Analysis of xx-top500-391-base.sdk
Contents
Original Sudoku
level: hard
position: 3..7...2......16..............2...7..16.......5.......8..42.3..9.....1........5.. initial
Autosolve
position: 36.75..21527..16..1....275.4.3216.75.165......5.....168714253699.5...1.26.21..5.7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E3: 8,9 => CTR => E3: 3,4,6 * DIS # G6: 8,9 => CTR => G6: 2,4 * DIS # G6: 8,9 => CTR => G6: 2,4 * CNT 3 HDP CHAINS / 19 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E3: 8,9 => CTR => E3: 3,4,6 * DIS E3: 3,4,6 # G6: 8,9 => CTR => G6: 2,4 * STA E3: 3,4,6 + G6: 2,4 * CNT 2 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction Position
position: 36.75..21527..16..1....275.4.3216.75.165......5.....168714253699.5...1.26.21..5.7 pair_reduction
See section Pair Reduction for the HDP chains leading to this result.
Deep Pair Reduction
Time used: 0:00:58.997110
The following important HDP chains were detected:
* DIS # C1: 8,9 # D3: 3,6 => CTR => D3: 8,9 * DIS # C1: 8,9 + D3: 8,9 # E6: 8,9 => CTR => E6: 3,4,7 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 # F6: 8,9 => CTR => F6: 3,4,7 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 # G5: 2,4 => CTR => G5: 8,9 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # E5: 9 => CTR => E5: 7,8 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 # F8: 3 => CTR => F8: 7,8 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 + F8: 7,8 # F5: 7 => CTR => F5: 8,9 * DIS # C3: 8,9 # E2: 8,9 => CTR => E2: 3,4 * PRF # C3: 8,9 + E2: 3,4 # F6: 8,9 => SOL * STA # C3: 8,9 + E2: 3,4 + F6: 8,9 * CNT 9 HDP CHAINS / 46 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3..7...2......16..............2...7..16.......5.......8..42.3..9.....1........5.. | initial |
| 36.75..21527..16..1....275.4.3216.75.165......5.....168714253699.5...1.26.21..5.7 | autosolve |
| 36.75..21527..16..1....275.4.3216.75.165......5.....168714253699.5...1.26.21..5.7 | pair_reduction |
| 364758921527941638189632754493216875716584293258379416871425369935867142642193587 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (12) B3: 8,9 H2: 3,9 B4: 8,9 A5: 2,7 A6: 2,7 C6: 8,9 G4: 8,9 H5: 3,9 B8: 3,4 B9: 3,4 H8: 4,8 H9: 4,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A5,A6: 2.. / A5 = 2 => 10 pairs (_) / A6 = 2 => 10 pairs (_) G5,G6: 2.. / G5 = 2 => 10 pairs (_) / G6 = 2 => 10 pairs (_) A5,G5: 2.. / A5 = 2 => 10 pairs (_) / G5 = 2 => 10 pairs (_) A6,G6: 2.. / A6 = 2 => 10 pairs (_) / G6 = 2 => 10 pairs (_) H5,I5: 3.. / H5 = 3 => 13 pairs (_) / I5 = 3 => 0 pairs (*) B8,B9: 3.. / B8 = 3 => 12 pairs (_) / B9 = 3 => 12 pairs (_) H2,H5: 3.. / H2 = 3 => 0 pairs (*) / H5 = 3 => 0 pairs (X) C1,C3: 4.. / C1 = 4 => 20 pairs (_) / C3 = 4 => 14 pairs (_) B8,B9: 4.. / B8 = 4 => 12 pairs (_) / B9 = 4 => 12 pairs (_) H8,H9: 4.. / H8 = 4 => 12 pairs (_) / H9 = 4 => 12 pairs (_) E2,I2: 4.. / E2 = 4 => 14 pairs (_) / I2 = 4 => 18 pairs (_) B8,H8: 4.. / B8 = 4 => 12 pairs (_) / H8 = 4 => 12 pairs (_) B9,H9: 4.. / B9 = 4 => 12 pairs (_) / H9 = 4 => 12 pairs (_) D3,E3: 6.. / D3 = 6 => 13 pairs (_) / E3 = 6 => 12 pairs (_) D8,E8: 6.. / D8 = 6 => 12 pairs (_) / E8 = 6 => 13 pairs (_) D3,D8: 6.. / D3 = 6 => 13 pairs (_) / D8 = 6 => 12 pairs (_) E3,E8: 6.. / E3 = 6 => 12 pairs (_) / E8 = 6 => 13 pairs (_) A5,A6: 7.. / A5 = 7 => 10 pairs (_) / A6 = 7 => 10 pairs (_) E8,F8: 7.. / E8 = 7 => 13 pairs (_) / F8 = 7 => 12 pairs (_) B4,C6: 8.. / B4 = 8 => 0 pairs (X) / C6 = 8 => 14 pairs (_) H8,H9: 8.. / H8 = 8 => 12 pairs (_) / H9 = 8 => 12 pairs (_) B4,G4: 8.. / B4 = 8 => 0 pairs (X) / G4 = 8 => 14 pairs (_) B3,B4: 8.. / B3 = 8 => 14 pairs (_) / B4 = 8 => 0 pairs (X) G1,H2: 9.. / G1 = 9 => 0 pairs (*) / H2 = 9 => 0 pairs (X) B4,C6: 9.. / B4 = 9 => 14 pairs (_) / C6 = 9 => 0 pairs (X) E9,F9: 9.. / E9 = 9 => 13 pairs (_) / F9 = 9 => 14 pairs (_) B4,G4: 9.. / B4 = 9 => 14 pairs (_) / G4 = 9 => 0 pairs (X) B3,B4: 9.. / B3 = 9 => 0 pairs (X) / B4 = 9 => 14 pairs (_) H2,H5: 9.. / H2 = 9 => 13 pairs (_) / H5 = 9 => 0 pairs (*) * DURATION: 0:00:47.378455 START: 16:11:22.945788 END: 16:12:10.324243 2017-05-04 * CP COUNT: (29) * SOLUTION FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:58.690843 START: 16:13:11.705911 END: 16:14:10.396754 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-391-base-pr-002.dot * REASONING * DIS # C1: 8,9 # D3: 3,6 => CTR => D3: 8,9 * DIS # C1: 8,9 + D3: 8,9 # E6: 8,9 => CTR => E6: 3,4,7 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 # F6: 8,9 => CTR => F6: 3,4,7 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 # G5: 2,4 => CTR => G5: 8,9 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # E5: 9 => CTR => E5: 7,8 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 # F8: 3 => CTR => F8: 7,8 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 + F8: 7,8 # F5: 7 => CTR => F5: 8,9 * DIS # C3: 8,9 # E2: 8,9 => CTR => E2: 3,4 * PRF # C3: 8,9 + E2: 3,4 # F6: 8,9 => SOL * STA # C3: 8,9 + E2: 3,4 + F6: 8,9 * CNT 9 HDP CHAINS / 46 HYP OPENED
Header Info
Top 500 Minimum 17 391 solution: 364758921527941638189632754493216875716584293258379416871425369935867142642193587 info: 50712 FNBXYK S8.f 29540 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 364758921527941638189632754493216875716584293258379416871425369935867142642193587 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 # C1: 8,9 => UNS * INC # C3: 8,9 => UNS * INC # D3: 8,9 => UNS * DIS # E3: 8,9 => CTR => E3: 3,4,6 * INC # E3: 3,4,6 => UNS * INC # D2: 3,9 => UNS * INC # E2: 3,9 => UNS * INC # D6: 8,9 => UNS * INC # E6: 8,9 => UNS * INC # F6: 8,9 => UNS * DIS # G6: 8,9 => CTR => G6: 2,4 * INC # G6: 2,4 => UNS * INC # C1: 8,9 => UNS * INC # C3: 8,9 => UNS * INC # G5: 8,9 => UNS * DIS # G6: 8,9 => CTR => G6: 2,4 * INC # G6: 2,4 => UNS * INC # G1: 8,9 => UNS * INC # G1: 4 => UNS * CNT 19 HDP CHAINS / 19 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 8,9 => UNS * INC # C3: 8,9 => UNS * INC # D3: 8,9 => UNS * DIS # E3: 8,9 => CTR => E3: 3,4,6 * INC E3: 3,4,6 # D3: 8,9 => UNS * INC E3: 3,4,6 # D3: 3,6 => UNS * INC E3: 3,4,6 # C1: 8,9 => UNS * INC E3: 3,4,6 # C3: 8,9 => UNS * INC E3: 3,4,6 # D3: 8,9 => UNS * INC E3: 3,4,6 # D3: 3,6 => UNS * INC E3: 3,4,6 # D2: 3,9 => UNS * INC E3: 3,4,6 # E2: 3,9 => UNS * INC E3: 3,4,6 # D6: 8,9 => UNS * INC E3: 3,4,6 # E6: 8,9 => UNS * INC E3: 3,4,6 # F6: 8,9 => UNS * DIS E3: 3,4,6 # G6: 8,9 => CTR => G6: 2,4 * INC E3: 3,4,6 + G6: 2,4 # C1: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # C3: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # D6: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # E6: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # F6: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # C1: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # C3: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # G5: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # G5: 2,4 => UNS * INC E3: 3,4,6 + G6: 2,4 # G1: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # G1: 4 => UNS * INC E3: 3,4,6 + G6: 2,4 # C1: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # C3: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # D3: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # D3: 3,6 => UNS * INC E3: 3,4,6 + G6: 2,4 # D2: 3,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # E2: 3,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # D6: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # E6: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # F6: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # C1: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # C3: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # G5: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # G5: 2,4 => UNS * INC E3: 3,4,6 + G6: 2,4 # G1: 8,9 => UNS * INC E3: 3,4,6 + G6: 2,4 # G1: 4 => UNS * INC E3: 3,4,6 + G6: 2,4 # G5: 2,4 => UNS * INC E3: 3,4,6 + G6: 2,4 # G5: 8,9 => UNS * STA E3: 3,4,6 + G6: 2,4 * CNT 44 HDP CHAINS / 44 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # C1: 8,9 => UNS * INC # C3: 8,9 => UNS * INC # D3: 8,9 => UNS * INC # D3: 3,6 => UNS * INC # D2: 3,9 => UNS * INC # E2: 3,9 => UNS * INC # D6: 8,9 => UNS * INC # E6: 8,9 => UNS * INC # F6: 8,9 => UNS * INC # C1: 8,9 => UNS * INC # C3: 8,9 => UNS * INC # G5: 8,9 => UNS * INC # G5: 2,4 => UNS * INC # G1: 8,9 => UNS * INC # G1: 4 => UNS * INC # G5: 2,4 => UNS * INC # G5: 8,9 => UNS * INC # C1: 8,9 # F1: 8,9 => UNS * INC # C1: 8,9 # G1: 8,9 => UNS * INC # C1: 8,9 # D3: 8,9 => UNS * DIS # C1: 8,9 # D3: 3,6 => CTR => D3: 8,9 * INC # C1: 8,9 + D3: 8,9 # D6: 8,9 => UNS * DIS # C1: 8,9 + D3: 8,9 # E6: 8,9 => CTR => E6: 3,4,7 * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 # F6: 8,9 => CTR => F6: 3,4,7 * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 # G5: 8,9 => UNS * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 # G5: 2,4 => CTR => G5: 8,9 * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # F5: 8,9 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # F9: 8,9 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # E5: 8,9 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # F5: 8,9 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # E5: 8,9 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # F5: 8,9 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # F8: 7,8 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # F8: 3 => UNS * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # E5: 7,8 => UNS * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 # E5: 9 => CTR => E5: 7,8 * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 # F8: 7,8 => UNS * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 # F8: 3 => CTR => F8: 7,8 * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 + F8: 7,8 # F5: 8,9 => UNS * DIS # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 + F8: 7,8 # F5: 7 => CTR => F5: 8,9 * INC # C1: 8,9 + D3: 8,9 + E6: 3,4,7 + F6: 3,4,7 + G5: 8,9 + E5: 7,8 + F8: 7,8 + F5: 8,9 => UNS * INC # C3: 8,9 # D2: 8,9 => UNS * DIS # C3: 8,9 # E2: 8,9 => CTR => E2: 3,4 * INC # C3: 8,9 + E2: 3,4 # F5: 8,9 => UNS * PRF # C3: 8,9 + E2: 3,4 # F6: 8,9 => SOL * STA # C3: 8,9 + E2: 3,4 + F6: 8,9 * CNT 45 HDP CHAINS / 46 HYP OPENED