Analysis of xx-top500-087-base.sdk
Contents
Original Sudoku
level: medium
position: 47..........5..1.........3..4......2....34.......8.6..8.1....4......75.....2..... initial
Autosolve
position: 47..........54.1........43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D1: 6,9 => CTR => D1: 1,3,8 * PRF # E1: 6,9 => SOL * DIS # E1: 2 => CTR => E1: 6,9 * DIS # F1: 6,9 => CTR => F1: 1,3 * DIS # F2: 6,9 => CTR => F2: 3 * DIS # D3: 6,9 => CTR => D3: 7,8 * DIS # E3: 6,9 => CTR => E3: 2,7 * DIS # F4: 6,9 => CTR => F4: 1,5 * DIS # H1: 2,8 => CTR => H1: 5,6,9 * PRF # H2: 2,8 => SOL * DIS # H2: 6,7,9 => CTR => H2: 2,8 * DIS # C1: 2,8 => CTR => C1: 3,5,6,9 * DIS # I5: 7,8 => CTR => I5: 1,5,9 * DIS # I2: 8,9 => CTR => I2: 6,7 * DIS # H8: 1,6 => CTR => H8: 2,8 * DIS # I8: 1,6 => CTR => I8: 3,8 * DIS # I9: 1,6 => CTR => I9: 3 * DIS # E9: 5 => CTR => E9: 1,6 * CNT 18 HDP CHAINS / 41 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D1: 6,9 => CTR => D1: 1,3,8 * PRF D1: 1,3,8 # E1: 6,9 => SOL * STA D1: 1,3,8 + E1: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 47..........5..1.........3..4......2....34.......8.6..8.1....4......75.....2..... | initial |
| 47..........54.1........43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. | autosolve |
| 473891265269543187185726439648175392592634871317982654821359746936417528754268913 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) F3: 6,9 G1: 2,8 G5: 7,8 G7: 2,7 I7: 6,7 H9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A3,B3: 1.. / A3 = 1 => 7 pairs (_) / B3 = 1 => 7 pairs (_) D1,F1: 1.. / D1 = 1 => 0 pairs (X) / F1 = 1 => 6 pairs (_) E8,E9: 1.. / E8 = 1 => 7 pairs (_) / E9 = 1 => 0 pairs (X) F1,F4: 1.. / F1 = 1 => 6 pairs (_) / F4 = 1 => 0 pairs (X) E1,E3: 2.. / E1 = 2 => 0 pairs (X) / E3 = 2 => 0 pairs (_) G7,H8: 2.. / G7 = 2 => 0 pairs (X) / H8 = 2 => 0 pairs (_) B7,G7: 2.. / B7 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) G1,G7: 2.. / G1 = 2 => 0 pairs (*) / G7 = 2 => 0 pairs (X) D7,F7: 3.. / D7 = 3 => 6 pairs (_) / F7 = 3 => 0 pairs (X) I8,I9: 3.. / I8 = 3 => 0 pairs (X) / I9 = 3 => 7 pairs (_) B9,I9: 3.. / B9 = 3 => 0 pairs (X) / I9 = 3 => 7 pairs (_) D1,D7: 3.. / D1 = 3 => 0 pairs (X) / D7 = 3 => 6 pairs (_) E4,F4: 5.. / E4 = 5 => 0 pairs (X) / F4 = 5 => 6 pairs (_) B7,B9: 5.. / B7 = 5 => 0 pairs (X) / B9 = 5 => 7 pairs (_) B9,E9: 5.. / B9 = 5 => 7 pairs (_) / E9 = 5 => 0 pairs (X) F4,F7: 5.. / F4 = 5 => 6 pairs (_) / F7 = 5 => 0 pairs (X) D3,E3: 7.. / D3 = 7 => 0 pairs (*) / E3 = 7 => 0 pairs (X) H2,I2: 7.. / H2 = 7 => 0 pairs (X) / I2 = 7 => 0 pairs (_) G7,I7: 7.. / G7 = 7 => 0 pairs (*) / I7 = 7 => 0 pairs (X) E3,E4: 7.. / E3 = 7 => 0 pairs (X) / E4 = 7 => 0 pairs (_) G5,G7: 7.. / G5 = 7 => 0 pairs (X) / G7 = 7 => 0 pairs (_) D1,D3: 8.. / D1 = 8 => 0 pairs (*) / D3 = 8 => 0 pairs (X) H8,I8: 8.. / H8 = 8 => 0 pairs (X) / I8 = 8 => 7 pairs (_) C4,H4: 8.. / C4 = 8 => 6 pairs (_) / H4 = 8 => 0 pairs (X) G1,G5: 8.. / G1 = 8 => 0 pairs (X) / G5 = 8 => 0 pairs (_) * DURATION: 0:00:35.775510 START: 05:45:25.534498 END: 05:46:01.310008 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F3,G1,G5,G7,H9,I7) * 47..........54.1........43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. * PAIR F3: 6,9 BLK 2 D1: 6,9,1,3,8 # reduction candidate for 6,9 D1: 6,9 => CTR * 473.218.....543127...87.43..4....3.2....347......826.48.13...4....4.75..7.42.89.. D1: 1,3,8 # 6 pairs E1: 6,9,2 # reduction candidate for 6,9 E1: 6,9 => SOLVED * 473891265269543187185726439648175392592634871317982654821359746936417528754268913 E1: 2 => CTR * 47..2.8.....54.127...87.43..4....3.2....347......826.48.1....4....4.75..7.42.89.. F1: 6,9,1,3 # reduction candidate for 6,9 F1: 6,9 => CTR * 47312.8.....543127...87.43..4..513.2....347......826.48.13.5.4....4.75..7542.89.3 F1: 1,3 # 7 pairs F2: 6,9,3 # reduction candidate for 6,9 F2: 6,9 => CTR * 47..2.8.....54.127...87.43..4....3.2....347......826.48.1....4....4.75..7.42.89.. F2: 3 # 6 pairs D3: 6,9,7,8 # reduction candidate for 6,9 D3: 6,9 => CTR * 47.8.12.....5431........43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. D3: 7,8 # 7 pairs E3: 6,9,2,7 # reduction candidate for 6,9 E3: 6,9 => CTR * 47..2.8.....54.127......43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. E3: 2,7 # 7 pairs * PAIR F3: 6,9 ROW 3 A3: 6,9,1,2,5 # reduction candidate for 6,9 A3: 6,9 # 11 pairs B3: 6,9,1,2,8 # reduction candidate for 6,9 B3: 6,9 # 11 pairs C3: 6,9,2,5,8 # reduction candidate for 6,9 C3: 6,9 # 10 pairs I3: 6,9,5,8 # reduction candidate for 6,9 I3: 6,9 # 9 pairs * PAIR F3: 6,9 COL F F4: 6,9,1,5 # reduction candidate for 6,9 F4: 6,9 => CTR * 473.218.....543127...87.43..4..5.3.2....347......826.48.13.5.4....4.75..7542.89.3 F4: 1,5 # 7 pairs F7: 6,9,3,5 # reduction candidate for 6,9 F7: 6,9 # 7 pairs * PAIR G1: 2,8 BLK 3 H1: 2,8,5,6,9 # reduction candidate for 2,8 H1: 2,8 => CTR * 47..........54.1.....8..43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. H1: 5,6,9 # 6 pairs H2: 2,8,6,7,9 # reduction candidate for 2,8 H2: 2,8 => SOLVED * 473891265269543187185726439648175392592634871317982654821359746936417528754268913 H2: 6,7,9 => CTR * 47.8.12.....5431.....72.43..4..753.2....348......826.482135974....4.75..7.42.89.. * PAIR G1: 2,8 ROW 1 C1: 2,8,3,5,6,9 # reduction candidate for 2,8 C1: 2,8 => CTR * 47..........54.1........43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. C1: 3,5,6,9 # 6 pairs * PAIR G5: 7,8 BLK 6 H4: 7,8,1,9 # reduction candidate for 7,8 H4: 7,8 # 7 pairs H5: 7,8,1,5,9 # reduction candidate for 7,8 H5: 7,8 # 9 pairs I5: 7,8,1,5,9 # reduction candidate for 7,8 I5: 7,8 => CTR * 47....82....54.17....8..43..4....3.2....347.8....826.48.1...247...4.758.7.42.896. I5: 1,5,9 # 6 pairs * PAIR G5: 7,8 ROW 5 C5: 7,8,2,5,6,9 # reduction candidate for 7,8 C5: 7,8 # 7 pairs C5: 2,5,6,9 # 6 pairs * PAIR I7: 6,7 COL I I2: 6,7,8,9 # reduction candidate for 6,7 I2: 8,9 => CTR * 47.8.12.....54317....72.43..4..753.2....348.7..7.826.482135974....4.75..7.42.89.. I2: 6,7 # 8 pairs * PAIR H9: 1,6 BLK 9 H8: 1,6,2,8 # reduction candidate for 1,6 H8: 1,6 => CTR * 47..2.8.....54.17....87.43..4....3.2....347.1....826.48.1...247...4.75.87.42.89.3 H8: 2,8 # 7 pairs I8: 1,6,3,8 # reduction candidate for 1,6 I8: 1,6 => CTR * 47..2.8...8.54.17....87.43..487..3.2....347.8..7.826.48.1...247...4.7581754218963 I8: 3,8 # 7 pairs I9: 1,6,3 # reduction candidate for 1,6 I9: 1,6 => CTR * 47..218...8.54.17....87.43..487.53.2....347.83.7.82654851...247...417583734258961 I9: 3 # 7 pairs * PAIR H9: 1,6 ROW 9 E9: 1,6,5 # reduction candidate for 1,6 E9: 5 => CTR * 47..218.....54.17....87.43..4...53.2....347......826.4851...247...4175..7.42589.. E9: 1,6 # 7 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-087-base-pr-000.dot * REASONING * DIS # D1: 6,9 => CTR => D1: 1,3,8 * PRF # E1: 6,9 => SOL * DIS # E1: 2 => CTR => E1: 6,9 * DIS # F1: 6,9 => CTR => F1: 1,3 * DIS # F2: 6,9 => CTR => F2: 3 * DIS # D3: 6,9 => CTR => D3: 7,8 * DIS # E3: 6,9 => CTR => E3: 2,7 * DIS # F4: 6,9 => CTR => F4: 1,5 * DIS # H1: 2,8 => CTR => H1: 5,6,9 * PRF # H2: 2,8 => SOL * DIS # H2: 6,7,9 => CTR => H2: 2,8 * DIS # C1: 2,8 => CTR => C1: 3,5,6,9 * DIS # I5: 7,8 => CTR => I5: 1,5,9 * DIS # I2: 8,9 => CTR => I2: 6,7 * DIS # H8: 1,6 => CTR => H8: 2,8 * DIS # I8: 1,6 => CTR => I8: 3,8 * DIS # I9: 1,6 => CTR => I9: 3 * DIS # E9: 5 => CTR => E9: 1,6 * CNT 18 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (F3,G1,G5,G7,H9,I7) * 47..........54.1........43..4....3.2....34.......826.48.1....4....4.75..7.42.89.. * PAIR F3: 6,9 BLK 2 D1: 6,9,1,3,8 # reduction candidate for 6,9 D1: 6,9 => CTR * 473.218.....543127...87.43..4....3.2....347......826.48.13...4....4.75..7.42.89.. E1: 6,9,2 # reduction candidate for 6,9 E1: 6,9 => SOLVED * 473891265269543187185726439648175392592634871317982654821359746936417528754268913 * DURATION: 0:00:03.392595 START: 05:46:30.359873 END: 05:46:33.752468 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-087-base-pr-001.dot * REASONING * DIS # D1: 6,9 => CTR => D1: 1,3,8 * PRF D1: 1,3,8 # E1: 6,9 => SOL * STA D1: 1,3,8 + E1: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
Top 500 Minimum 17 087 solution: 473891265269543187185726439648175392592634871317982654821359746936417528754268913 info: 1559 FNBHXY S8.f 31766 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 473891265269543187185726439648175392592634871317982654821359746936417528754268913 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 # D1: 6,9 => CTR => D1: 1,3,8 * INC # D1: 1,3,8 => UNS * PRF # E1: 6,9 => SOL * DIS # E1: 2 => CTR => E1: 6,9 * DIS # F1: 6,9 => CTR => F1: 1,3 * INC # F1: 1,3 => UNS * DIS # F2: 6,9 => CTR => F2: 3 * INC # F2: 3 => UNS * DIS # D3: 6,9 => CTR => D3: 7,8 * INC # D3: 7,8 => UNS * DIS # E3: 6,9 => CTR => E3: 2,7 * INC # E3: 2,7 => UNS * INC # A3: 6,9 => UNS * INC # B3: 6,9 => UNS * INC # C3: 6,9 => UNS * INC # I3: 6,9 => UNS * DIS # F4: 6,9 => CTR => F4: 1,5 * INC # F4: 1,5 => UNS * INC # F7: 6,9 => UNS * DIS # H1: 2,8 => CTR => H1: 5,6,9 * INC # H1: 5,6,9 => UNS * PRF # H2: 2,8 => SOL * DIS # H2: 6,7,9 => CTR => H2: 2,8 * DIS # C1: 2,8 => CTR => C1: 3,5,6,9 * INC # C1: 3,5,6,9 => UNS * INC # H4: 7,8 => UNS * INC # H5: 7,8 => UNS * DIS # I5: 7,8 => CTR => I5: 1,5,9 * INC # I5: 1,5,9 => UNS * INC # C5: 7,8 => UNS * INC # C5: 2,5,6,9 => UNS * INC # I2: 6,7 => UNS * DIS # I2: 8,9 => CTR => I2: 6,7 * DIS # H8: 1,6 => CTR => H8: 2,8 * INC # H8: 2,8 => UNS * DIS # I8: 1,6 => CTR => I8: 3,8 * INC # I8: 3,8 => UNS * DIS # I9: 1,6 => CTR => I9: 3 * INC # I9: 3 => UNS * INC # E9: 1,6 => UNS * DIS # E9: 5 => CTR => E9: 1,6 * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D1: 6,9 => CTR => D1: 1,3,8 * PRF D1: 1,3,8 # E1: 6,9 => SOL * STA D1: 1,3,8 + E1: 6,9 * CNT 2 HDP CHAINS / 2 HYP OPENED