Analysis of xx-top500-495-base.sdk
Contents
Original Sudoku
level: medium
position: .......72.8.6......1.......4...97.........8..3........7.3....4....18.6.....5..... initial
Autosolve
position: 63.....72.876......1.7...8642..97...17....8..39....7..753...148.4.1836578615742.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C3: 2 => CTR => C3: 4,9 * DIS # G1: 4,9 => CTR => G1: 5 * DIS # I2: 5 => CTR => I2: 1,3 * PRF # H4: 1,3 => SOL * DIS # C6: 5,6 => CTR => C6: 8 * DIS # E5: 5,6 => CTR => E5: 2,4 * PRF # I4: 3,5 => SOL * DIS # I5: 3,5 => CTR => I5: 4,9 * DIS # G2: 3,5 => CTR => G2: 4,9 * DIS # G3: 3,5 => CTR => G3: 4,9 * PRF # H5: 2,6 => SOL * DIS # E6: 2,6 => CTR => E6: 1,4,5 * PRF # E6: 1,4,5 => SOL * DIS # I5: 4,5 => CTR => I5: 3,9 * PRF # E6: 4,5 => SOL * DIS # E6: 1,2,6 => CTR => E6: 4,5 * DIS # C3: 2,9 => CTR => C3: 4 * PRF # C3: 4 => SOL * PRF # F7: 2,9 => SOL * DIS # F7: 6 => CTR => F7: 2,9 * PRF # F7: 2,6 => SOL * DIS # F7: 9 => CTR => F7: 2,6 * DIS # E5: 2,6 => CTR => E5: 4,5 * DIS # E6: 2,6 => CTR => E6: 1,4,5 * PRF # E6: 1,4,5 => SOL * PRF # H5: 2,6 => SOL * DIS # I5: 4,5 => CTR => I5: 3,9 * CNT 27 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C3: 2 => CTR => C3: 4,9 * DIS C3: 4,9 # G1: 4,9 => CTR => G1: 5 * DIS C3: 4,9 + G1: 5 # E5: 5,6 => CTR => E5: 2,4 * PRF C3: 4,9 + G1: 5 + E5: 2,4 # F7: 2,9 => SOL * STA C3: 4,9 + G1: 5 + E5: 2,4 + F7: 2,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......72.8.6......1.......4...97.........8..3........7.3....4....18.6.....5..... | initial |
| 63.....72.876......1.7...8642..97...17....8..39....7..753...148.4.1836578615742.. | autosolve |
| 639418572587629431214735986426897315175346829398251764753962148942183657861574293 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) C1: 4,9 F1: 1,8 H2: 1,3 C5: 5,6 D4: 3,8 F6: 1,8 G4: 3,5 H6: 2,6 I6: 4,5 A8: 2,9 C8: 2,9 D7: 2,9 E7: 2,6 H9: 3,9 I9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,F1: 1.. / E1 = 1 => 19 pairs (_) / F1 = 1 => 0 pairs (X) H2,I2: 1.. / H2 = 1 => 16 pairs (_) / I2 = 1 => 0 pairs (*) E6,F6: 1.. / E6 = 1 => 0 pairs (X) / F6 = 1 => 19 pairs (_) H4,I4: 1.. / H4 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) E1,E6: 1.. / E1 = 1 => 19 pairs (_) / E6 = 1 => 0 pairs (X) F1,F6: 1.. / F1 = 1 => 0 pairs (X) / F6 = 1 => 19 pairs (_) H2,H4: 1.. / H2 = 1 => 16 pairs (_) / H4 = 1 => 0 pairs (*) I2,I4: 1.. / I2 = 1 => 0 pairs (*) / I4 = 1 => 0 pairs (X) H5,H6: 2.. / H5 = 2 => 0 pairs (*) / H6 = 2 => 0 pairs (X) A8,C8: 2.. / A8 = 2 => 0 pairs (X) / C8 = 2 => 16 pairs (_) C3,C8: 2.. / C3 = 2 => 0 pairs (X) / C8 = 2 => 16 pairs (_) E2,E3: 3.. / E2 = 3 => 0 pairs (X) / E3 = 3 => 15 pairs (_) D4,D5: 3.. / D4 = 3 => 0 pairs (X) / D5 = 3 => 19 pairs (_) H9,I9: 3.. / H9 = 3 => 14 pairs (_) / I9 = 3 => 16 pairs (_) E3,G3: 3.. / E3 = 3 => 15 pairs (_) / G3 = 3 => 0 pairs (X) C1,C3: 4.. / C1 = 4 => 0 pairs (X) / C3 = 4 => 0 pairs (_) I5,I6: 4.. / I5 = 4 => 0 pairs (X) / I6 = 4 => 15 pairs (_) E2,G2: 4.. / E2 = 4 => 0 pairs (X) / G2 = 4 => 16 pairs (_) A2,A3: 5.. / A2 = 5 => 23 pairs (_) / A3 = 5 => 17 pairs (_) E1,G1: 5.. / E1 = 5 => 0 pairs (X) / G1 = 5 => 19 pairs (_) E7,F7: 6.. / E7 = 6 => 0 pairs (*) / F7 = 6 => 0 pairs (X) C4,H4: 6.. / C4 = 6 => 0 pairs (*) / H4 = 6 => 0 pairs (X) F5,F7: 6.. / F5 = 6 => 0 pairs (*) / F7 = 6 => 0 pairs (X) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 19 pairs (_) C4,C6: 8.. / C4 = 8 => 0 pairs (X) / C6 = 8 => 19 pairs (_) C4,D4: 8.. / C4 = 8 => 0 pairs (X) / D4 = 8 => 19 pairs (_) F1,F6: 8.. / F1 = 8 => 19 pairs (_) / F6 = 8 => 0 pairs (X) H5,I5: 9.. / H5 = 9 => 14 pairs (_) / I5 = 9 => 16 pairs (_) A8,C8: 9.. / A8 = 9 => 16 pairs (_) / C8 = 9 => 0 pairs (X) D7,F7: 9.. / D7 = 9 => 0 pairs (*) / F7 = 9 => 0 pairs (X) H9,I9: 9.. / H9 = 9 => 16 pairs (_) / I9 = 9 => 14 pairs (_) D1,D7: 9.. / D1 = 9 => 0 pairs (X) / D7 = 9 => 0 pairs (_) H5,H9: 9.. / H5 = 9 => 14 pairs (_) / H9 = 9 => 16 pairs (_) I5,I9: 9.. / I5 = 9 => 16 pairs (_) / I9 = 9 => 14 pairs (_) * DURATION: 0:00:58.932219 START: 19:35:08.389572 END: 19:36:07.321791 2017-05-04 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C1,C5,C8,D4,D7,E7,F1,F6,G4,H2,H6,H9,I6,I9) * 63.....72.876......1.7...8642..97...17....8..39....7..753...148.4.1836578615742.. * PAIR C1: 4,9 BLK 1 C3: 4,9,2 # reduction candidate for 4,9 C3: 2 => CTR * 6349.85725876.2913912735486425897361176.2.8..39....72.7532691482491836578615742.. C3: 4,9 # 16 pairs * PAIR C1: 4,9 ROW 1 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 # 19 pairs G1: 4,9,5 # reduction candidate for 4,9 G1: 4,9 => CTR * 63.851.72.876......1.7...86428397561176..58..39..187..753..6148.4.1836578615742.. G1: 5 # 19 pairs * PAIR H2: 1,3 BLK 3 I2: 1,3,5 # reduction candidate for 1,3 I2: 5 => CTR * 63..51.72.876...1551.7...86428397561176..58..395...7.4753..6148.4.1836578615742.. I2: 1,3 # 19 pairs * PAIR H2: 1,3 COL H H4: 1,3,6 # reduction candidate for 1,3 H4: 1,3 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 H4: 6 # 17 pairs * PAIR C5: 5,6 BLK 4 C4: 5,6,8 # reduction candidate for 5,6 C4: 5,6 # 19 pairs C6: 5,6,8 # reduction candidate for 5,6 C6: 5,6 => CTR * 63..51.72.876...1551.7...8642839756117...58..3958..724753...148.4.1836578615742.. C6: 8 # 19 pairs * PAIR C5: 5,6 ROW 5 E5: 5,6,2,4 # reduction candidate for 5,6 E5: 5,6 => CTR * 63.....72.876...1..1.7...8642..97.6117...28..39....72.75326.148.4.1836578615742.. E5: 2,4 # 24 pairs F5: 5,6,2 # reduction candidate for 5,6 F5: 5,6 # 24 pairs * PAIR G4: 3,5 BLK 6 I4: 3,5,1 # reduction candidate for 3,5 I4: 3,5 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 I4: 1 # 16 pairs I5: 3,5,4,9 # reduction candidate for 3,5 I5: 3,5 => CTR * 63..18572.876...13.1.73..8642..97.6117....89.39.8.1724753...148.4.183657861574239 I5: 4,9 # 16 pairs * PAIR G4: 3,5 COL G G2: 3,5,4,9 # reduction candidate for 3,5 G2: 3,5 => CTR * 63.851.72.8764.....1.73..8642..97...17....8..39....7..753...148.4.1836578615742.. G2: 4,9 # 16 pairs G3: 3,5,4,9 # reduction candidate for 3,5 G3: 3,5 => CTR * 63.851.72.876......1.7...8642839756117...58..395...7..753...148.4.1836578615742.. G3: 4,9 # 16 pairs * PAIR H6: 2,6 BLK 6 H5: 2,6,3,9 # reduction candidate for 2,6 H5: 2,6 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 H5: 3,9 # 17 pairs * PAIR H6: 2,6 ROW 6 E6: 2,6,1,4,5 # reduction candidate for 2,6 E6: 2,6 => CTR * 63..18572.876......1.73..864258973611763..8.43984617257532..148.4.1836578615742.. E6: 1,4,5 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 * PAIR I6: 4,5 BLK 6 I5: 4,5,3,9 # reduction candidate for 4,5 I5: 4,5 => CTR * 63.9.8.72.876...13.1.73..8642.89736117.3.689.39....72.753269148.4.183657861574239 I5: 3,9 # 19 pairs * PAIR I6: 4,5 ROW 6 E6: 4,5,1,2,6 # reduction candidate for 4,5 E6: 4,5 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 E6: 1,2,6 => CTR * 63..18572.876......1.7...8642..97361176...8..39..6172.753.26148.4.1836578615742.. * PAIR A8: 2,9 COL A A2: 2,9,5 # reduction candidate for 2,9 A2: 2,9 # 17 pairs A3: 2,9,5 # reduction candidate for 2,9 A3: 2,9 # 23 pairs * PAIR C8: 2,9 COL C C3: 2,9,4 # reduction candidate for 2,9 C3: 2,9 => CTR * 6349.8572.876..913.1.73.486425897361176...8..39....72.753269148.4.1836578615742.. C3: 4 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 * PAIR D7: 2,9 BLK 8 F7: 2,9,6 # reduction candidate for 2,9 F7: 2,9 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 F7: 6 => CTR * 63.418572.876..4...147..98642..9736.176.458..39..61724753926148.4.1836578615742.. * PAIR E7: 2,6 BLK 8 F7: 2,6,9 # reduction candidate for 2,6 F7: 2,6 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 F7: 9 => CTR * 634918572.876......1.7...8642..973.5175..68..39..517.4753269148.4.1836578615742.. * PAIR E7: 2,6 COL E E5: 2,6,4,5 # reduction candidate for 2,6 E5: 2,6 => CTR * 63.9.8.72.876...1..1.7...8642839756117542.8..396...72.753269148.4.1836578615742.. E5: 4,5 # 16 pairs E6: 2,6,1,4,5 # reduction candidate for 2,6 E6: 2,6 => CTR * 63..18572.876......1.73..864258973611763..8.43984617257532..148.4.1836578615742.. E6: 1,4,5 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 * PAIR H9: 3,9 COL H H5: 3,9,2,6 # reduction candidate for 3,9 H5: 2,6 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 H5: 3,9 # 17 pairs * PAIR I9: 3,9 COL I I5: 3,9,4,5 # reduction candidate for 3,9 I5: 4,5 => CTR * 63.9.8.72.876...13.1.73..8642.89736117.3.689.39....72.753269148.4.183657861574239 I5: 3,9 # 19 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-495-base-pr-000.dot * REASONING * DIS # C3: 2 => CTR => C3: 4,9 * DIS # G1: 4,9 => CTR => G1: 5 * DIS # I2: 5 => CTR => I2: 1,3 * PRF # H4: 1,3 => SOL * DIS # C6: 5,6 => CTR => C6: 8 * DIS # E5: 5,6 => CTR => E5: 2,4 * PRF # I4: 3,5 => SOL * DIS # I5: 3,5 => CTR => I5: 4,9 * DIS # G2: 3,5 => CTR => G2: 4,9 * DIS # G3: 3,5 => CTR => G3: 4,9 * PRF # H5: 2,6 => SOL * DIS # E6: 2,6 => CTR => E6: 1,4,5 * PRF # E6: 1,4,5 => SOL * DIS # I5: 4,5 => CTR => I5: 3,9 * PRF # E6: 4,5 => SOL * DIS # E6: 1,2,6 => CTR => E6: 4,5 * DIS # C3: 2,9 => CTR => C3: 4 * PRF # C3: 4 => SOL * PRF # F7: 2,9 => SOL * DIS # F7: 6 => CTR => F7: 2,9 * PRF # F7: 2,6 => SOL * DIS # F7: 9 => CTR => F7: 2,6 * DIS # E5: 2,6 => CTR => E5: 4,5 * DIS # E6: 2,6 => CTR => E6: 1,4,5 * PRF # E6: 1,4,5 => SOL * PRF # H5: 2,6 => SOL * DIS # I5: 4,5 => CTR => I5: 3,9 * CNT 27 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,C1,C5,C8,D4,D7,E7,F1,F6,G4,H2,H6,H9,I6,I9) * 63.....72.876......1.7...8642..97...17....8..39....7..753...148.4.1836578615742.. * PAIR C1: 4,9 BLK 1 C3: 4,9,2 # reduction candidate for 4,9 C3: 2 => CTR * 6349.85725876.2913912735486425897361176.2.8..39....72.7532691482491836578615742.. * PAIR C1: 4,9 ROW 1 D1: 4,9,8 # reduction candidate for 4,9 D1: 4,9 # 21 pairs G1: 4,9,5 # reduction candidate for 4,9 G1: 4,9 => CTR * 63.851.72.876......1.7...86428397561176..58..39..187..753..61489421836578615742.. * RESTART * PAIR RESTART * PAIR C5: 5,6 ROW 5 E5: 5,6,2,4 # reduction candidate for 5,6 E5: 5,6 => CTR * 63..18572.876....3.1.73..864258973611763528943984617.5753...1489421836578615742.9 * RESTART * PAIR RESTART * PAIR D7: 2,9 BLK 8 F7: 2,9,6 # reduction candidate for 2,9 F7: 2,9 => SOLVED * 639418572587629431214735986426897315175346829398251764753962148942183657861574293 * DURATION: 0:00:08.947809 START: 19:36:58.672478 END: 19:37:07.620287 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-495-base-pr-001.dot * REASONING * DIS # C3: 2 => CTR => C3: 4,9 * DIS C3: 4,9 # G1: 4,9 => CTR => G1: 5 * DIS C3: 4,9 + G1: 5 # E5: 5,6 => CTR => E5: 2,4 * PRF C3: 4,9 + G1: 5 + E5: 2,4 # F7: 2,9 => SOL * STA C3: 4,9 + G1: 5 + E5: 2,4 + F7: 2,9 * CNT 4 HDP CHAINS / 6 HYP OPENED
Header Info
Top 500 Minimum 17 495 solution: 639418572587629431214735986426897315175346829398251764753962148942183657861574293 info: 96454 FNBHYK S8.f 626 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 639418572587629431214735986426897315175346829398251764753962148942183657861574293 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:
* INC # C3: 4,9 => UNS * DIS # C3: 2 => CTR => C3: 4,9 * INC # D1: 4,9 => UNS * DIS # G1: 4,9 => CTR => G1: 5 * INC # G1: 5 => UNS * INC # I2: 1,3 => UNS * DIS # I2: 5 => CTR => I2: 1,3 * PRF # H4: 1,3 => SOL * INC # H4: 6 => UNS * INC # C4: 5,6 => UNS * DIS # C6: 5,6 => CTR => C6: 8 * INC # C6: 8 => UNS * DIS # E5: 5,6 => CTR => E5: 2,4 * INC # E5: 2,4 => UNS * INC # F5: 5,6 => UNS * PRF # I4: 3,5 => SOL * INC # I4: 1 => UNS * DIS # I5: 3,5 => CTR => I5: 4,9 * INC # I5: 4,9 => UNS * DIS # G2: 3,5 => CTR => G2: 4,9 * INC # G2: 4,9 => UNS * DIS # G3: 3,5 => CTR => G3: 4,9 * INC # G3: 4,9 => UNS * PRF # H5: 2,6 => SOL * INC # H5: 3,9 => UNS * DIS # E6: 2,6 => CTR => E6: 1,4,5 * PRF # E6: 1,4,5 => SOL * DIS # I5: 4,5 => CTR => I5: 3,9 * INC # I5: 3,9 => UNS * PRF # E6: 4,5 => SOL * DIS # E6: 1,2,6 => CTR => E6: 4,5 * INC # A2: 2,9 => UNS * INC # A3: 2,9 => UNS * DIS # C3: 2,9 => CTR => C3: 4 * PRF # C3: 4 => SOL * PRF # F7: 2,9 => SOL * DIS # F7: 6 => CTR => F7: 2,9 * PRF # F7: 2,6 => SOL * DIS # F7: 9 => CTR => F7: 2,6 * DIS # E5: 2,6 => CTR => E5: 4,5 * INC # E5: 4,5 => UNS * DIS # E6: 2,6 => CTR => E6: 1,4,5 * PRF # E6: 1,4,5 => SOL * INC # H5: 3,9 => UNS * PRF # H5: 2,6 => SOL * INC # I5: 3,9 => UNS * DIS # I5: 4,5 => CTR => I5: 3,9 * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C3: 4,9 => UNS * DIS # C3: 2 => CTR => C3: 4,9 * INC C3: 4,9 # D1: 4,9 => UNS * DIS C3: 4,9 # G1: 4,9 => CTR => G1: 5 * DIS C3: 4,9 + G1: 5 # E5: 5,6 => CTR => E5: 2,4 * PRF C3: 4,9 + G1: 5 + E5: 2,4 # F7: 2,9 => SOL * STA C3: 4,9 + G1: 5 + E5: 2,4 + F7: 2,9 * CNT 6 HDP CHAINS / 6 HYP OPENED