Analysis of xx-top500-047-base.sdk
Contents
Original Sudoku
level: medium
position: 4.....6......7..5......1......43.2...17.......5.....3.8..6..3.....2............1. initial
Autosolve
position: 4315..6.7....7.15.7.5..1......435271317...5..2541.7.3.87.61.3.51..25.7..5..7...1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # B2: 6,9 => CTR => B2: 2,8 * PRF # G3: 8,9 => SOL * DIS # H3: 8,9 => CTR => H3: 2,4 * DIS # F1: 8,9 => CTR => F1: 2 * DIS # H8: 8,9 => CTR => H8: 4,6 * DIS # E5: 8,9 => CTR => E5: 2,6 * PRF # F5: 8,9 => SOL * DIS # I5: 8,9 => CTR => I5: 4,6 * DIS # I5: 8,9 => CTR => I5: 4,6 * PRF # I6: 8,9 => SOL * PRF # E6: 6 => SOL * PRF # G3: 8,9 => SOL * DIS # C9: 2,9 => CTR => C9: 3,6 * PRF # H7: 2,9 => SOL * PRF # F8: 4,9 => SOL * DIS # F9: 4,9 => CTR => F9: 3,8 * DIS # H7: 2 => CTR => H7: 4,9 * CNT 17 HDP CHAINS / 52 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # B2: 6,9 => CTR => B2: 2,8 * PRF B2: 2,8 # G3: 8,9 => SOL * STA B2: 2,8 + G3: 8,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4.....6......7..5......1......43.2...17.......5.....3.8..6..3.....2............1. | initial |
| 4315..6.7....7.15.7.5..1......435271317...5..2541.7.3.87.61.3.51..25.7..5..7...1. | autosolve |
| 431592687928376154765841923689435271317928546254167839872614395143259768596783412 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A2: 6,9 F2: 4,6 E3: 4,6 H1: 8,9 A4: 6,9 D5: 8,9 G6: 8,9 C7: 2,9 F7: 4,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 2.. / E1 = 2 => 0 pairs (X) / F1 = 2 => 10 pairs (_) E5,F5: 2.. / E5 = 2 => 10 pairs (_) / F5 = 2 => 0 pairs (X) H7,I9: 2.. / H7 = 2 => 0 pairs (X) / I9 = 2 => 11 pairs (_) C7,H7: 2.. / C7 = 2 => 11 pairs (_) / H7 = 2 => 0 pairs (X) E1,E5: 2.. / E1 = 2 => 0 pairs (X) / E5 = 2 => 10 pairs (_) F1,F5: 2.. / F1 = 2 => 10 pairs (_) / F5 = 2 => 0 pairs (X) H3,H7: 2.. / H3 = 2 => 11 pairs (_) / H7 = 2 => 0 pairs (X) D2,D3: 3.. / D2 = 3 => 10 pairs (_) / D3 = 3 => 17 pairs (_) I2,I3: 3.. / I2 = 3 => 17 pairs (_) / I3 = 3 => 10 pairs (_) C8,C9: 3.. / C8 = 3 => 9 pairs (_) / C9 = 3 => 14 pairs (_) F8,F9: 3.. / F8 = 3 => 14 pairs (_) / F9 = 3 => 9 pairs (_) D2,I2: 3.. / D2 = 3 => 10 pairs (_) / I2 = 3 => 17 pairs (_) D3,I3: 3.. / D3 = 3 => 17 pairs (_) / I3 = 3 => 10 pairs (_) C8,F8: 3.. / C8 = 3 => 9 pairs (_) / F8 = 3 => 14 pairs (_) C9,F9: 3.. / C9 = 3 => 14 pairs (_) / F9 = 3 => 9 pairs (_) F2,E3: 4.. / F2 = 4 => 15 pairs (_) / E3 = 4 => 0 pairs (*) H5,I5: 4.. / H5 = 4 => 0 pairs (*) / I5 = 4 => 0 pairs (X) B8,B9: 4.. / B8 = 4 => 9 pairs (_) / B9 = 4 => 0 pairs (X) F2,I2: 4.. / F2 = 4 => 15 pairs (_) / I2 = 4 => 0 pairs (*) F7,H7: 4.. / F7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) E3,E9: 4.. / E3 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) G3,G9: 4.. / G3 = 4 => 15 pairs (_) / G9 = 4 => 0 pairs (*) F2,E3: 6.. / F2 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) B3,E3: 6.. / B3 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) E6,I6: 6.. / E6 = 6 => 0 pairs (*) / I6 = 6 => 0 pairs (X) A2,A4: 6.. / A2 = 6 => 16 pairs (_) / A4 = 6 => 10 pairs (_) F2,F5: 6.. / F2 = 6 => 0 pairs (*) / F5 = 6 => 0 pairs (X) H5,H8: 6.. / H5 = 6 => 0 pairs (X) / H8 = 6 => 11 pairs (_) B4,C4: 8.. / B4 = 8 => 11 pairs (_) / C4 = 8 => 10 pairs (_) C2,C4: 8.. / C2 = 8 => 11 pairs (_) / C4 = 8 => 10 pairs (_) A2,A4: 9.. / A2 = 9 => 10 pairs (_) / A4 = 9 => 16 pairs (_) * DURATION: 0:00:49.354619 START: 04:16:12.656731 END: 04:17:02.011350 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,C7,D5,E3,F2,F7,G6,H1) * 4315..6.7....7.15.7.5..1......435271317...5..2541.7.3.87.61.3.51..25.7..5..7...1. * PAIR A2: 6,9 BLK 1 B2: 6,9,2,8 # reduction candidate for 6,9 B2: 6,9 => CTR * 4315.26.7..2.7415.7.5.61......435271317..65..2541.7.3687.61934514.25.76.5..74..12 B2: 2,8 # 10 pairs C2: 6,9,2,8 # reduction candidate for 6,9 C2: 6,9 # 20 pairs B3: 6,9,2,8 # reduction candidate for 6,9 B3: 6,9 # 13 pairs * PAIR H1: 8,9 BLK 3 I2: 8,9,2,3,4 # reduction candidate for 8,9 I2: 8,9 # 17 pairs G3: 8,9,4 # reduction candidate for 8,9 G3: 8,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 G3: 4 # 15 pairs H3: 8,9,2,4 # reduction candidate for 8,9 H3: 8,9 => CTR * 4315..6.7....76154765..1......435271317...5..2541.7.3.8796143251..25.7..5..7...1. H3: 2,4 # 10 pairs I3: 8,9,2,3,4 # reduction candidate for 8,9 I3: 8,9 # 17 pairs * PAIR H1: 8,9 ROW 1 E1: 8,9,2 # reduction candidate for 8,9 E1: 8,9 # 10 pairs F1: 8,9,2 # reduction candidate for 8,9 F1: 8,9 => CTR * 43152.6.7928376154765.41.23689435271317..254.2541.7.3.872614395143259768596783412 F1: 2 # 10 pairs * PAIR H1: 8,9 COL H H5: 8,9,4,6 # reduction candidate for 8,9 H5: 8,9 # 15 pairs H8: 8,9,4,6 # reduction candidate for 8,9 H8: 8,9 => CTR * 4315..6.7....7.15.7.5..1......435271317...564254167.3.87.61.3.51..25.7..5..7...1. H8: 4,6 # 10 pairs * PAIR A4: 6,9 BLK 4 B4: 6,9,8 # reduction candidate for 6,9 B4: 6,9 # 10 pairs C4: 6,9,8 # reduction candidate for 6,9 C4: 6,9 # 11 pairs * PAIR D5: 8,9 BLK 5 E5: 8,9,2,6 # reduction candidate for 8,9 E5: 8,9 => CTR * 43152.6.7928376154765.41.23689435271317..2546254167.3.872614395143259768596783412 E5: 2,6 # 10 pairs F5: 8,9,2,6 # reduction candidate for 8,9 F5: 8,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 F5: 2,6 # 10 pairs E6: 8,9,6 # reduction candidate for 8,9 E6: 8,9 # 14 pairs * PAIR D5: 8,9 ROW 5 H5: 8,9,4,6 # reduction candidate for 8,9 H5: 8,9 # 15 pairs I5: 8,9,4,6 # reduction candidate for 8,9 I5: 8,9 => CTR * 43152.6.7928376154765.41.23689435271317.6254.2541.7.36872614395143259768596783412 I5: 4,6 # 10 pairs * PAIR D5: 8,9 COL D D2: 8,9,3 # reduction candidate for 8,9 D2: 8,9 # 17 pairs D3: 8,9,3 # reduction candidate for 8,9 D3: 8,9 # 10 pairs * PAIR G6: 8,9 BLK 6 H5: 8,9,4,6 # reduction candidate for 8,9 H5: 8,9 # 15 pairs I5: 8,9,4,6 # reduction candidate for 8,9 I5: 8,9 => CTR * 43152.6.7928376154765.41.23689435271317.6254.2541.7.36872614395143259768596783412 I5: 4,6 # 10 pairs I6: 8,9,6 # reduction candidate for 8,9 I6: 8,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 I6: 6 # 14 pairs * PAIR G6: 8,9 ROW 6 E6: 8,9,6 # reduction candidate for 8,9 E6: 6 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 E6: 8,9 # 14 pairs * PAIR G6: 8,9 COL G G3: 8,9,4 # reduction candidate for 8,9 G3: 8,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 G3: 4 # 15 pairs G9: 8,9,4 # reduction candidate for 8,9 G9: 8,9 # 15 pairs * PAIR C7: 2,9 BLK 7 B9: 2,9,4,6 # reduction candidate for 2,9 B9: 2,9 # 13 pairs C9: 2,9,3,6 # reduction candidate for 2,9 C9: 2,9 => CTR * 4315.26.7....7415.7.5.6142....435271317.265.4254187936872619345143258769569743812 C9: 3,6 # 10 pairs * PAIR C7: 2,9 ROW 7 H7: 2,9,4 # reduction candidate for 2,9 H7: 2,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 H7: 4 # 15 pairs * PAIR C7: 2,9 COL C C2: 2,9,6,8 # reduction candidate for 2,9 C2: 2,9 # 14 pairs C2: 6,8 # 10 pairs * PAIR F7: 4,9 BLK 8 F8: 4,9,3,8 # reduction candidate for 4,9 F8: 4,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 F8: 3,8 # 10 pairs E9: 4,9,8 # reduction candidate for 4,9 E9: 4,9 # 13 pairs F9: 4,9,3,8 # reduction candidate for 4,9 F9: 4,9 => CTR * 4315..6.7....76154765.41..36..435271317...54.2541.7.3.87.6143.51462537..5.378941. F9: 3,8 # 10 pairs * PAIR F7: 4,9 ROW 7 H7: 4,9,2 # reduction candidate for 4,9 H7: 2 => CTR * 4315..6.7....76154765..1......435271317...5..2541.7.3.87.6143251..25.7..5..7...1. H7: 4,9 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-047-base-pr-000.dot * REASONING * DIS # B2: 6,9 => CTR => B2: 2,8 * PRF # G3: 8,9 => SOL * DIS # H3: 8,9 => CTR => H3: 2,4 * DIS # F1: 8,9 => CTR => F1: 2 * DIS # H8: 8,9 => CTR => H8: 4,6 * DIS # E5: 8,9 => CTR => E5: 2,6 * PRF # F5: 8,9 => SOL * DIS # I5: 8,9 => CTR => I5: 4,6 * DIS # I5: 8,9 => CTR => I5: 4,6 * PRF # I6: 8,9 => SOL * PRF # E6: 6 => SOL * PRF # G3: 8,9 => SOL * DIS # C9: 2,9 => CTR => C9: 3,6 * PRF # H7: 2,9 => SOL * PRF # F8: 4,9 => SOL * DIS # F9: 4,9 => CTR => F9: 3,8 * DIS # H7: 2 => CTR => H7: 4,9 * CNT 17 HDP CHAINS / 52 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A4,C7,D5,E3,F2,F7,G6,H1) * 4315..6.7....7.15.7.5..1......435271317...5..2541.7.3.87.61.3.51..25.7..5..7...1. * PAIR A2: 6,9 BLK 1 B2: 6,9,2,8 # reduction candidate for 6,9 B2: 6,9 => CTR * 4315.26.7..2.7415.7.5.61......435271317..65..2541.7.3687.61934514.25.76.5..74..12 C2: 6,9,2,8 # reduction candidate for 6,9 C2: 6,9 # 20 pairs B3: 6,9,2,8 # reduction candidate for 6,9 B3: 6,9 # 13 pairs * PAIR H1: 8,9 BLK 3 I2: 8,9,2,3,4 # reduction candidate for 8,9 I2: 8,9 # 17 pairs G3: 8,9,4 # reduction candidate for 8,9 G3: 8,9 => SOLVED * 431592687928376154765841923689435271317928546254167839872614395143259768596783412 * DURATION: 0:00:06.286330 START: 04:17:50.894435 END: 04:17:57.180765 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-047-base-pr-001.dot * REASONING * DIS # B2: 6,9 => CTR => B2: 2,8 * PRF B2: 2,8 # G3: 8,9 => SOL * STA B2: 2,8 + G3: 8,9 * CNT 2 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 047 solution: 431592687928376154765841923689435271317928546254167839872614395143259768596783412 info: 1378 FNBHWXY S8.f 30475 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 431592687928376154765841923689435271317928546254167839872614395143259768596783412 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 # B2: 6,9 => CTR => B2: 2,8 * INC # B2: 2,8 => UNS * INC # C2: 6,9 => UNS * INC # B3: 6,9 => UNS * INC # I2: 8,9 => UNS * PRF # G3: 8,9 => SOL * INC # G3: 4 => UNS * DIS # H3: 8,9 => CTR => H3: 2,4 * INC # H3: 2,4 => UNS * INC # I3: 8,9 => UNS * INC # E1: 8,9 => UNS * DIS # F1: 8,9 => CTR => F1: 2 * INC # F1: 2 => UNS * INC # H5: 8,9 => UNS * DIS # H8: 8,9 => CTR => H8: 4,6 * INC # H8: 4,6 => UNS * INC # B4: 6,9 => UNS * INC # C4: 6,9 => UNS * DIS # E5: 8,9 => CTR => E5: 2,6 * INC # E5: 2,6 => UNS * PRF # F5: 8,9 => SOL * INC # F5: 2,6 => UNS * INC # E6: 8,9 => UNS * INC # H5: 8,9 => UNS * DIS # I5: 8,9 => CTR => I5: 4,6 * INC # I5: 4,6 => UNS * INC # D2: 8,9 => UNS * INC # D3: 8,9 => UNS * INC # H5: 8,9 => UNS * DIS # I5: 8,9 => CTR => I5: 4,6 * INC # I5: 4,6 => UNS * PRF # I6: 8,9 => SOL * INC # I6: 6 => UNS * INC # E6: 8,9 => UNS * PRF # E6: 6 => SOL * PRF # G3: 8,9 => SOL * INC # G3: 4 => UNS * INC # G9: 8,9 => UNS * INC # B9: 2,9 => UNS * DIS # C9: 2,9 => CTR => C9: 3,6 * INC # C9: 3,6 => UNS * PRF # H7: 2,9 => SOL * INC # H7: 4 => UNS * INC # C2: 2,9 => UNS * INC # C2: 6,8 => UNS * PRF # F8: 4,9 => SOL * INC # F8: 3,8 => UNS * INC # E9: 4,9 => UNS * DIS # F9: 4,9 => CTR => F9: 3,8 * INC # F9: 3,8 => UNS * INC # H7: 4,9 => UNS * DIS # H7: 2 => CTR => H7: 4,9 * CNT 52 HDP CHAINS / 52 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # B2: 6,9 => CTR => B2: 2,8 * INC B2: 2,8 # C2: 6,9 => UNS * INC B2: 2,8 # B3: 6,9 => UNS * INC B2: 2,8 # I2: 8,9 => UNS * PRF B2: 2,8 # G3: 8,9 => SOL * STA B2: 2,8 + G3: 8,9 * CNT 5 HDP CHAINS / 5 HYP OPENED