: 4,7 => UNS * DIS # F5: 4,7 => CTR => F5: 9 * INC # F5: 9 => UNS * PRF # G6: 7,9 => SOL * INC # G6: 4,6 => UNS * DIS # I6: 7,9 => CTR => I6: 4,6 * INC # I6: 4,6 => UNS * INC # H1: 7,9 => UNS * PRF # H1: 8 => SOL * INC # B8: 6,9 => UNS * DIS # B9: 6,9 => CTR => B9: 8 * INC # B9: 8 => UNS * INC # E9: 6,9 => UNS * DIS # F9: 6,9 => CTR => F9: 4,7,8 * INC # F9: 4,7,8 => UNS * DIS # F7: 7,9 => CTR => F7: 8 * INC # F7: 8 => UNS * DIS # E9: 7,9 => CTR => E9: 4,6 * INC # E9: 4,6 => UNS * INC # F9: 7,9 => UNS * INC # G7: 7,9 => UNS * DIS # G7: 8 => CTR => G7: 7,9 * PRF # E5: 7,9 => SOL * DIS # E5: 4 => CTR => E5: 7,9 * DIS # G7: 8,9 => CTR => G7: 7 * PRF # G7: 7 => SOL * PRF # G8: 8,9 => SOL * DIS # G8: 4 => CTR => G8: 8,9 * DIS # B8: 8,9 => CTR => B8: 6 * INC # B8: 6 => UNS * DIS # F8: 8,9 => CTR => F8: 4,6 * INC # F8: 4,6 => UNS * PRF # H1: 8,9 => SOL * DIS # H1: 7 => CTR => H1: 8,9 * CNT 57 HDP CHAINS / 57 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # E1: 4,7 => SOL * STA E1: 4,7 * CNT 1 HDP CHAINS / 1 HYP OPENED