Analysis of xx-top500-085-base.sdk
Contents
Original Sudoku
level: medium
position: 14....7........4.....8.....8.2..3.......4.6.........1..6.57.......1....2.......8. initial
Autosolve
position: 14.3257.828.7.143..3.8.42.18.26139...1394862..9.2578133685721.....18.3.2.2143.58. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C2: 6,9 => CTR => C2: 5 * DIS # C3: 6,9 => CTR => C3: 5,7 * DIS # C2: 6,9 => CTR => C2: 5 * DIS # C3: 6,9 => CTR => C3: 5,7 * DIS # H3: 6,9 => CTR => H3: 5 * DIS # H3: 6,9 => CTR => H3: 5 * PRF # I4: 5,7 => SOL * DIS # A3: 5,7 => CTR => A3: 6,9 * DIS # A8: 5,7 => CTR => A8: 4,9 * PRF # I4: 5,7 => SOL * DIS # A8: 5,7 => CTR => A8: 4,9 * DIS # C8: 5,7 => CTR => C8: 4,9 * PRF # A8: 7,9 => SOL * DIS # C8: 7,9 => CTR => C8: 4,5 * DIS # A3: 7,9 => CTR => A3: 5,6 * CNT 15 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:
* DIS # C2: 6,9 => CTR => C2: 5 * DIS C2: 5 # C3: 6,9 => CTR => C3: 7 * PRF C2: 5 + C3: 7 # I4: 5,7 => SOL * STA C2: 5 + C3: 7 + I4: 5,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 14....7........4.....8.....8.2..3.......4.6.........1..6.57.......1....2.......8. | initial |
| 14.3257.828.7.143..3.8.42.18.26139...1394862..9.2578133685721.....18.3.2.2143.58. | autosolve |
| 149325768285761439637894251872613945513948627496257813368572194954186372721439586 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) C1: 6,9 E2: 6,9 E3: 6,9 H1: 6,9 B4: 5,7 A5: 5,7 A6: 4,6 C6: 4,6 I5: 5,7 B8: 5,7 A9: 7,9 F8: 6,9 F9: 6,9 H7: 4,9 I7: 4,9 H8: 6,7 I9: 6,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A6,C6: 4.. / A6 = 4 => 0 pairs (*) / C6 = 4 => 0 pairs (X) H4,I4: 4.. / H4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) A8,C8: 4.. / A8 = 4 => 15 pairs (_) / C8 = 4 => 0 pairs (*) H7,I7: 4.. / H7 = 4 => 17 pairs (_) / I7 = 4 => 0 pairs (*) A6,A8: 4.. / A6 = 4 => 0 pairs (*) / A8 = 4 => 0 pairs (X) C6,C8: 4.. / C6 = 4 => 15 pairs (_) / C8 = 4 => 0 pairs (*) H4,H7: 4.. / H4 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) I4,I7: 4.. / I4 = 4 => 17 pairs (_) / I7 = 4 => 0 pairs (*) I2,H3: 5.. / I2 = 5 => 0 pairs (X) / H3 = 5 => 19 pairs (_) B4,A5: 5.. / B4 = 5 => 0 pairs (X) / A5 = 5 => 0 pairs (_) C2,I2: 5.. / C2 = 5 => 19 pairs (_) / I2 = 5 => 0 pairs (X) A5,I5: 5.. / A5 = 5 => 0 pairs (*) / I5 = 5 => 0 pairs (X) B4,B8: 5.. / B4 = 5 => 0 pairs (X) / B8 = 5 => 0 pairs (_) H3,H4: 5.. / H3 = 5 => 19 pairs (_) / H4 = 5 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 0 pairs (*) / E3 = 6 => 0 pairs (X) A6,C6: 6.. / A6 = 6 => 15 pairs (_) / C6 = 6 => 0 pairs (*) F8,F9: 6.. / F8 = 6 => 0 pairs (*) / F9 = 6 => 0 pairs (X) H8,I9: 6.. / H8 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C1,H1: 6.. / C1 = 6 => 15 pairs (_) / H1 = 6 => 0 pairs (*) F8,H8: 6.. / F8 = 6 => 0 pairs (*) / H8 = 6 => 0 pairs (X) F9,I9: 6.. / F9 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) A3,A6: 6.. / A3 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) I2,I9: 6.. / I2 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) A3,C3: 7.. / A3 = 7 => 0 pairs (X) / C3 = 7 => 17 pairs (_) B4,A5: 7.. / B4 = 7 => 0 pairs (*) / A5 = 7 => 0 pairs (X) H8,I9: 7.. / H8 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) A5,I5: 7.. / A5 = 7 => 0 pairs (X) / I5 = 7 => 0 pairs (_) A9,I9: 7.. / A9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) B4,B8: 7.. / B4 = 7 => 0 pairs (*) / B8 = 7 => 0 pairs (X) C3,C8: 7.. / C3 = 7 => 17 pairs (_) / C8 = 7 => 0 pairs (X) H4,H8: 7.. / H4 = 7 => 0 pairs (X) / H8 = 7 => 0 pairs (_) E2,E3: 9.. / E2 = 9 => 15 pairs (_) / E3 = 9 => 0 pairs (*) F8,F9: 9.. / F8 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) H7,I7: 9.. / H7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) C1,H1: 9.. / C1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) A9,F9: 9.. / A9 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) I2,I7: 9.. / I2 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) * DURATION: 0:01:06.799833 START: 05:41:15.470124 END: 05:42:22.269957 2017-05-04 * CP COUNT: (37) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A9,B4,B8,C1,C6,E2,E3,F8,F9,H1,H7,H8,I5,I7,I9) * 14.3257.828.7.143..3.8.42.18.26139...1394862..9.2578133685721.....18.3.2.2143.58. * PAIR C1: 6,9 BLK 1 C2: 6,9,5 # reduction candidate for 6,9 C2: 6,9 => CTR * 14.3257.828.7.1435.3.8.42.18.2613954513948627.9.257813368572149.5.18.372721439586 C2: 5 # 19 pairs A3: 6,9,5,7 # reduction candidate for 6,9 A3: 6,9 # 21 pairs C3: 6,9,5,7 # reduction candidate for 6,9 C3: 6,9 => CTR * 14.3257.828.7.143.73.8.4251872613945513948627694257813368572194457189362.2143.58. C3: 5,7 # 18 pairs * PAIR E2: 6,9 ROW 2 C2: 6,9,5 # reduction candidate for 6,9 C2: 6,9 => CTR * 14.3257.828.7.1435.3.8.42.18.2613954513948627.9.257813368572149.5.18.372721439586 C2: 5 # 19 pairs I2: 6,9,5 # reduction candidate for 6,9 I2: 6,9 # 19 pairs * PAIR E3: 6,9 ROW 3 A3: 6,9,5,7 # reduction candidate for 6,9 A3: 6,9 # 21 pairs C3: 6,9,5,7 # reduction candidate for 6,9 C3: 6,9 => CTR * 14.3257.828.7.143.73.8.4251872613945513948627694257813368572194457189362.2143.58. C3: 5,7 # 18 pairs H3: 6,9,5 # reduction candidate for 6,9 H3: 6,9 => CTR * 14.3257.828.7.1435.3.8.42.18.2613954513948627.9.257813368572149.5.18.372721439586 H3: 5 # 19 pairs * PAIR H1: 6,9 BLK 3 I2: 6,9,5 # reduction candidate for 6,9 I2: 6,9 # 19 pairs H3: 6,9,5 # reduction candidate for 6,9 H3: 6,9 => CTR * 14.3257.828.7.1435.3.8.42.18.2613954513948627.9.257813368572149.5.18.372721439586 H3: 5 # 19 pairs * PAIR B4: 5,7 ROW 4 H4: 5,7,4 # reduction candidate for 5,7 H4: 5,7 # 17 pairs I4: 5,7,4 # reduction candidate for 5,7 I4: 5,7 => SOLVED * 149325768285761439637894251872613945513948627496257813368572194954186372721439586 I4: 4 # 17 pairs * PAIR A5: 5,7 COL A A3: 5,7,6,9 # reduction candidate for 5,7 A3: 5,7 => CTR * 14.3257.828.7.1436.3.8642518.2613974.1394862.6942578133685721..4..18.3.2921436587 A3: 6,9 # 21 pairs A8: 5,7,4,9 # reduction candidate for 5,7 A8: 5,7 => CTR * 14.3257.828.7.143..3.8.42.18.26139...1394862.4962578133685721....4189362921436587 A8: 4,9 # 18 pairs * PAIR I5: 5,7 BLK 6 H4: 5,7,4 # reduction candidate for 5,7 H4: 5,7 # 17 pairs I4: 5,7,4 # reduction candidate for 5,7 I4: 5,7 => SOLVED * 149325768285761439637894251872613945513948627496257813368572194954186372721439586 I4: 4 # 17 pairs * PAIR B8: 5,7 BLK 7 A8: 5,7,4,9 # reduction candidate for 5,7 A8: 5,7 => CTR * 14.3257.828.7.143..3.8.42.18.26139...1394862.4962578133685721....4189362921436587 A8: 4,9 # 18 pairs C8: 5,7,4,9 # reduction candidate for 5,7 C8: 5,7 => CTR * 14632579828.7.1436.3.8642518.2613974.1394862..942578133685721..4..189362921436587 C8: 4,9 # 21 pairs * PAIR A9: 7,9 BLK 7 A8: 7,9,4,5 # reduction candidate for 7,9 A8: 7,9 => SOLVED * 149325768285761439637894251872613945513948627496257813368572194954186372721439586 A8: 4,5 # 18 pairs C8: 7,9,4,5 # reduction candidate for 7,9 C8: 7,9 => CTR * 14.3257.828.7.143.9378642518726139..5139486276942578133685721..45.18.372721439586 C8: 4,5 # 19 pairs * PAIR A9: 7,9 COL A A3: 7,9,5,6 # reduction candidate for 7,9 A3: 7,9 => CTR * 14.3257.828.7.143.9378642518.26139..5139486276942578133685721..45.18.372721439586 A3: 5,6 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-085-base-pr-000.dot * REASONING * DIS # C2: 6,9 => CTR => C2: 5 * DIS # C3: 6,9 => CTR => C3: 5,7 * DIS # C2: 6,9 => CTR => C2: 5 * DIS # C3: 6,9 => CTR => C3: 5,7 * DIS # H3: 6,9 => CTR => H3: 5 * DIS # H3: 6,9 => CTR => H3: 5 * PRF # I4: 5,7 => SOL * DIS # A3: 5,7 => CTR => A3: 6,9 * DIS # A8: 5,7 => CTR => A8: 4,9 * PRF # I4: 5,7 => SOL * DIS # A8: 5,7 => CTR => A8: 4,9 * DIS # C8: 5,7 => CTR => C8: 4,9 * PRF # A8: 7,9 => SOL * DIS # C8: 7,9 => CTR => C8: 4,5 * DIS # A3: 7,9 => CTR => A3: 5,6 * CNT 15 HDP CHAINS / 36 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,A9,B4,B8,C1,C6,E2,E3,F8,F9,H1,H7,H8,I5,I7,I9) * 14.3257.828.7.143..3.8.42.18.26139...1394862..9.2578133685721.....18.3.2.2143.58. * PAIR C1: 6,9 BLK 1 C2: 6,9,5 # reduction candidate for 6,9 C2: 6,9 => CTR * 14.3257.828.7.1435.3.8.42.18.2613954513948627.9.257813368572149.5.18.372721439586 A3: 6,9,7 # reduction candidate for 6,9 A3: 6,9 # 21 pairs C3: 6,9,7 # reduction candidate for 6,9 C3: 6,9 => CTR * 14.3257.82857.143.73.8.4251872613945513948627694257813368572194457189362.2143.58. * RESTART * PAIR B4: 5,7 ROW 4 I4: 5,7,4 # reduction candidate for 5,7 I4: 5,7 => SOLVED * 149325768285761439637894251872613945513948627496257813368572194954186372721439586 * DURATION: 0:00:05.508183 START: 05:42:59.703374 END: 05:43:05.211557 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-085-base-pr-001.dot * REASONING * DIS # C2: 6,9 => CTR => C2: 5 * DIS C2: 5 # C3: 6,9 => CTR => C3: 7 * PRF C2: 5 + C3: 7 # I4: 5,7 => SOL * STA C2: 5 + C3: 7 + I4: 5,7 * CNT 3 HDP CHAINS / 4 HYP OPENED
Header Info
Top 500 Minimum 17 085 solution: 149325768285761439637894251872613945513948627496257813368572194954186372721439586 info: 1558 FNBWXY S8.f 26423 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 149325768285761439637894251872613945513948627496257813368572194954186372721439586 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 # C2: 6,9 => CTR => C2: 5 * INC # C2: 5 => UNS * INC # A3: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 5,7 * INC # C3: 5,7 => UNS * DIS # C2: 6,9 => CTR => C2: 5 * INC # C2: 5 => UNS * INC # I2: 6,9 => UNS * INC # A3: 6,9 => UNS * DIS # C3: 6,9 => CTR => C3: 5,7 * INC # C3: 5,7 => UNS * DIS # H3: 6,9 => CTR => H3: 5 * INC # H3: 5 => UNS * INC # I2: 6,9 => UNS * DIS # H3: 6,9 => CTR => H3: 5 * INC # H3: 5 => UNS * INC # H4: 5,7 => UNS * PRF # I4: 5,7 => SOL * INC # I4: 4 => UNS * DIS # A3: 5,7 => CTR => A3: 6,9 * INC # A3: 6,9 => UNS * DIS # A8: 5,7 => CTR => A8: 4,9 * INC # A8: 4,9 => UNS * INC # H4: 5,7 => UNS * PRF # I4: 5,7 => SOL * INC # I4: 4 => UNS * DIS # A8: 5,7 => CTR => A8: 4,9 * INC # A8: 4,9 => UNS * DIS # C8: 5,7 => CTR => C8: 4,9 * INC # C8: 4,9 => UNS * PRF # A8: 7,9 => SOL * INC # A8: 4,5 => UNS * DIS # C8: 7,9 => CTR => C8: 4,5 * INC # C8: 4,5 => UNS * DIS # A3: 7,9 => CTR => A3: 5,6 * INC # A3: 5,6 => UNS * CNT 36 HDP CHAINS / 36 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C2: 6,9 => CTR => C2: 5 * INC C2: 5 # A3: 6,9 => UNS * DIS C2: 5 # C3: 6,9 => CTR => C3: 7 * PRF C2: 5 + C3: 7 # I4: 5,7 => SOL * STA C2: 5 + C3: 7 + I4: 5,7 * CNT 4 HDP CHAINS / 4 HYP OPENED