Analysis of xx-top500-208-base.sdk
Contents
Original Sudoku
level: medium
position: .429.........6..3..8..........4..2..1......5.............8..4.13...1.9..5........ initial
Autosolve
position: .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A3: 6,7 => CTR => A3: 9 * PRF # A3: 9 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 6 => CTR => A3: 7,9 * DIS # D8: 2,7 => CTR => D8: 6 * PRF # D8: 6 => SOL * DIS # A3: 6,7 => CTR => A3: 9 * PRF # A3: 9 => SOL * DIS # E6: 7,9 => CTR => E6: 2 * PRF # B4: 7,9 => SOL * DIS # B4: 6 => CTR => B4: 7,9 * DIS # H4: 7,9 => CTR => H4: 6 * PRF # H4: 6 => SOL * DIS # H6: 6,7 => CTR => H6: 9 * PRF # B7: 6,7 => SOL * PRF # D8: 6,7 => SOL * DIS # D8: 2 => CTR => D8: 6,7 * PRF # B4: 9 => SOL * DIS # D8: 2,7 => CTR => D8: 6 * PRF # D8: 6 => SOL * DIS # F6: 2,7 => CTR => F6: 6 * PRF # D8: 6,7 => SOL * DIS # D8: 2 => CTR => D8: 6,7 * PRF # B7: 6,7 => SOL * DIS # H6: 6,7 => CTR => H6: 9 * CNT 25 HDP CHAINS / 42 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A3: 6,7 => CTR => A3: 9 * PRF A3: 9 => SOL * STA A3: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .429.........6..3..8..........4..2..1......5.............8..4.13...1.9..5........ | initial |
| .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932. | autosolve |
| 642983517751264839983157642895471263126398754437526198269835471374612985518749326 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) A1: 6,7 A2: 7,9 E1: 3,8 F1: 3,8 D2: 2,7 I1: 6,7 I2: 2,9 G3: 6,7 I3: 2,9 E4: 7,9 G5: 6,7 B8: 6,7 E7: 3,5 F7: 3,5 F8: 2,7 D9: 6,7 H7: 6,7 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I2,I3: 2.. / I2 = 2 => 0 pairs (X) / I3 = 2 => 0 pairs (_) E6,F6: 2.. / E6 = 2 => 20 pairs (_) / F6 = 2 => 0 pairs (X) D8,F8: 2.. / D8 = 2 => 0 pairs (X) / F8 = 2 => 0 pairs (_) D2,I2: 2.. / D2 = 2 => 0 pairs (*) / I2 = 2 => 0 pairs (X) D2,D8: 2.. / D2 = 2 => 0 pairs (*) / D8 = 2 => 0 pairs (X) E3,E6: 2.. / E3 = 2 => 0 pairs (X) / E6 = 2 => 20 pairs (_) E1,F1: 3.. / E1 = 3 => 19 pairs (_) / F1 = 3 => 18 pairs (_) E7,F7: 3.. / E7 = 3 => 18 pairs (_) / F7 = 3 => 19 pairs (_) E1,E7: 3.. / E1 = 3 => 19 pairs (_) / E7 = 3 => 18 pairs (_) F1,F7: 3.. / F1 = 3 => 18 pairs (_) / F7 = 3 => 19 pairs (_) E3,F3: 5.. / E3 = 5 => 18 pairs (_) / F3 = 5 => 19 pairs (_) E7,F7: 5.. / E7 = 5 => 19 pairs (_) / F7 = 5 => 18 pairs (_) E3,E7: 5.. / E3 = 5 => 18 pairs (_) / E7 = 5 => 19 pairs (_) F3,F7: 5.. / F3 = 5 => 19 pairs (_) / F7 = 5 => 18 pairs (_) A1,A3: 6.. / A1 = 6 => 0 pairs (*) / A3 = 6 => 0 pairs (X) I1,G3: 6.. / I1 = 6 => 0 pairs (X) / G3 = 6 => 0 pairs (_) F5,F6: 6.. / F5 = 6 => 0 pairs (X) / F6 = 6 => 22 pairs (_) D8,D9: 6.. / D8 = 6 => 0 pairs (*) / D9 = 6 => 0 pairs (X) H7,I9: 6.. / H7 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) A1,I1: 6.. / A1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) A3,G3: 6.. / A3 = 6 => 0 pairs (X) / G3 = 6 => 0 pairs (_) B4,H4: 6.. / B4 = 6 => 0 pairs (X) / H4 = 6 => 0 pairs (_) B8,D8: 6.. / B8 = 6 => 0 pairs (X) / D8 = 6 => 0 pairs (_) D9,I9: 6.. / D9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) G3,G5: 6.. / G3 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) I1,I9: 6.. / I1 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) I1,G3: 7.. / I1 = 7 => 0 pairs (*) / G3 = 7 => 0 pairs (X) H7,I9: 7.. / H7 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) A1,I1: 7.. / A1 = 7 => 0 pairs (X) / I1 = 7 => 0 pairs (_) A2,D2: 7.. / A2 = 7 => 0 pairs (*) / D2 = 7 => 0 pairs (X) D9,I9: 7.. / D9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) G3,G5: 7.. / G3 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) I1,I9: 7.. / I1 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) E1,F1: 8.. / E1 = 8 => 18 pairs (_) / F1 = 8 => 19 pairs (_) E5,F5: 8.. / E5 = 8 => 19 pairs (_) / F5 = 8 => 18 pairs (_) E1,E5: 8.. / E1 = 8 => 18 pairs (_) / E5 = 8 => 19 pairs (_) F1,F5: 8.. / F1 = 8 => 19 pairs (_) / F5 = 8 => 18 pairs (_) A2,A3: 9.. / A2 = 9 => 0 pairs (X) / A3 = 9 => 0 pairs (_) I2,I3: 9.. / I2 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) H4,H6: 9.. / H4 = 9 => 0 pairs (X) / H6 = 9 => 21 pairs (_) B7,C7: 9.. / B7 = 9 => 20 pairs (_) / C7 = 9 => 0 pairs (*) A2,I2: 9.. / A2 = 9 => 0 pairs (X) / I2 = 9 => 0 pairs (_) A3,I3: 9.. / A3 = 9 => 0 pairs (*) / I3 = 9 => 0 pairs (X) C5,E5: 9.. / C5 = 9 => 22 pairs (_) / E5 = 9 => 20 pairs (_) B4,B7: 9.. / B4 = 9 => 0 pairs (*) / B7 = 9 => 0 pairs (X) * DURATION: 0:01:42.421195 START: 09:55:36.589786 END: 09:57:19.010981 2017-05-04 * CP COUNT: (45) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B8,D2,D9,E1,E4,E7,F1,F7,F8,G3,G5,H7,I1,I2,I3,I9) * .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932. * PAIR A1: 6,7 BLK 1 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 => CTR * 7429..5169517648326831..7498.54.12.312.3..65443.5.61.82.68..4.13.4217985518649327 A3: 9 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 * PAIR A2: 7,9 BLK 1 A3: 7,9,6 # reduction candidate for 7,9 A3: 7,9 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 A3: 6 => CTR * .429..51.9517648326831..7498.54.12.312.3..65443.5.61.82.68..4713.4.1.985518.4932. * PAIR D2: 2,7 BLK 2 E3: 2,7,5 # reduction candidate for 2,7 E3: 2,7 # 19 pairs F3: 2,7,5 # reduction candidate for 2,7 F3: 2,7 # 18 pairs * PAIR D2: 2,7 COL D D8: 2,7,6 # reduction candidate for 2,7 D8: 2,7 => CTR * 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364.1.985518649327 D8: 6 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 * PAIR G3: 6,7 ROW 3 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 => CTR * 7429..5169517648326831..7498.54.12.312.3..65443.5.61.82.68..4.13.4217985518649327 A3: 9 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 * PAIR E4: 7,9 BLK 5 E5: 7,9,8 # reduction candidate for 7,9 E5: 7,9 # 18 pairs E6: 7,9,2 # reduction candidate for 7,9 E6: 7,9 => CTR * 7429385169517648326831257498.54.12.312.386.5443.5.21.82..8534.13.4217985518649327 E6: 2 # 20 pairs * PAIR E4: 7,9 ROW 4 B4: 7,9,6 # reduction candidate for 7,9 B4: 7,9 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 B4: 6 => CTR * 6429..5177512648399831..64286547129312.3.6.5443.5..1.82968..471374612985518749326 H4: 7,9,6 # reduction candidate for 7,9 H4: 7,9 => CTR * 6429..5177512648399831..64286547129312.3.6.5443.5..1.82968..471374612985518749326 H4: 6 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 * PAIR G5: 6,7 BLK 6 H4: 6,7,9 # reduction candidate for 6,7 H4: 6,7 # 21 pairs H6: 6,7,9 # reduction candidate for 6,7 H6: 6,7 => CTR * .429..51..51.6483..831...4.86547129312.3...5443.5..1.82968..471374612985518749326 H6: 9 # 21 pairs * PAIR G5: 6,7 ROW 5 C5: 6,7,9 # reduction candidate for 6,7 C5: 6,7 # 20 pairs F5: 6,7,8 # reduction candidate for 6,7 F5: 6,7 # 19 pairs * PAIR B8: 6,7 BLK 7 B7: 6,7,9 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 B7: 9 # 20 pairs C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 # 20 pairs * PAIR B8: 6,7 ROW 8 D8: 6,7,2 # reduction candidate for 6,7 D8: 6,7 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 D8: 2 => CTR * 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364217985518649327 * PAIR B8: 6,7 COL B B4: 6,7,9 # reduction candidate for 6,7 B4: 9 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 B4: 6,7 # 20 pairs * PAIR F8: 2,7 BLK 8 D8: 2,7,6 # reduction candidate for 2,7 D8: 2,7 => CTR * 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364.1.985518649327 D8: 6 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 * PAIR F8: 2,7 COL F F3: 2,7,5 # reduction candidate for 2,7 F3: 2,7 # 18 pairs F6: 2,7,6 # reduction candidate for 2,7 F6: 2,7 => CTR * 6429.85177512648399831..6428.54712.312.3.675443.5..1.82..8..471374612985518749326 F6: 6 # 22 pairs * PAIR D9: 6,7 BLK 8 D8: 6,7,2 # reduction candidate for 6,7 D8: 6,7 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 D8: 2 => CTR * 7429..5169517648326831..7498.54.126312.3...5443.5..1.82..8..4.1364217985518649327 * PAIR H7: 6,7 ROW 7 B7: 6,7,9 # reduction candidate for 6,7 B7: 6,7 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 B7: 9 # 20 pairs C7: 6,7,9 # reduction candidate for 6,7 C7: 6,7 # 20 pairs * PAIR H7: 6,7 COL H H4: 6,7,9 # reduction candidate for 6,7 H4: 6,7 # 21 pairs H6: 6,7,9 # reduction candidate for 6,7 H6: 6,7 => CTR * .429..51..51.6483..831...4.86547129312.3...5443.5..1.82968..471374612985518749326 H6: 9 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-208-base-pr-000.dot * REASONING * DIS # A3: 6,7 => CTR => A3: 9 * PRF # A3: 9 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 6 => CTR => A3: 7,9 * DIS # D8: 2,7 => CTR => D8: 6 * PRF # D8: 6 => SOL * DIS # A3: 6,7 => CTR => A3: 9 * PRF # A3: 9 => SOL * DIS # E6: 7,9 => CTR => E6: 2 * PRF # B4: 7,9 => SOL * DIS # B4: 6 => CTR => B4: 7,9 * DIS # H4: 7,9 => CTR => H4: 6 * PRF # H4: 6 => SOL * DIS # H6: 6,7 => CTR => H6: 9 * PRF # B7: 6,7 => SOL * PRF # D8: 6,7 => SOL * DIS # D8: 2 => CTR => D8: 6,7 * PRF # B4: 9 => SOL * DIS # D8: 2,7 => CTR => D8: 6 * PRF # D8: 6 => SOL * DIS # F6: 2,7 => CTR => F6: 6 * PRF # D8: 6,7 => SOL * DIS # D8: 2 => CTR => D8: 6,7 * PRF # B7: 6,7 => SOL * DIS # H6: 6,7 => CTR => H6: 9 * CNT 25 HDP CHAINS / 42 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A2,B8,D2,D9,E1,E4,E7,F1,F7,F8,G3,G5,H7,I1,I2,I3,I9) * .429..51..51.6483..831...4.8.54.12.312.3...5443.5..1.82..8..4.13.4.1.985518.4932. * PAIR A1: 6,7 BLK 1 A3: 6,7,9 # reduction candidate for 6,7 A3: 6,7 => CTR * 7429..5169517648326831..7498.54.12.312.3..65443.5.61.82.68..4.13.4217985518649327 A3: 9 => SOLVED * 642983517751264839983157642895471263126398754437526198269835471374612985518749326 * DURATION: 0:00:03.714368 START: 09:58:16.792333 END: 09:58:20.506701 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-208-base-pr-001.dot * REASONING * DIS # A3: 6,7 => CTR => A3: 9 * PRF A3: 9 => SOL * STA A3: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 208 solution: 642983517751264839983157642895471263126398754437526198269835471374612985518749326 info: 1915 FNBTHWX S8.f 39526 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 642983517751264839983157642895471263126398754437526198269835471374612985518749326 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 # A3: 6,7 => CTR => A3: 9 * PRF # A3: 9 => SOL * PRF # A3: 7,9 => SOL * DIS # A3: 6 => CTR => A3: 7,9 * INC # E3: 2,7 => UNS * INC # F3: 2,7 => UNS * DIS # D8: 2,7 => CTR => D8: 6 * PRF # D8: 6 => SOL * DIS # A3: 6,7 => CTR => A3: 9 * PRF # A3: 9 => SOL * INC # E5: 7,9 => UNS * DIS # E6: 7,9 => CTR => E6: 2 * INC # E6: 2 => UNS * PRF # B4: 7,9 => SOL * DIS # B4: 6 => CTR => B4: 7,9 * DIS # H4: 7,9 => CTR => H4: 6 * PRF # H4: 6 => SOL * INC # H4: 6,7 => UNS * DIS # H6: 6,7 => CTR => H6: 9 * INC # H6: 9 => UNS * INC # C5: 6,7 => UNS * INC # F5: 6,7 => UNS * PRF # B7: 6,7 => SOL * INC # B7: 9 => UNS * INC # C7: 6,7 => UNS * PRF # D8: 6,7 => SOL * DIS # D8: 2 => CTR => D8: 6,7 * INC # B4: 6,7 => UNS * PRF # B4: 9 => SOL * DIS # D8: 2,7 => CTR => D8: 6 * PRF # D8: 6 => SOL * INC # F3: 2,7 => UNS * DIS # F6: 2,7 => CTR => F6: 6 * INC # F6: 6 => UNS * PRF # D8: 6,7 => SOL * DIS # D8: 2 => CTR => D8: 6,7 * PRF # B7: 6,7 => SOL * INC # B7: 9 => UNS * INC # C7: 6,7 => UNS * INC # H4: 6,7 => UNS * DIS # H6: 6,7 => CTR => H6: 9 * INC # H6: 9 => UNS * CNT 42 HDP CHAINS / 42 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A3: 6,7 => CTR => A3: 9 * PRF A3: 9 => SOL * STA A3: 9 * CNT 2 HDP CHAINS / 1 HYP OPENED