Analysis of xx-top500-423-base.sdk
Contents
Original Sudoku
level: medium
position: .......31.28..................2.84..73.....6....5.....16..7.......4..2..3........ initial
Autosolve
position: .76....31.28.......13....286912384..735...862284567...16..7....85.4..2..34....... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E2: 5,9 => CTR => E2: 1 * PRF # E2: 1 => SOL * PRF # G2: 5,9 => SOL * DIS # H2: 5,9 => CTR => H2: 4,7 * DIS # I2: 5,9 => CTR => I2: 4,6,7 * DIS # D9: 8,9 => CTR => D9: 1,6 * PRF # G2: 5,9 => SOL * DIS # H2: 5,9 => CTR => H2: 4,7 * DIS # I2: 5,9 => CTR => I2: 4,6,7 * DIS # G3: 5,9 => CTR => G3: 6,7 * DIS # G7: 5,9 => CTR => G7: 3 * DIS # G9: 5,9 => CTR => G9: 1,6,7 * DIS # E5: 1,9 => CTR => E5: 4 * DIS # D2: 1,9 => CTR => D2: 3,6,7 * DIS # D9: 1,9 => CTR => D9: 6,8 * PRF # H2: 5,7 => SOL * DIS # G6: 3 => CTR => G6: 1,9 * DIS # H9: 1,9 => CTR => H9: 5,7,8 * DIS # G6: 3,9 => CTR => G6: 1 * DIS # C9: 7 => CTR => C9: 2,9 * DIS # C9: 2 => CTR => C9: 7,9 * DIS # H8: 7,9 => CTR => H8: 1 * PRF # H8: 1 => SOL * DIS # D9: 1,9 => CTR => D9: 6,8 * DIS # H8: 7 => CTR => H8: 1,9 * DIS # E5: 1,9 => CTR => E5: 4 * PRF # F2: 3,6 => SOL * DIS # F2: 1,9 => CTR => F2: 3,6 * CNT 28 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E2: 5,9 => CTR => E2: 1 * PRF E2: 1 => SOL * STA E2: 1 * CNT 2 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .......31.28..................2.84..73.....6....5.....16..7.......4..2..3........ | initial |
| .76....31.28.......13....286912384..735...862284567...16..7....85.4..2..34....... | autosolve |
| 476982531528316974913754628691238457735149862284567193162875349857493216349621785 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) A2: 5,9 D1: 8,9 E1: 2,8 G1: 5,9 D5: 1,9 H4: 5,7 I4: 5,7 H6: 1,9 I6: 3,9 C7: 2,9 C8: 7,9 E8: 1,9 F8: 3,6 E9: 2,8 I8: 3,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G6,H6: 1.. / G6 = 1 => 14 pairs (_) / H6 = 1 => 0 pairs (X) E8,H8: 1.. / E8 = 1 => 0 pairs (X) / H8 = 1 => 0 pairs (_) G6,G9: 1.. / G6 = 1 => 14 pairs (_) / G9 = 1 => 0 pairs (X) E1,F1: 2.. / E1 = 2 => 16 pairs (_) / F1 = 2 => 20 pairs (_) C7,C9: 2.. / C7 = 2 => 15 pairs (_) / C9 = 2 => 0 pairs (X) C7,F7: 2.. / C7 = 2 => 15 pairs (_) / F7 = 2 => 0 pairs (X) E1,E9: 2.. / E1 = 2 => 16 pairs (_) / E9 = 2 => 20 pairs (_) D2,F2: 3.. / D2 = 3 => 15 pairs (_) / F2 = 3 => 0 pairs (X) G6,I6: 3.. / G6 = 3 => 0 pairs (X) / I6 = 3 => 15 pairs (_) F8,I8: 3.. / F8 = 3 => 15 pairs (_) / I8 = 3 => 0 pairs (X) D2,D7: 3.. / D2 = 3 => 15 pairs (_) / D7 = 3 => 0 pairs (X) G6,G7: 3.. / G6 = 3 => 0 pairs (X) / G7 = 3 => 15 pairs (_) A1,A3: 4.. / A1 = 4 => 21 pairs (_) / A3 = 4 => 19 pairs (_) H2,I2: 4.. / H2 = 4 => 15 pairs (_) / I2 = 4 => 20 pairs (_) E5,F5: 4.. / E5 = 4 => 17 pairs (_) / F5 = 4 => 0 pairs (X) H7,I7: 4.. / H7 = 4 => 20 pairs (_) / I7 = 4 => 15 pairs (_) A1,F1: 4.. / A1 = 4 => 21 pairs (_) / F1 = 4 => 19 pairs (_) E3,E5: 4.. / E3 = 4 => 0 pairs (X) / E5 = 4 => 17 pairs (_) H2,H7: 4.. / H2 = 4 => 15 pairs (_) / H7 = 4 => 20 pairs (_) I2,I7: 4.. / I2 = 4 => 20 pairs (_) / I7 = 4 => 15 pairs (_) E2,E3: 5.. / E2 = 5 => 0 pairs (X) / E3 = 5 => 18 pairs (_) H4,I4: 5.. / H4 = 5 => 13 pairs (_) / I4 = 5 => 16 pairs (_) F7,F9: 5.. / F7 = 5 => 16 pairs (_) / F9 = 5 => 15 pairs (_) A1,G1: 5.. / A1 = 5 => 19 pairs (_) / G1 = 5 => 16 pairs (_) F8,I8: 6.. / F8 = 6 => 0 pairs (X) / I8 = 6 => 15 pairs (_) D2,D3: 7.. / D2 = 7 => 0 pairs (X) / D3 = 7 => 15 pairs (_) H4,I4: 7.. / H4 = 7 => 16 pairs (_) / I4 = 7 => 13 pairs (_) C8,C9: 7.. / C8 = 7 => 16 pairs (_) / C9 = 7 => 0 pairs (X) D3,G3: 7.. / D3 = 7 => 15 pairs (_) / G3 = 7 => 0 pairs (X) C8,H8: 7.. / C8 = 7 => 16 pairs (_) / H8 = 7 => 0 pairs (X) D1,E1: 8.. / D1 = 8 => 16 pairs (_) / E1 = 8 => 20 pairs (_) H7,H9: 8.. / H7 = 8 => 16 pairs (_) / H9 = 8 => 18 pairs (_) D7,H7: 8.. / D7 = 8 => 18 pairs (_) / H7 = 8 => 16 pairs (_) E1,E9: 8.. / E1 = 8 => 20 pairs (_) / E9 = 8 => 16 pairs (_) * DURATION: 0:00:59.451157 START: 17:15:10.266439 END: 17:16:09.717596 2017-05-04 * CP COUNT: (34) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C7,C8,D1,D5,E1,E8,E9,F8,G1,H4,H6,I4,I6,I8) * .76....31.28.......13....286912384..735...862284567...16..7....85.4..2..34....... * PAIR A2: 5,9 BLK 1 A1: 5,9,4 # reduction candidate for 5,9 A1: 5,9 # 19 pairs A3: 5,9,4 # reduction candidate for 5,9 A3: 5,9 # 21 pairs * PAIR A2: 5,9 ROW 2 E2: 5,9,1 # reduction candidate for 5,9 E2: 5,9 => CTR * .76....31.283.16...137.6.286912384..7351..862284567...16..7....85.4132.634.6..71. E2: 1 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 G2: 5,9,6,7 # reduction candidate for 5,9 G2: 5,9 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 G2: 6,7 # 16 pairs H2: 5,9,4,7 # reduction candidate for 5,9 H2: 5,9 => CTR * 476982531.283..794913754628691238457735149862284567.1.16287..4.85.4..2..34..2..8. H2: 4,7 # 16 pairs I2: 5,9,4,6,7 # reduction candidate for 5,9 I2: 5,9 => CTR * .76....31.2831674..1375.6286912384..73514986228456719316987.3.485749321634.6.1... I2: 4,6,7 # 15 pairs * PAIR D1: 8,9 COL D D7: 8,9,3 # reduction candidate for 8,9 D7: 8,9 # 15 pairs D9: 8,9,1,6 # reduction candidate for 8,9 D9: 8,9 => CTR * .76....31.28.13....13.5..286912384..735149862284567...16.37..8485.49621334.821... D9: 1,6 # 16 pairs * PAIR G1: 5,9 BLK 3 G2: 5,9,6,7 # reduction candidate for 5,9 G2: 5,9 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 G2: 6,7 # 16 pairs H2: 5,9,4,7 # reduction candidate for 5,9 H2: 5,9 => CTR * 476982531.283..794913754628691238457735149862284567.1.16287..4.85.4..2..34..2..8. H2: 4,7 # 16 pairs I2: 5,9,4,6,7 # reduction candidate for 5,9 I2: 5,9 => CTR * .76....31.2831674..1375.6286912384..73514986228456719316987.3.485749321634.6.1... I2: 4,6,7 # 15 pairs G3: 5,9,6,7 # reduction candidate for 5,9 G3: 5,9 => CTR * .769...31.283..6...137.6.286912384..7351..86228456719316..7.3..85749321634.6.17.. G3: 6,7 # 16 pairs * PAIR G1: 5,9 ROW 1 A1: 5,9,4 # reduction candidate for 5,9 A1: 4 # 21 pairs A1: 5,9 # 19 pairs * PAIR G1: 5,9 COL G G7: 5,9,3 # reduction candidate for 5,9 G7: 5,9 => CTR * .76....31.28.......13....286912384..735...86228456731916..7....85.41.2..34....1.. G7: 3 # 15 pairs G9: 5,9,1,6,7 # reduction candidate for 5,9 G9: 5,9 => CTR * .76982531.283167...1375.6286912384..73514986228456719316..753..85.49321634.621.87 G9: 1,6,7 # 15 pairs * PAIR D5: 1,9 BLK 5 E5: 1,9,4 # reduction candidate for 1,9 E5: 1,9 => CTR * 476...5319283516..5137469286912384..735..486228456719316..7.3..85.4.32.634.6..71. E5: 4 # 17 pairs F5: 1,9,4 # reduction candidate for 1,9 F5: 1,9 # 17 pairs * PAIR D5: 1,9 COL D D2: 1,9,3,6,7 # reduction candidate for 1,9 D2: 1,9 => CTR * .76....31.28..3....137.6.286912384..735...862284567...16..7....85.4..2..34....... D2: 3,6,7 # 15 pairs D9: 1,9,6,8 # reduction candidate for 1,9 D9: 1,9 => CTR * .7682..31.28.13....13.5..286912384..735.41862284567...16.37..8485.49621334.18.... D9: 6,8 # 16 pairs * PAIR H4: 5,7 COL H H2: 5,7,4,9 # reduction candidate for 5,7 H2: 5,7 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 H2: 4,9 # 16 pairs H9: 5,7,1,8,9 # reduction candidate for 5,7 H9: 5,7 # 18 pairs * PAIR I4: 5,7 COL I I2: 5,7,4,6,9 # reduction candidate for 5,7 I2: 5,7 # 19 pairs I9: 5,7,6,9 # reduction candidate for 5,7 I9: 5,7 # 16 pairs * PAIR H6: 1,9 BLK 6 G6: 1,9,3 # reduction candidate for 1,9 G6: 3 => CTR * .76....31.28.......13....286912384..735...86228456731916..7....85.41.2..34....1.. G6: 1,9 # 15 pairs * PAIR H6: 1,9 COL H H8: 1,9,7 # reduction candidate for 1,9 H8: 1,9 # 16 pairs H9: 1,9,5,7,8 # reduction candidate for 1,9 H9: 1,9 => CTR * .76....31.28...746.137.6.28691238457735...862284567...162.7..8485941327.347...... H9: 5,7,8 # 15 pairs * PAIR I6: 3,9 BLK 6 G6: 3,9,1 # reduction candidate for 3,9 G6: 3,9 => CTR * .76....31.28.......13....286912384..735...862284567.1.16..7....85.41.2..34....1.. G6: 1 # 14 pairs * PAIR I6: 3,9 COL I I7: 3,9,4,5 # reduction candidate for 3,9 I7: 3,9 # 20 pairs I7: 4,5 # 16 pairs * PAIR C7: 2,9 BLK 7 C9: 2,9,7 # reduction candidate for 2,9 C9: 7 => CTR * .76....31.28...746.137.6.28691238457735...862284567...162.7...485941327.347...... C9: 2,9 # 16 pairs * PAIR C7: 2,9 ROW 7 F7: 2,9,3,5 # reduction candidate for 2,9 F7: 2,9 # 18 pairs F7: 3,5 # 16 pairs * PAIR C8: 7,9 BLK 7 C9: 7,9,2 # reduction candidate for 7,9 C9: 2 => CTR * 576824931928..3.45413.59.28691238457735.418622845673191693725848574.62.3342.85... C9: 7,9 # 15 pairs * PAIR C8: 7,9 ROW 8 H8: 7,9,1 # reduction candidate for 7,9 H8: 7,9 => CTR * .76....31.283.16...137.6.286912384..7351..862284567...16..7....85.4132.634.6..71. H8: 1 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 * PAIR E8: 1,9 BLK 8 D9: 1,9,6,8 # reduction candidate for 1,9 D9: 1,9 => CTR * .7682..31.28.13....13.5..286912384..735.41862284567...16.37..8485.49621334.18.... D9: 6,8 # 16 pairs F9: 1,9,2,5,6 # reduction candidate for 1,9 F9: 1,9 # 22 pairs * PAIR E8: 1,9 ROW 8 H8: 1,9,7 # reduction candidate for 1,9 H8: 7 => CTR * .76....31.28...746.137.6.28691238457735...862284567...162.7...485941327.347...... H8: 1,9 # 16 pairs * PAIR E8: 1,9 COL E E2: 1,9,5 # reduction candidate for 1,9 E2: 1,9 # 18 pairs E5: 1,9,4 # reduction candidate for 1,9 E5: 1,9 => CTR * 476...5319283516..5137469286912384..735..486228456719316..7.3..85.4.32.634.6..71. E5: 4 # 17 pairs * PAIR F8: 3,6 COL F F2: 3,6,1,9 # reduction candidate for 3,6 F2: 3,6 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 F2: 1,9 => CTR * .769...31.283..6...137.6.286912384..7351..86228456719316..7.3..85749321634.6.17.. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-423-base-pr-000.dot * REASONING * DIS # E2: 5,9 => CTR => E2: 1 * PRF # E2: 1 => SOL * PRF # G2: 5,9 => SOL * DIS # H2: 5,9 => CTR => H2: 4,7 * DIS # I2: 5,9 => CTR => I2: 4,6,7 * DIS # D9: 8,9 => CTR => D9: 1,6 * PRF # G2: 5,9 => SOL * DIS # H2: 5,9 => CTR => H2: 4,7 * DIS # I2: 5,9 => CTR => I2: 4,6,7 * DIS # G3: 5,9 => CTR => G3: 6,7 * DIS # G7: 5,9 => CTR => G7: 3 * DIS # G9: 5,9 => CTR => G9: 1,6,7 * DIS # E5: 1,9 => CTR => E5: 4 * DIS # D2: 1,9 => CTR => D2: 3,6,7 * DIS # D9: 1,9 => CTR => D9: 6,8 * PRF # H2: 5,7 => SOL * DIS # G6: 3 => CTR => G6: 1,9 * DIS # H9: 1,9 => CTR => H9: 5,7,8 * DIS # G6: 3,9 => CTR => G6: 1 * DIS # C9: 7 => CTR => C9: 2,9 * DIS # C9: 2 => CTR => C9: 7,9 * DIS # H8: 7,9 => CTR => H8: 1 * PRF # H8: 1 => SOL * DIS # D9: 1,9 => CTR => D9: 6,8 * DIS # H8: 7 => CTR => H8: 1,9 * DIS # E5: 1,9 => CTR => E5: 4 * PRF # F2: 3,6 => SOL * DIS # F2: 1,9 => CTR => F2: 3,6 * CNT 28 HDP CHAINS / 66 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,C7,C8,D1,D5,E1,E8,E9,F8,G1,H4,H6,I4,I6,I8) * .76....31.28.......13....286912384..735...862284567...16..7....85.4..2..34....... * PAIR A2: 5,9 BLK 1 A1: 5,9,4 # reduction candidate for 5,9 A1: 5,9 # 19 pairs A3: 5,9,4 # reduction candidate for 5,9 A3: 5,9 # 21 pairs * PAIR A2: 5,9 ROW 2 E2: 5,9,1 # reduction candidate for 5,9 E2: 5,9 => CTR * .76....31.283.16...137.6.286912384..7351..862284567...16..7....85.4132.634.6..71. E2: 1 => SOLVED * 476982531528316974913754628691238457735149862284567193162875349857493216349621785 * DURATION: 0:00:03.808163 START: 17:17:13.477356 END: 17:17:17.285519 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-423-base-pr-001.dot * REASONING * DIS # E2: 5,9 => CTR => E2: 1 * PRF E2: 1 => SOL * STA E2: 1 * CNT 2 HDP CHAINS / 3 HYP OPENED
Header Info
Top 500 Minimum 17 423 solution: 476982531528316974913754628691238457735149862284567193162875349857493216349621785 info: 95136 FNBHYK S8.f 210 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 476982531528316974913754628691238457735149862284567193162875349857493216349621785 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 # A1: 5,9 => UNS * INC # A3: 5,9 => UNS * DIS # E2: 5,9 => CTR => E2: 1 * PRF # E2: 1 => SOL * PRF # G2: 5,9 => SOL * INC # G2: 6,7 => UNS * DIS # H2: 5,9 => CTR => H2: 4,7 * INC # H2: 4,7 => UNS * DIS # I2: 5,9 => CTR => I2: 4,6,7 * INC # I2: 4,6,7 => UNS * INC # D7: 8,9 => UNS * DIS # D9: 8,9 => CTR => D9: 1,6 * INC # D9: 1,6 => UNS * PRF # G2: 5,9 => SOL * INC # G2: 6,7 => UNS * DIS # H2: 5,9 => CTR => H2: 4,7 * INC # H2: 4,7 => UNS * DIS # I2: 5,9 => CTR => I2: 4,6,7 * INC # I2: 4,6,7 => UNS * DIS # G3: 5,9 => CTR => G3: 6,7 * INC # G3: 6,7 => UNS * INC # A1: 5,9 => UNS * INC # A1: 4 => UNS * DIS # G7: 5,9 => CTR => G7: 3 * INC # G7: 3 => UNS * DIS # G9: 5,9 => CTR => G9: 1,6,7 * INC # G9: 1,6,7 => UNS * DIS # E5: 1,9 => CTR => E5: 4 * INC # E5: 4 => UNS * INC # F5: 1,9 => UNS * DIS # D2: 1,9 => CTR => D2: 3,6,7 * INC # D2: 3,6,7 => UNS * DIS # D9: 1,9 => CTR => D9: 6,8 * INC # D9: 6,8 => UNS * PRF # H2: 5,7 => SOL * INC # H2: 4,9 => UNS * INC # H9: 5,7 => UNS * INC # I2: 5,7 => UNS * INC # I9: 5,7 => UNS * INC # G6: 1,9 => UNS * DIS # G6: 3 => CTR => G6: 1,9 * INC # H8: 1,9 => UNS * DIS # H9: 1,9 => CTR => H9: 5,7,8 * INC # H9: 5,7,8 => UNS * DIS # G6: 3,9 => CTR => G6: 1 * INC # G6: 1 => UNS * INC # I7: 3,9 => UNS * INC # I7: 4,5 => UNS * INC # C9: 2,9 => UNS * DIS # C9: 7 => CTR => C9: 2,9 * INC # F7: 2,9 => UNS * INC # F7: 3,5 => UNS * INC # C9: 7,9 => UNS * DIS # C9: 2 => CTR => C9: 7,9 * DIS # H8: 7,9 => CTR => H8: 1 * PRF # H8: 1 => SOL * DIS # D9: 1,9 => CTR => D9: 6,8 * INC # D9: 6,8 => UNS * INC # F9: 1,9 => UNS * INC # H8: 1,9 => UNS * DIS # H8: 7 => CTR => H8: 1,9 * INC # E2: 1,9 => UNS * DIS # E5: 1,9 => CTR => E5: 4 * INC # E5: 4 => UNS * PRF # F2: 3,6 => SOL * DIS # F2: 1,9 => CTR => F2: 3,6 * CNT 66 HDP CHAINS / 66 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,9 => UNS * INC # A3: 5,9 => UNS * DIS # E2: 5,9 => CTR => E2: 1 * PRF E2: 1 => SOL * STA E2: 1 * CNT 4 HDP CHAINS / 3 HYP OPENED