Analysis of xx-top500-195-base.sdk
Contents
Original Sudoku
level: medium
position: 6...2...........41....8.......5..2........36..17.......5.1.7...3.....8.....4..... initial
Autosolve
position: 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I4: 4,8 => CTR => I4: 7 * PRF # I4: 7 => SOL * DIS # A7: 9 => CTR => A7: 4,8 * PRF # I4: 4,7 => SOL * DIS # I4: 8 => CTR => I4: 4,7 * PRF # I5: 7,8 => SOL * DIS # I5: 4 => CTR => I5: 7,8 * DIS # D6: 3,6 => CTR => D6: 8 * PRF # D6: 8 => SOL * DIS # F2: 3,6 => CTR => F2: 5 * PRF # B8: 7,9 => SOL * DIS # B9: 7,9 => CTR => B9: 2,6 * DIS # A2: 8 => CTR => A2: 7,9 * DIS # I8: 5,6 => CTR => I8: 4,9 * DIS # F2: 3 => CTR => F2: 5,6 * CNT 15 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I4: 4,8 => CTR => I4: 7 * PRF I4: 7 => SOL * STA I4: 7 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 6...2...........41....8.......5..2........36..17.......5.1.7...3.....8.....4..... | initial |
| 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81.. | autosolve |
| 674921583982375641135684792863549217549712368217863459458137926391256874726498135 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) A4: 4,8 B4: 3,6 C4: 3,6 E4: 4,7 D5: 7,8 E6: 4,6 F6: 3,6 A9: 7,9 F8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,C2: 2.. / B2 = 2 => 0 pairs (X) / C2 = 2 => 10 pairs (_) H3,I3: 2.. / H3 = 2 => 10 pairs (_) / I3 = 2 => 10 pairs (_) B2,B9: 2.. / B2 = 2 => 0 pairs (X) / B9 = 2 => 10 pairs (_) B4,C4: 3.. / B4 = 3 => 9 pairs (_) / C4 = 3 => 8 pairs (_) D6,F6: 3.. / D6 = 3 => 0 pairs (X) / F6 = 3 => 10 pairs (_) E7,E9: 3.. / E7 = 3 => 10 pairs (_) / E9 = 3 => 11 pairs (_) F2,F6: 3.. / F2 = 3 => 0 pairs (X) / F6 = 3 => 10 pairs (_) B1,C1: 4.. / B1 = 4 => 0 pairs (X) / C1 = 4 => 10 pairs (_) E4,E6: 4.. / E4 = 4 => 0 pairs (*) / E6 = 4 => 0 pairs (X) B8,I8: 4.. / B8 = 4 => 0 pairs (X) / I8 = 4 => 0 pairs (_) A4,A7: 4.. / A4 = 4 => 0 pairs (X) / A7 = 4 => 0 pairs (_) G6,G7: 4.. / G6 = 4 => 0 pairs (*) / G7 = 4 => 0 pairs (X) C1,C3: 5.. / C1 = 5 => 0 pairs (X) / C3 = 5 => 9 pairs (_) E2,F2: 5.. / E2 = 5 => 0 pairs (X) / F2 = 5 => 11 pairs (_) F2,F8: 5.. / F2 = 5 => 11 pairs (_) / F8 = 5 => 0 pairs (X) B4,C4: 6.. / B4 = 6 => 8 pairs (_) / C4 = 6 => 9 pairs (_) E4,D5: 7.. / E4 = 7 => 0 pairs (X) / D5 = 7 => 0 pairs (_) I4,I5: 7.. / I4 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) H8,H9: 7.. / H8 = 7 => 9 pairs (_) / H9 = 7 => 0 pairs (X) E4,I4: 7.. / E4 = 7 => 0 pairs (X) / I4 = 7 => 0 pairs (_) D5,I5: 7.. / D5 = 7 => 0 pairs (*) / I5 = 7 => 0 pairs (X) B8,H8: 7.. / B8 = 7 => 0 pairs (X) / H8 = 7 => 9 pairs (_) A2,A9: 7.. / A2 = 7 => 0 pairs (X) / A9 = 7 => 9 pairs (_) E2,E4: 7.. / E2 = 7 => 0 pairs (*) / E4 = 7 => 0 pairs (X) H1,I1: 8.. / H1 = 8 => 10 pairs (_) / I1 = 8 => 0 pairs (X) D5,D6: 8.. / D5 = 8 => 0 pairs (X) / D6 = 8 => 0 pairs (_) A7,C7: 8.. / A7 = 8 => 0 pairs (X) / C7 = 8 => 11 pairs (_) A4,I4: 8.. / A4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) B2,B5: 8.. / B2 = 8 => 14 pairs (_) / B5 = 8 => 0 pairs (X) H1,H6: 8.. / H1 = 8 => 10 pairs (_) / H6 = 8 => 0 pairs (X) B5,C5: 9.. / B5 = 9 => 15 pairs (_) / C5 = 9 => 12 pairs (_) * DURATION: 0:00:50.306642 START: 09:24:47.238453 END: 09:25:37.545095 2017-05-04 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8) * 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81.. * PAIR A4: 4,8 BLK 4 B5: 4,8,9 # reduction candidate for 4,8 B5: 4,8 # 12 pairs C5: 4,8,9 # reduction candidate for 4,8 C5: 4,8 # 15 pairs * PAIR A4: 4,8 ROW 4 I4: 4,8,7 # reduction candidate for 4,8 I4: 4,8 => CTR * 6...21..........411...84......57921.5..812367217.4.....5.1.74..3412..87....4.81.. I4: 7 => SOLVED * 674921583982375641135684792863549217549712368217863459458137926391256874726498135 * PAIR A4: 4,8 COL A A7: 4,8,9 # reduction candidate for 4,8 A7: 9 => CTR * 6...21..........411...84...4..5792185...1236.217.......5.1.7...3.12..8.....4.81.. A7: 4,8 # 14 pairs * PAIR E4: 4,7 ROW 4 I4: 4,7,8 # reduction candidate for 4,7 I4: 4,7 => SOLVED * 674921583982375641135684792863549217549712368217863459458137926391256874726498135 I4: 8 => CTR * 6...21..........411...84......5792185..812367217.4.....5.1.74..3412..87....4.81.. * PAIR D5: 7,8 ROW 5 I5: 7,8,4 # reduction candidate for 7,8 I5: 7,8 => SOLVED * 674921583982375641135684792863549217549712368217863459458137926391256874726498135 I5: 4 => CTR * 6...21..........411...84......5.92175..71236421784.....5.1.7...3.12..8.....4.81.. * PAIR F6: 3,6 BLK 5 D6: 3,6,8 # reduction candidate for 3,6 D6: 3,6 => CTR * 6...21....82....411...84...8..5792145..812367217.4....4581.7...3.12..8...2.4.81.. D6: 8 => SOLVED * 674921583982375641135684792863549217549712368217863459458137926391256874726498135 * PAIR F6: 3,6 COL F F2: 3,6,5 # reduction candidate for 3,6 F2: 3,6 => CTR * 6...21.......5..411...84......57921.5..812367217.4.....5.1.74..3412.587....4.81.. F2: 5 # 11 pairs * PAIR A9: 7,9 BLK 7 B8: 7,9,4,6 # reduction candidate for 7,9 B8: 7,9 => SOLVED * 674921583982375641135684792863549217549712368217863459458137926391256874726498135 B8: 4,6 # 10 pairs B9: 7,9,2,6 # reduction candidate for 7,9 B9: 7,9 => CTR * 6...21....2.....411...84......5.921.589712364217.......5.1.7...3.12..8.....4.81.. B9: 2,6 # 10 pairs * PAIR A9: 7,9 ROW 9 H9: 7,9,2,3,5 # reduction candidate for 7,9 H9: 7,9 # 14 pairs H9: 2,3,5 # 9 pairs * PAIR A9: 7,9 COL A A2: 7,9,8 # reduction candidate for 7,9 A2: 8 => CTR * 6...21...8......411...84...4..5792185...1236.217.......5.1.7...3.12..8.....4.81.. A2: 7,9 # 14 pairs * PAIR F8: 5,6 BLK 8 E8: 5,6,9 # reduction candidate for 5,6 E8: 5,6 # 14 pairs E9: 5,6,3,9 # reduction candidate for 5,6 E9: 5,6 # 12 pairs * PAIR F8: 5,6 ROW 8 I8: 5,6,4,9 # reduction candidate for 5,6 I8: 5,6 => CTR * 6.4.21..........411.5.84...4..5792185...1236.217.......5.1.7...3412..87....4.81.. I8: 4,9 # 10 pairs * PAIR F8: 5,6 COL F F2: 5,6,3 # reduction candidate for 5,6 F2: 3 => CTR * 6...21.......53.411...84......57921.5..812367217346....5.1.74..3412.587....4.81.. F2: 5,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-195-base-pr-000.dot * REASONING * DIS # I4: 4,8 => CTR => I4: 7 * PRF # I4: 7 => SOL * DIS # A7: 9 => CTR => A7: 4,8 * PRF # I4: 4,7 => SOL * DIS # I4: 8 => CTR => I4: 4,7 * PRF # I5: 7,8 => SOL * DIS # I5: 4 => CTR => I5: 7,8 * DIS # D6: 3,6 => CTR => D6: 8 * PRF # D6: 8 => SOL * DIS # F2: 3,6 => CTR => F2: 5 * PRF # B8: 7,9 => SOL * DIS # B9: 7,9 => CTR => B9: 2,6 * DIS # A2: 8 => CTR => A2: 7,9 * DIS # I8: 5,6 => CTR => I8: 4,9 * DIS # F2: 3 => CTR => F2: 5,6 * CNT 15 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A9,B4,C4,D5,E4,E6,F6,F8) * 6...21..........411...84......5.921.5...1236.217.......5.1.7...3.12..8.....4.81.. * PAIR A4: 4,8 BLK 4 B5: 4,8,9 # reduction candidate for 4,8 B5: 4,8 # 12 pairs C5: 4,8,9 # reduction candidate for 4,8 C5: 4,8 # 15 pairs * PAIR A4: 4,8 ROW 4 I4: 4,8,7 # reduction candidate for 4,8 I4: 4,8 => CTR * 6...21..........411...84......57921.5..812367217.4.....5.1.74..3412..87....4.81.. I4: 7 => SOLVED * 674921583982375641135684792863549217549712368217863459458137926391256874726498135 * DURATION: 0:00:04.999004 START: 09:26:04.446184 END: 09:26:09.445188 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-195-base-pr-001.dot * REASONING * DIS # I4: 4,8 => CTR => I4: 7 * PRF I4: 7 => SOL * STA I4: 7 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 195 solution: 674921583982375641135684792863549217549712368217863459458137926391256874726498135 info: 1880 FNBHWY S8.f 34518 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 674921583982375641135684792863549217549712368217863459458137926391256874726498135 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:
* INC # B5: 4,8 => UNS * INC # C5: 4,8 => UNS * DIS # I4: 4,8 => CTR => I4: 7 * PRF # I4: 7 => SOL * INC # A7: 4,8 => UNS * DIS # A7: 9 => CTR => A7: 4,8 * PRF # I4: 4,7 => SOL * DIS # I4: 8 => CTR => I4: 4,7 * PRF # I5: 7,8 => SOL * DIS # I5: 4 => CTR => I5: 7,8 * DIS # D6: 3,6 => CTR => D6: 8 * PRF # D6: 8 => SOL * DIS # F2: 3,6 => CTR => F2: 5 * INC # F2: 5 => UNS * PRF # B8: 7,9 => SOL * INC # B8: 4,6 => UNS * DIS # B9: 7,9 => CTR => B9: 2,6 * INC # B9: 2,6 => UNS * INC # H9: 7,9 => UNS * INC # H9: 2,3,5 => UNS * INC # A2: 7,9 => UNS * DIS # A2: 8 => CTR => A2: 7,9 * INC # E8: 5,6 => UNS * INC # E9: 5,6 => UNS * DIS # I8: 5,6 => CTR => I8: 4,9 * INC # I8: 4,9 => UNS * INC # F2: 5,6 => UNS * DIS # F2: 3 => CTR => F2: 5,6 * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B5: 4,8 => UNS * INC # C5: 4,8 => UNS * DIS # I4: 4,8 => CTR => I4: 7 * PRF I4: 7 => SOL * STA I4: 7 * CNT 4 HDP CHAINS / 3 HYP OPENED