Analysis of xx-top500-088-base.sdk
Contents
Original Sudoku
level: hard
position: ....5.1.3.2.6.........4.....8.2...6.......9......3.......7..24.3.1......5........ initial
Autosolve
position: 46.95.1.3.236.15.4.1534....18429536723.1.4958.5983.412.9.71324534152....5724.9.31 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:32.500596
The following important HDP chains were detected:
* DIS # A2: 7,8 # G8: 7,8 => CTR => G8: 6 * DIS # A2: 7,8 + G8: 6 => CTR => A2: 9 * PRF A2: 9 # H1: 7,8 => SOL * STA A2: 9 + H1: 7,8 * CNT 3 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....5.1.3.2.6.........4.....8.2...6.......9......3.......7..24.3.1......5........ | initial |
| 46.95.1.3.236.15.4.1534....18429536723.1.4958.5983.412.9.71324534152....5724.9.31 | autosolve |
| 467952183923681574815347629184295367236174958759836412698713245341528796572469831 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C1: 7,8 E2: 7,8 I3: 6,9 C5: 6,7 A6: 6,7 E5: 6,7 F6: 6,7 A7: 6,8 C7: 6,8 F8: 6,8 E9: 6,8 I8: 6,9 G9: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F1,F3: 2.. / F1 = 2 => 15 pairs (_) / F3 = 2 => 14 pairs (_) H1,H3: 2.. / H1 = 2 => 14 pairs (_) / H3 = 2 => 15 pairs (_) F1,H1: 2.. / F1 = 2 => 15 pairs (_) / H1 = 2 => 14 pairs (_) F3,H3: 2.. / F3 = 2 => 14 pairs (_) / H3 = 2 => 15 pairs (_) G3,I3: 6.. / G3 = 6 => 0 pairs (*) / I3 = 6 => 0 pairs (X) C5,A6: 6.. / C5 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) E5,F6: 6.. / E5 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) A7,C7: 6.. / A7 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) F8,E9: 6.. / F8 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) C5,E5: 6.. / C5 = 6 => 0 pairs (*) / E5 = 6 => 0 pairs (X) A6,F6: 6.. / A6 = 6 => 0 pairs (X) / F6 = 6 => 0 pairs (_) E9,G9: 6.. / E9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) A6,A7: 6.. / A6 = 6 => 0 pairs (X) / A7 = 6 => 0 pairs (_) C5,C7: 6.. / C5 = 6 => 0 pairs (*) / C7 = 6 => 0 pairs (X) E5,E9: 6.. / E5 = 6 => 0 pairs (X) / E9 = 6 => 0 pairs (_) F6,F8: 6.. / F6 = 6 => 0 pairs (*) / F8 = 6 => 0 pairs (X) I3,I8: 6.. / I3 = 6 => 13 pairs (_) / I8 = 6 => 0 pairs (*) C5,A6: 7.. / C5 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) E5,F6: 7.. / E5 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) G8,H8: 7.. / G8 = 7 => 15 pairs (_) / H8 = 7 => 16 pairs (_) C5,E5: 7.. / C5 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) A6,F6: 7.. / A6 = 7 => 0 pairs (*) / F6 = 7 => 0 pairs (X) C1,C5: 7.. / C1 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) E2,E5: 7.. / E2 = 7 => 0 pairs (X) / E5 = 7 => 0 pairs (_) G3,G8: 7.. / G3 = 7 => 16 pairs (_) / G8 = 7 => 15 pairs (_) A7,C7: 8.. / A7 = 8 => 0 pairs (X) / C7 = 8 => 0 pairs (_) F8,E9: 8.. / F8 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) E9,G9: 8.. / E9 = 8 => 0 pairs (X) / G9 = 8 => 0 pairs (_) C1,C7: 8.. / C1 = 8 => 0 pairs (X) / C7 = 8 => 0 pairs (_) E2,E9: 8.. / E2 = 8 => 0 pairs (*) / E9 = 8 => 0 pairs (X) A2,A3: 9.. / A2 = 9 => 15 pairs (_) / A3 = 9 => 14 pairs (_) H8,I8: 9.. / H8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) A2,H2: 9.. / A2 = 9 => 15 pairs (_) / H2 = 9 => 14 pairs (_) I3,I8: 9.. / I3 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) * DURATION: 0:01:07.653005 START: 05:46:48.859512 END: 05:47:56.512517 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:32.346677 START: 05:48:29.428984 END: 05:49:01.775661 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-088-base-pr-002.dot * REASONING * DIS # A2: 7,8 # G8: 7,8 => CTR => G8: 6 * DIS # A2: 7,8 + G8: 6 => CTR => A2: 9 * PRF A2: 9 # H1: 7,8 => SOL * STA A2: 9 + H1: 7,8 * CNT 3 HDP CHAINS / 26 HYP OPENED
Header Info
Top 500 Minimum 17 088 solution: 467952183923681574815347629184295367236174958759836412698713245341528796572469831 info: 1560 FNBWXY S8.f 4802 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 467952183923681574815347629184295367236174958759836412698713245341528796572469831 solved
See section Deep 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 # A2: 7,8 => UNS * INC # A3: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # H1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # F3: 7,8 => UNS * INC # A2: 7,8 => UNS * INC # H2: 7,8 => UNS * INC # G8: 6,8 => UNS * INC # G8: 7 => UNS * INC # G8: 6,8 => UNS * INC # G8: 7 => UNS * INC # G3: 6,8 => UNS * INC # G3: 7 => UNS * CNT 14 HDP CHAINS / 14 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 7,8 => UNS * INC # A3: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # H1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # F3: 7,8 => UNS * INC # A2: 7,8 => UNS * INC # H2: 7,8 => UNS * INC # G8: 6,8 => UNS * INC # G8: 7 => UNS * INC # G8: 6,8 => UNS * INC # G8: 7 => UNS * INC # G3: 6,8 => UNS * INC # G3: 7 => UNS * CNT 14 HDP CHAINS / 14 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 7,8 => UNS * INC # A3: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # H1: 7,8 => UNS * INC # F1: 7,8 => UNS * INC # F3: 7,8 => UNS * INC # A2: 7,8 => UNS * INC # H2: 7,8 => UNS * INC # G8: 6,8 => UNS * INC # G8: 7 => UNS * INC # G8: 6,8 => UNS * INC # G8: 7 => UNS * INC # G3: 6,8 => UNS * INC # G3: 7 => UNS * INC # A2: 7,8 # F1: 7,8 => UNS * INC # A2: 7,8 # H1: 7,8 => UNS * INC # A2: 7,8 # F1: 7,8 => UNS * INC # A2: 7,8 # F3: 7,8 => UNS * INC # A2: 7,8 # H1: 7,8 => UNS * INC # A2: 7,8 # H3: 7,8 => UNS * INC # A2: 7,8 # F3: 7,8 => UNS * INC # A2: 7,8 # F3: 2 => UNS * DIS # A2: 7,8 # G8: 7,8 => CTR => G8: 6 * DIS # A2: 7,8 + G8: 6 => CTR => A2: 9 * INC A2: 9 # F1: 7,8 => UNS * PRF A2: 9 # H1: 7,8 => SOL * STA A2: 9 + H1: 7,8 * CNT 26 HDP CHAINS / 26 HYP OPENED