Analysis of xx-top500-240-base.sdk
Contents
Original Sudoku
level: medium
position: .5.2.1.........37....5..6..8.3.4............14............3.48..2.1.............. initial
Autosolve
position: 3562718942814..375.4.583612813.4.2..56.328.414.2.1..381.5.3248..281.4..3.3485.12. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A9: 7,9 => SOL * DIS # F9: 6,9 => CTR => F9: 7 * PRF # D6: 7,9 => SOL * DIS # G6: 7,9 => CTR => G6: 5 * DIS # F4: 7,9 => CTR => F4: 5 * PRF # D6: 7,9 => SOL * DIS # I4: 6 => CTR => I4: 7,9 * PRF # D7: 6 => SOL * DIS # G6: 7,9 => CTR => G6: 5 * DIS # G8: 5 => CTR => G8: 7,9 * PRF # A9: 7,9 => SOL * PRF # I7: 7,9 => SOL * DIS # F9: 6,9 => CTR => F9: 7 * PRF # A8: 6,9 => SOL * CNT 14 HDP CHAINS / 36 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A9: 7,9 => SOL * STA A9: 7,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.2.1.........37....5..6..8.3.4............14............3.48..2.1.............. | initial |
| 3562718942814..375.4.583612813.4.2..56.328.414.2.1..381.5.3248..281.4..3.3485.12. | autosolve |
| 356271894281469375749583612813945267567328941492716538175632489628194753934857126 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (12) A3: 7,9 C3: 7,9 E2: 6,9 F2: 6,9 C5: 7,9 B6: 7,9 D4: 7,9 H4: 5,6 G5: 7,9 B7: 7,9 E8: 6,9 H8: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F4,F6: 5.. / F4 = 5 => 12 pairs (_) / F6 = 5 => 0 pairs (X) H4,G6: 5.. / H4 = 5 => 0 pairs (X) / G6 = 5 => 12 pairs (_) G8,H8: 5.. / G8 = 5 => 0 pairs (X) / H8 = 5 => 12 pairs (_) F4,H4: 5.. / F4 = 5 => 12 pairs (_) / H4 = 5 => 0 pairs (X) F6,G6: 5.. / F6 = 5 => 0 pairs (X) / G6 = 5 => 12 pairs (_) G6,G8: 5.. / G6 = 5 => 12 pairs (_) / G8 = 5 => 0 pairs (X) H4,H8: 5.. / H4 = 5 => 0 pairs (X) / H8 = 5 => 12 pairs (_) E2,F2: 6.. / E2 = 6 => 15 pairs (_) / F2 = 6 => 14 pairs (_) D6,F6: 6.. / D6 = 6 => 15 pairs (_) / F6 = 6 => 0 pairs (*) H4,I4: 6.. / H4 = 6 => 12 pairs (_) / I4 = 6 => 0 pairs (X) A8,A9: 6.. / A8 = 6 => 0 pairs (*) / A9 = 6 => 0 pairs (X) D7,I7: 6.. / D7 = 6 => 0 pairs (*) / I7 = 6 => 0 pairs (X) D6,D7: 6.. / D6 = 6 => 15 pairs (_) / D7 = 6 => 0 pairs (*) E2,E8: 6.. / E2 = 6 => 15 pairs (_) / E8 = 6 => 14 pairs (_) H4,H8: 6.. / H4 = 6 => 12 pairs (_) / H8 = 6 => 0 pairs (X) A3,C3: 7.. / A3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) C5,B6: 7.. / C5 = 7 => 0 pairs (*) / B6 = 7 => 0 pairs (X) D7,F9: 7.. / D7 = 7 => 0 pairs (X) / F9 = 7 => 16 pairs (_) C5,G5: 7.. / C5 = 7 => 0 pairs (*) / G5 = 7 => 0 pairs (X) A8,G8: 7.. / A8 = 7 => 16 pairs (_) / G8 = 7 => 0 pairs (*) B6,B7: 7.. / B6 = 7 => 16 pairs (_) / B7 = 7 => 0 pairs (*) C3,C5: 7.. / C3 = 7 => 16 pairs (_) / C5 = 7 => 0 pairs (*) A3,C3: 9.. / A3 = 9 => 16 pairs (_) / C3 = 9 => 0 pairs (*) E2,F2: 9.. / E2 = 9 => 14 pairs (_) / F2 = 9 => 15 pairs (_) C5,B6: 9.. / C5 = 9 => 16 pairs (_) / B6 = 9 => 0 pairs (*) C5,G5: 9.. / C5 = 9 => 16 pairs (_) / G5 = 9 => 0 pairs (*) B6,B7: 9.. / B6 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) C3,C5: 9.. / C3 = 9 => 0 pairs (*) / C5 = 9 => 0 pairs (X) E2,E8: 9.. / E2 = 9 => 14 pairs (_) / E8 = 9 => 15 pairs (_) * DURATION: 0:00:57.211893 START: 11:00:20.058345 END: 11:01:17.270238 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,B7,C3,C5,D4,E2,E8,F2,G5,H4,H8) * 3562718942814..375.4.583612813.4.2..56.328.414.2.1..381.5.3248..281.4..3.3485.12. * PAIR A3: 7,9 COL A A8: 7,9,6 # reduction candidate for 7,9 A8: 7,9 # 15 pairs A9: 7,9,6 # reduction candidate for 7,9 A9: 7,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 A9: 6 # 15 pairs * PAIR F2: 6,9 COL F F6: 6,9,5,7 # reduction candidate for 6,9 F6: 6,9 # 16 pairs F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 3562718942814..375.4.583612813945267567328941492.1..381.5732486.281.4.53.3485.12. F9: 7 # 16 pairs * PAIR B6: 7,9 ROW 6 D6: 7,9,6 # reduction candidate for 7,9 D6: 7,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 D6: 6 # 15 pairs F6: 7,9,5,6 # reduction candidate for 7,9 F6: 7,9 # 15 pairs G6: 7,9,5 # reduction candidate for 7,9 G6: 7,9 => CTR * 3562718942814..375.4.583612813.4.25656.328.414.2.15.381.563248..2819456363485712. G6: 5 # 12 pairs * PAIR D4: 7,9 BLK 5 F4: 7,9,5 # reduction candidate for 7,9 F4: 7,9 => CTR * 3562718942814..375.4.583612813.4.25656.328.414.2.15.381.563248..2819456363485712. F4: 5 # 12 pairs D6: 7,9,6 # reduction candidate for 7,9 D6: 7,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 D6: 6 # 15 pairs F6: 7,9,5,6 # reduction candidate for 7,9 F6: 7,9 # 15 pairs * PAIR D4: 7,9 ROW 4 I4: 7,9,6 # reduction candidate for 7,9 I4: 6 => CTR * 356271894281469375947583612813.4.2.656.328.414.2.1..381.563248..28194.63634857129 I4: 7,9 # 12 pairs * PAIR D4: 7,9 COL D D7: 7,9,6 # reduction candidate for 7,9 D7: 6 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 D7: 7,9 # 15 pairs * PAIR G5: 7,9 BLK 6 I4: 7,9,6 # reduction candidate for 7,9 I4: 7,9 # 12 pairs G6: 7,9,5 # reduction candidate for 7,9 G6: 7,9 => CTR * 3562718942814..375.4.583612813.4.25656.328.414.2.15.381.563248..2819456363485712. G6: 5 # 12 pairs * PAIR G5: 7,9 COL G G8: 7,9,5 # reduction candidate for 7,9 G8: 5 => CTR * 356271894281469375.4.583612813.4.2..56.328.414.2.1..381.5.3248.728194563634857129 G8: 7,9 # 12 pairs * PAIR B7: 7,9 BLK 7 A8: 7,9,6 # reduction candidate for 7,9 A8: 7,9 # 15 pairs A9: 7,9,6 # reduction candidate for 7,9 A9: 7,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 A9: 6 # 15 pairs * PAIR B7: 7,9 ROW 7 D7: 7,9,6 # reduction candidate for 7,9 D7: 7,9 # 15 pairs I7: 7,9,6 # reduction candidate for 7,9 I7: 7,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 I7: 6 # 15 pairs * PAIR E8: 6,9 BLK 8 D7: 6,9,7 # reduction candidate for 6,9 D7: 6,9 # 16 pairs F9: 6,9,7 # reduction candidate for 6,9 F9: 6,9 => CTR * 3562718942814..375.4.583612813945267567328941492.1..381.5732486.281.4.53.3485.12. F9: 7 # 16 pairs * PAIR E8: 6,9 ROW 8 A8: 6,9,7 # reduction candidate for 6,9 A8: 6,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 A8: 7 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-240-base-pr-000.dot * REASONING * PRF # A9: 7,9 => SOL * DIS # F9: 6,9 => CTR => F9: 7 * PRF # D6: 7,9 => SOL * DIS # G6: 7,9 => CTR => G6: 5 * DIS # F4: 7,9 => CTR => F4: 5 * PRF # D6: 7,9 => SOL * DIS # I4: 6 => CTR => I4: 7,9 * PRF # D7: 6 => SOL * DIS # G6: 7,9 => CTR => G6: 5 * DIS # G8: 5 => CTR => G8: 7,9 * PRF # A9: 7,9 => SOL * PRF # I7: 7,9 => SOL * DIS # F9: 6,9 => CTR => F9: 7 * PRF # A8: 6,9 => SOL * CNT 14 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B6,B7,C3,C5,D4,E2,E8,F2,G5,H4,H8) * 3562718942814..375.4.583612813.4.2..56.328.414.2.1..381.5.3248..281.4..3.3485.12. * PAIR A3: 7,9 COL A A8: 7,9,6 # reduction candidate for 7,9 A8: 7,9 # 15 pairs A9: 7,9,6 # reduction candidate for 7,9 A9: 7,9 => SOLVED * 356271894281469375749583612813945267567328941492716538175632489628194753934857126 * DURATION: 0:00:03.135529 START: 11:01:59.961400 END: 11:02:03.096929 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-240-base-pr-001.dot * REASONING * PRF # A9: 7,9 => SOL * STA A9: 7,9 * CNT 1 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 240 solution: 356271894281469375749583612813945267567328941492716538175632489628194753934857126 info: 2069 FNBWXY S8.f 20163 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 356271894281469375749583612813945267567328941492716538175632489628194753934857126 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 # A8: 7,9 => UNS * PRF # A9: 7,9 => SOL * INC # A9: 6 => UNS * INC # F6: 6,9 => UNS * DIS # F9: 6,9 => CTR => F9: 7 * INC # F9: 7 => UNS * PRF # D6: 7,9 => SOL * INC # D6: 6 => UNS * INC # F6: 7,9 => UNS * DIS # G6: 7,9 => CTR => G6: 5 * INC # G6: 5 => UNS * DIS # F4: 7,9 => CTR => F4: 5 * INC # F4: 5 => UNS * PRF # D6: 7,9 => SOL * INC # D6: 6 => UNS * INC # F6: 7,9 => UNS * INC # I4: 7,9 => UNS * DIS # I4: 6 => CTR => I4: 7,9 * INC # D7: 7,9 => UNS * PRF # D7: 6 => SOL * INC # I4: 7,9 => UNS * DIS # G6: 7,9 => CTR => G6: 5 * INC # G6: 5 => UNS * INC # G8: 7,9 => UNS * DIS # G8: 5 => CTR => G8: 7,9 * INC # A8: 7,9 => UNS * PRF # A9: 7,9 => SOL * INC # A9: 6 => UNS * INC # D7: 7,9 => UNS * PRF # I7: 7,9 => SOL * INC # I7: 6 => UNS * INC # D7: 6,9 => UNS * DIS # F9: 6,9 => CTR => F9: 7 * INC # F9: 7 => UNS * PRF # A8: 6,9 => SOL * INC # A8: 7 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A8: 7,9 => UNS * PRF # A9: 7,9 => SOL * STA A9: 7,9 * CNT 2 HDP CHAINS / 2 HYP OPENED