Analysis of xx-top500-375-base.sdk
Contents
Original Sudoku
level: medium
position: 1.9.........7...4.6............9.6.1.7.3.......8.......3....87......69......2.... initial
Autosolve
position: 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G5: 2,5 => SOL * DIS # A4: 2,5 => CTR => A4: 3,4 * PRF # C4: 2,5 => SOL * PRF # D4: 4 => SOL * DIS # F6: 4,5 => CTR => F6: 2 * DIS # G6: 2 => CTR => G6: 4,5 * PRF # G5: 2,5 => SOL * PRF # A5: 4 => SOL * DIS # I7: 4 => CTR => I7: 2,5 * DIS # A7: 4,5 => CTR => A7: 2 * PRF # A7: 2 => SOL * PRF # C8: 4,5 => SOL * DIS # C8: 2 => CTR => C8: 4,5 * DIS # C4: 4,5 => CTR => C4: 2,3 * DIS # A7: 4,5 => CTR => A7: 2 * PRF # A7: 2 => SOL * PRF # I7: 4,5 => SOL * DIS # I7: 2 => CTR => I7: 4,5 * PRF # C8: 4,5 => SOL * DIS # C8: 2 => CTR => C8: 4,5 * DIS # D3: 4,5 => CTR => D3: 2 * DIS # I7: 4 => CTR => I7: 2,5 * PRF # C8: 4 => SOL * PRF # I7: 4,5 => SOL * DIS # I7: 2 => CTR => I7: 4,5 * CNT 25 HDP CHAINS / 49 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G5: 2,5 => SOL * STA G5: 2,5 * CNT 1 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.9.........7...4.6............9.6.1.7.3.......8.......3....87......69......2.... | initial |
| 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316. | autosolve |
| 129634758583719246647285319352497681471368592968152437236941875814576923795823164 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) H1: 2,5 G2: 2,5 B4: 2,5 E6: 4,5 I5: 2,5 C9: 4,5 E7: 4,5 D8: 4,5 H8: 2,5 I9: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,G2: 2.. / H1 = 2 => 0 pairs (X) / G2 = 2 => 0 pairs (_) D4,F6: 2.. / D4 = 2 => 0 pairs (X) / F6 = 2 => 16 pairs (_) A7,C8: 2.. / A7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) I7,H8: 2.. / I7 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) F6,G6: 2.. / F6 = 2 => 16 pairs (_) / G6 = 2 => 0 pairs (X) A7,I7: 2.. / A7 = 2 => 0 pairs (*) / I7 = 2 => 0 pairs (X) C8,H8: 2.. / C8 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) D3,D4: 2.. / D3 = 2 => 16 pairs (_) / D4 = 2 => 0 pairs (X) H1,H8: 2.. / H1 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) I5,I7: 2.. / I5 = 2 => 0 pairs (*) / I7 = 2 => 0 pairs (X) A2,C2: 3.. / A2 = 3 => 12 pairs (_) / C2 = 3 => 11 pairs (_) A4,C4: 3.. / A4 = 3 => 11 pairs (_) / C4 = 3 => 12 pairs (_) A2,A4: 3.. / A2 = 3 => 12 pairs (_) / A4 = 3 => 11 pairs (_) C2,C4: 3.. / C2 = 3 => 11 pairs (_) / C4 = 3 => 12 pairs (_) B1,B3: 4.. / B1 = 4 => 12 pairs (_) / B3 = 4 => 14 pairs (_) G5,G6: 4.. / G5 = 4 => 15 pairs (_) / G6 = 4 => 0 pairs (*) E7,D8: 4.. / E7 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) I7,I9: 4.. / I7 = 4 => 0 pairs (X) / I9 = 4 => 12 pairs (_) B1,F1: 4.. / B1 = 4 => 12 pairs (_) / F1 = 4 => 14 pairs (_) A5,G5: 4.. / A5 = 4 => 0 pairs (*) / G5 = 4 => 0 pairs (X) C8,D8: 4.. / C8 = 4 => 0 pairs (*) / D8 = 4 => 0 pairs (X) C9,I9: 4.. / C9 = 4 => 0 pairs (X) / I9 = 4 => 12 pairs (_) E6,E7: 4.. / E6 = 4 => 18 pairs (_) / E7 = 4 => 0 pairs (*) H1,G2: 5.. / H1 = 5 => 0 pairs (*) / G2 = 5 => 0 pairs (X) E7,D8: 5.. / E7 = 5 => 18 pairs (_) / D8 = 5 => 0 pairs (*) C9,I9: 5.. / C9 = 5 => 12 pairs (_) / I9 = 5 => 0 pairs (X) E6,E7: 5.. / E6 = 5 => 0 pairs (*) / E7 = 5 => 0 pairs (X) H1,H8: 5.. / H1 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) * DURATION: 0:01:01.151814 START: 15:42:11.430307 END: 15:43:12.582121 2017-05-04 * CP COUNT: (28) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C9,D8,E6,E7,G2,H1,H8,I5,I9) * 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316. * PAIR H1: 2,5 ROW 1 B1: 2,5,4 # reduction candidate for 2,5 B1: 2,5 # 14 pairs F1: 2,5,4 # reduction candidate for 2,5 F1: 2,5 # 12 pairs * PAIR G2: 2,5 ROW 2 A2: 2,5,3 # reduction candidate for 2,5 A2: 2,5 # 11 pairs C2: 2,5,3 # reduction candidate for 2,5 C2: 2,5 # 12 pairs * PAIR G2: 2,5 COL G G5: 2,5,4 # reduction candidate for 2,5 G5: 2,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 G5: 4 # 15 pairs G6: 2,5,4 # reduction candidate for 2,5 G6: 2,5 # 15 pairs * PAIR B4: 2,5 BLK 4 A4: 2,5,3,4 # reduction candidate for 2,5 A4: 2,5 => CTR * 1.963.7.838.719.466.7.8.319..3497681471368.9.968152437.3694187.814576923795823164 A4: 3,4 # 11 pairs C4: 2,5,3,4 # reduction candidate for 2,5 C4: 2,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 C4: 3,4 # 11 pairs A5: 2,5,4 # reduction candidate for 2,5 A5: 2,5 # 15 pairs * PAIR B4: 2,5 ROW 4 D4: 2,5,4 # reduction candidate for 2,5 D4: 4 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 D4: 2,5 # 15 pairs * PAIR B4: 2,5 COL B B1: 2,5,4 # reduction candidate for 2,5 B1: 2,5 # 14 pairs B3: 2,5,4 # reduction candidate for 2,5 B3: 2,5 # 12 pairs * PAIR E6: 4,5 BLK 5 D4: 4,5,2 # reduction candidate for 4,5 D4: 4,5 # 16 pairs F6: 4,5,2 # reduction candidate for 4,5 F6: 4,5 => CTR * 1.963.7.8.8.719.466.7.8.319...2976812713684959681..237.369.1872812476953795823164 F6: 2 # 16 pairs * PAIR E6: 4,5 ROW 6 G6: 4,5,2 # reduction candidate for 4,5 G6: 2 => CTR * 1.963.72828.719.466.7.8.319....97681.713684959681..237.369.1872812476953795823164 G6: 4,5 # 16 pairs * PAIR I5: 2,5 BLK 6 G5: 2,5,4 # reduction candidate for 2,5 G5: 2,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 G5: 4 # 15 pairs G6: 2,5,4 # reduction candidate for 2,5 G6: 2,5 # 15 pairs * PAIR I5: 2,5 ROW 5 A5: 2,5,4 # reduction candidate for 2,5 A5: 4 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 A5: 2,5 # 15 pairs * PAIR I5: 2,5 COL I I7: 2,5,4 # reduction candidate for 2,5 I7: 4 => CTR * 129634758.8.71924664728531945..97681.71368.929681.2.3723695187481.476923794823165 I7: 2,5 # 12 pairs * PAIR C9: 4,5 BLK 7 A7: 4,5,2 # reduction candidate for 4,5 A7: 4,5 => CTR * 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164 A7: 2 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 C8: 4,5,2 # reduction candidate for 4,5 C8: 4,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 C8: 2 => CTR * 1.963.7282837195466.7.8.3193245976815713684929681...37.369.187.812476953795823164 * PAIR C9: 4,5 COL C C4: 4,5,2,3 # reduction candidate for 4,5 C4: 4,5 => CTR * 1.963.7282837195466.7.8.3193245976815713684929681...37.369.187.812476953795823164 C4: 2,3 # 12 pairs * PAIR E7: 4,5 ROW 7 A7: 4,5,2 # reduction candidate for 4,5 A7: 4,5 => CTR * 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164 A7: 2 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 I7: 4,5,2 # reduction candidate for 4,5 I7: 4,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 I7: 2 => CTR * 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164 * PAIR D8: 4,5 ROW 8 C8: 4,5,2 # reduction candidate for 4,5 C8: 4,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 C8: 2 => CTR * 1.963.7282837195466.7.8.3193245976815713684929681...37.369.187.812476953795823164 * PAIR D8: 4,5 COL D D3: 4,5,2 # reduction candidate for 4,5 D3: 4,5 => CTR * 1.963.7.8.8.719.466.7.8.319...2976812713684959681..237.369.1872812476953795823164 D3: 2 # 16 pairs D4: 4,5,2 # reduction candidate for 4,5 D4: 4,5 # 16 pairs * PAIR H8: 2,5 BLK 9 I7: 2,5,4 # reduction candidate for 2,5 I7: 4 => CTR * 129634758.8.71924664728531945..97681.71368.929681.2.3723695187481.476923794823165 I7: 2,5 # 12 pairs * PAIR H8: 2,5 ROW 8 C8: 2,5,4 # reduction candidate for 2,5 C8: 4 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 C8: 2,5 # 18 pairs * PAIR I9: 4,5 BLK 9 I7: 4,5,2 # reduction candidate for 4,5 I7: 4,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 I7: 2 => CTR * 1.963.7282837195466.7.8.319324597681571368.9.9681...37.369.1872812476953795823164 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-375-base-pr-000.dot * REASONING * PRF # G5: 2,5 => SOL * DIS # A4: 2,5 => CTR => A4: 3,4 * PRF # C4: 2,5 => SOL * PRF # D4: 4 => SOL * DIS # F6: 4,5 => CTR => F6: 2 * DIS # G6: 2 => CTR => G6: 4,5 * PRF # G5: 2,5 => SOL * PRF # A5: 4 => SOL * DIS # I7: 4 => CTR => I7: 2,5 * DIS # A7: 4,5 => CTR => A7: 2 * PRF # A7: 2 => SOL * PRF # C8: 4,5 => SOL * DIS # C8: 2 => CTR => C8: 4,5 * DIS # C4: 4,5 => CTR => C4: 2,3 * DIS # A7: 4,5 => CTR => A7: 2 * PRF # A7: 2 => SOL * PRF # I7: 4,5 => SOL * DIS # I7: 2 => CTR => I7: 4,5 * PRF # C8: 4,5 => SOL * DIS # C8: 2 => CTR => C8: 4,5 * DIS # D3: 4,5 => CTR => D3: 2 * DIS # I7: 4 => CTR => I7: 2,5 * PRF # C8: 4 => SOL * PRF # I7: 4,5 => SOL * DIS # I7: 2 => CTR => I7: 4,5 * CNT 25 HDP CHAINS / 49 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,C9,D8,E6,E7,G2,H1,H8,I5,I9) * 1.963.7.8.8.719.466.7.8.319....97681.71368.9.9681...37.369.187.81..769.379.82316. * PAIR H1: 2,5 ROW 1 B1: 2,5,4 # reduction candidate for 2,5 B1: 2,5 # 14 pairs F1: 2,5,4 # reduction candidate for 2,5 F1: 2,5 # 12 pairs * PAIR G2: 2,5 ROW 2 A2: 2,5,3 # reduction candidate for 2,5 A2: 2,5 # 11 pairs C2: 2,5,3 # reduction candidate for 2,5 C2: 2,5 # 12 pairs * PAIR G2: 2,5 COL G G5: 2,5,4 # reduction candidate for 2,5 G5: 2,5 => SOLVED * 129634758583719246647285319352497681471368592968152437236941875814576923795823164 * DURATION: 0:00:07.053847 START: 15:44:18.167611 END: 15:44:25.221458 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-375-base-pr-001.dot * REASONING * PRF # G5: 2,5 => SOL * STA G5: 2,5 * CNT 1 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 375 solution: 129634758583719246647285319352497681471368592968152437236941875814576923795823164 info: 7907 FNBHWX S8.f 26269 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 129634758583719246647285319352497681471368592968152437236941875814576923795823164 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 # B1: 2,5 => UNS * INC # F1: 2,5 => UNS * INC # A2: 2,5 => UNS * INC # C2: 2,5 => UNS * PRF # G5: 2,5 => SOL * INC # G5: 4 => UNS * INC # G6: 2,5 => UNS * DIS # A4: 2,5 => CTR => A4: 3,4 * INC # A4: 3,4 => UNS * PRF # C4: 2,5 => SOL * INC # C4: 3,4 => UNS * INC # A5: 2,5 => UNS * INC # D4: 2,5 => UNS * PRF # D4: 4 => SOL * INC # B1: 2,5 => UNS * INC # B3: 2,5 => UNS * INC # D4: 4,5 => UNS * DIS # F6: 4,5 => CTR => F6: 2 * INC # F6: 2 => UNS * INC # G6: 4,5 => UNS * DIS # G6: 2 => CTR => G6: 4,5 * PRF # G5: 2,5 => SOL * INC # G5: 4 => UNS * INC # G6: 2,5 => UNS * INC # A5: 2,5 => UNS * PRF # A5: 4 => SOL * INC # I7: 2,5 => UNS * DIS # I7: 4 => CTR => I7: 2,5 * DIS # A7: 4,5 => CTR => A7: 2 * PRF # A7: 2 => SOL * PRF # C8: 4,5 => SOL * DIS # C8: 2 => CTR => C8: 4,5 * DIS # C4: 4,5 => CTR => C4: 2,3 * INC # C4: 2,3 => UNS * DIS # A7: 4,5 => CTR => A7: 2 * PRF # A7: 2 => SOL * PRF # I7: 4,5 => SOL * DIS # I7: 2 => CTR => I7: 4,5 * PRF # C8: 4,5 => SOL * DIS # C8: 2 => CTR => C8: 4,5 * DIS # D3: 4,5 => CTR => D3: 2 * INC # D3: 2 => UNS * INC # D4: 4,5 => UNS * INC # I7: 2,5 => UNS * DIS # I7: 4 => CTR => I7: 2,5 * INC # C8: 2,5 => UNS * PRF # C8: 4 => SOL * PRF # I7: 4,5 => SOL * DIS # I7: 2 => CTR => I7: 4,5 * CNT 49 HDP CHAINS / 49 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 2,5 => UNS * INC # F1: 2,5 => UNS * INC # A2: 2,5 => UNS * INC # C2: 2,5 => UNS * PRF # G5: 2,5 => SOL * STA G5: 2,5 * CNT 5 HDP CHAINS / 5 HYP OPENED