Analysis of xx-top500-393-base.sdk
Contents
Original Sudoku
level: medium
position: 8.......14..6........3......6.....3.1...8..........6...58....7..1..2.......4..9.. initial
Autosolve
position: 8.......14..6........3......6.....3.143.86....8....6...58....7..1482.......4..9.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # A9: 2,7 => CTR => A9: 3,6 * DIS # C9: 2,7 => CTR => C9: 6 * DIS # B1: 2,7 => CTR => B1: 3,9 * DIS # E7: 1,9 => CTR => E7: 3,6 * DIS # F7: 1,9 => CTR => F7: 3 * DIS # G7: 2,4 => CTR => G7: 1 * PRF # G7: 1 => SOL * DIS # I3: 2,4 => CTR => I3: 5,6,7,8,9 * DIS # I4: 2,4 => CTR => I4: 5,7,8,9 * DIS # I6: 2,4 => CTR => I6: 5,7,9 * DIS # I8: 3,5 => CTR => I8: 6 * DIS # I8: 3 => CTR => I8: 5,6 * DIS # H3: 5,6 => CTR => H3: 2,4,8,9 * PRF # H9: 2,8 => SOL * DIS # H9: 1 => CTR => H9: 2,8 * DIS # I2: 2,8 => CTR => I2: 3,5,7,9 * DIS # I3: 2,8 => CTR => I3: 4,5,6,7,9 * PRF # I4: 2,8 => SOL * DIS # I4: 4,5,7,9 => CTR => I4: 2,8 * CNT 19 HDP CHAINS / 44 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # A9: 2,7 => CTR => A9: 3,6 * DIS A9: 3,6 # C9: 2,7 => CTR => C9: 6 * DIS A9: 3,6 + C9: 6 # G7: 2,4 => CTR => G7: 1 * PRF A9: 3,6 + C9: 6 + G7: 1 => SOL * STA A9: 3,6 + C9: 6 + G7: 1 * CNT 4 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 8.......14..6........3......6.....3.1...8..........6...58....7..1..2.......4..9.. | initial |
| 8.......14..6........3......6.....3.143.86....8....6...58....7..1482.......4..9.. | autosolve |
| 837549261425618793691372845762195438143786529589234617258963174914827356376451982 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) A8: 7,9 B9: 2,7 D7: 1,9 F8: 7,9 I7: 2,4 G8: 3,5 H8: 5,6 I9: 2,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,C3: 1.. / C2 = 1 => 8 pairs (_) / C3 = 1 => 8 pairs (_) G4,H6: 1.. / G4 = 1 => 0 pairs (X) / H6 = 1 => 0 pairs (_) G7,H9: 1.. / G7 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) G4,G7: 1.. / G4 = 1 => 0 pairs (X) / G7 = 1 => 0 pairs (_) H6,H9: 1.. / H6 = 1 => 0 pairs (*) / H9 = 1 => 0 pairs (X) B1,B2: 3.. / B1 = 3 => 8 pairs (_) / B2 = 3 => 0 pairs (X) E6,F6: 3.. / E6 = 3 => 8 pairs (_) / F6 = 3 => 0 pairs (X) A7,A9: 3.. / A7 = 3 => 0 pairs (X) / A9 = 3 => 8 pairs (_) G8,I8: 3.. / G8 = 3 => 8 pairs (_) / I8 = 3 => 0 pairs (X) B1,G1: 3.. / B1 = 3 => 8 pairs (_) / G1 = 3 => 0 pairs (X) I2,I8: 3.. / I2 = 3 => 8 pairs (_) / I8 = 3 => 0 pairs (X) G7,I7: 4.. / G7 = 4 => 0 pairs (X) / I7 = 4 => 0 pairs (_) E9,F9: 5.. / E9 = 5 => 8 pairs (_) / F9 = 5 => 8 pairs (_) E7,E9: 6.. / E7 = 6 => 8 pairs (_) / E9 = 6 => 0 pairs (X) H8,I8: 6.. / H8 = 6 => 0 pairs (X) / I8 = 6 => 7 pairs (_) C1,H1: 6.. / C1 = 6 => 0 pairs (X) / H1 = 6 => 7 pairs (_) A7,E7: 6.. / A7 = 6 => 0 pairs (X) / E7 = 6 => 8 pairs (_) I3,I8: 6.. / I3 = 6 => 0 pairs (X) / I8 = 6 => 7 pairs (_) A8,F8: 7.. / A8 = 7 => 0 pairs (X) / F8 = 7 => 6 pairs (_) F2,F3: 8.. / F2 = 8 => 8 pairs (_) / F3 = 8 => 8 pairs (_) G4,I4: 8.. / G4 = 8 => 0 pairs (X) / I4 = 8 => 0 pairs (_) H9,I9: 8.. / H9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) C4,C6: 9.. / C4 = 9 => 8 pairs (_) / C6 = 9 => 8 pairs (_) A7,A8: 9.. / A7 = 9 => 0 pairs (X) / A8 = 9 => 6 pairs (_) A8,F8: 9.. / A8 = 9 => 6 pairs (_) / F8 = 9 => 0 pairs (X) * DURATION: 0:00:33.228350 START: 16:16:35.337581 END: 16:17:08.565931 2017-05-04 * CP COUNT: (25) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,D7,F8,G8,H8,I7,I9) * 8.......14..6........3......6.....3.143.86....8....6...58....7..1482.......4..9.. * PAIR B9: 2,7 BLK 7 A9: 2,7,3,6 # reduction candidate for 2,7 A9: 2,7 => CTR * 83.....614..6....36..3......6....83.143.86....8....61.358.6..7.914827356..64..9.8 A9: 3,6 # 9 pairs C9: 2,7,6 # reduction candidate for 2,7 C9: 2,7 => CTR * 8.......14..6........3......6....138143.86....8....6...58....7..1482.......4..9.. C9: 6 # 7 pairs * PAIR B9: 2,7 COL B B1: 2,7,3,9 # reduction candidate for 2,7 B1: 2,7 => CTR * 8.6...3.143.6......9.3....6.6....138143.86....8....6...58....7..1482.563...4..9.. B1: 3,9 # 9 pairs B2: 2,7,3,9 # reduction candidate for 2,7 B2: 2,7 # 9 pairs B3: 2,7,9 # reduction candidate for 2,7 B3: 2,7 # 11 pairs * PAIR D7: 1,9 BLK 8 E7: 1,9,3,6 # reduction candidate for 1,9 E7: 1,9 => CTR * 8.......14..6........3......6.....3.143.86....8....6..658..3.7.914827...3..465918 E7: 3,6 # 9 pairs F7: 1,9,3 # reduction candidate for 1,9 F7: 1,9 => CTR * 8.......14..6........3......6....138143.86....8....6...58....7.914827......4..9.. F7: 3 # 8 pairs * PAIR D7: 1,9 COL D D4: 1,9,2,5,7 # reduction candidate for 1,9 D4: 1,9 # 9 pairs D6: 1,9,2,5,7 # reduction candidate for 1,9 D6: 1,9 # 9 pairs * PAIR F8: 7,9 COL F F1: 7,9,2,4,5 # reduction candidate for 7,9 F1: 7,9 # 10 pairs F2: 7,9,1,2,5,8 # reduction candidate for 7,9 F2: 7,9 # 10 pairs F3: 7,9,1,2,4,5,8 # reduction candidate for 7,9 F3: 7,9 # 10 pairs F4: 7,9,1,2,4,5 # reduction candidate for 7,9 F4: 7,9 # 10 pairs F6: 7,9,1,2,3,4,5 # reduction candidate for 7,9 F6: 7,9 # 10 pairs * PAIR I7: 2,4 BLK 9 G7: 2,4,1 # reduction candidate for 2,4 G7: 2,4 => CTR * 8.......14..6........3......6....138143.86....8....6...58....7..1482.......4..9.. G7: 1 => SOLVED * 837549261425618793691372845762195438143786529589234617258963174914827356376451982 * PAIR I7: 2,4 COL I I3: 2,4,5,6,7,8,9 # reduction candidate for 2,4 I3: 2,4 => CTR * 83......14..6....3...3......6.....3.143.86....8....6...58....7..1482.356...4..9.. I3: 5,6,7,8,9 # 8 pairs I4: 2,4,5,7,8,9 # reduction candidate for 2,4 I4: 2,4 => CTR * 8.......14..6........3......6....83.143.86....8....61..58...174.1482.......4..9.. I4: 5,7,8,9 # 8 pairs I6: 2,4,5,7,9 # reduction candidate for 2,4 I6: 2,4 => CTR * 8.......14..6........3......6....83.143.86....8....614.58....7..1482.......4..9.8 I6: 5,7,9 # 10 pairs * PAIR G8: 3,5 BLK 9 I8: 3,5,6 # reduction candidate for 3,5 I8: 3,5 => CTR * 8.6.....14..6........3....6.6....138143.86....8....6...58....7..1482..6....4..9.. I8: 6 # 7 pairs * PAIR G8: 3,5 COL G G1: 3,5,2,4,7 # reduction candidate for 3,5 G1: 3,5 # 10 pairs G2: 3,5,2,7,8 # reduction candidate for 3,5 G2: 3,5 # 10 pairs * PAIR H8: 5,6 BLK 9 I8: 5,6,3 # reduction candidate for 5,6 I8: 3 => CTR * 8.6.....14..6........3....6.6....138143.86....8....6...58....7..1482.563...4..9.. I8: 5,6 # 8 pairs * PAIR H8: 5,6 COL H H1: 5,6,2,4,9 # reduction candidate for 5,6 H1: 5,6 # 10 pairs H3: 5,6,2,4,8,9 # reduction candidate for 5,6 H3: 5,6 => CTR * 8.6.....14..6........3......6....138143.86....8....6...58....7..1482.......4..9.. H3: 2,4,8,9 # 8 pairs * PAIR I9: 2,8 BLK 9 H9: 2,8,1 # reduction candidate for 2,8 H9: 2,8 => SOLVED * 837549261425618793691372845762195438143786529589234617258963174914827356376451982 H9: 1 => CTR * 8.......14..6........3......6.....3.143.86....8....6...58....7..1482.......4..918 * PAIR I9: 2,8 COL I I2: 2,8,3,5,7,9 # reduction candidate for 2,8 I2: 2,8 => CTR * 8.6.....14..6........3....6.6.....3.143.86....8....6...58....7..1482.563...4..9.. I2: 3,5,7,9 # 8 pairs I3: 2,8,4,5,6,7,9 # reduction candidate for 2,8 I3: 2,8 => CTR * 83......14..6....3...3......6.....3.143.86....8....6...58....7..1482.356...4..9.. I3: 4,5,6,7,9 # 8 pairs I4: 2,8,4,5,7,9 # reduction candidate for 2,8 I4: 2,8 => SOLVED * 837549261425618793691372845762195438143786529589234617258963174914827356376451982 I4: 4,5,7,9 => CTR * 8.......14..6........3......6....83.143.86....8....61..58...174.1482.......4..9.. * INCONCLUSIVE * SAVE PR GRAPH xx-top500-393-base-pr-000.dot * REASONING * DIS # A9: 2,7 => CTR => A9: 3,6 * DIS # C9: 2,7 => CTR => C9: 6 * DIS # B1: 2,7 => CTR => B1: 3,9 * DIS # E7: 1,9 => CTR => E7: 3,6 * DIS # F7: 1,9 => CTR => F7: 3 * DIS # G7: 2,4 => CTR => G7: 1 * PRF # G7: 1 => SOL * DIS # I3: 2,4 => CTR => I3: 5,6,7,8,9 * DIS # I4: 2,4 => CTR => I4: 5,7,8,9 * DIS # I6: 2,4 => CTR => I6: 5,7,9 * DIS # I8: 3,5 => CTR => I8: 6 * DIS # I8: 3 => CTR => I8: 5,6 * DIS # H3: 5,6 => CTR => H3: 2,4,8,9 * PRF # H9: 2,8 => SOL * DIS # H9: 1 => CTR => H9: 2,8 * DIS # I2: 2,8 => CTR => I2: 3,5,7,9 * DIS # I3: 2,8 => CTR => I3: 4,5,6,7,9 * PRF # I4: 2,8 => SOL * DIS # I4: 4,5,7,9 => CTR => I4: 2,8 * CNT 19 HDP CHAINS / 44 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,B9,D7,F8,G8,H8,I7,I9) * 8.......14..6........3......6.....3.143.86....8....6...58....7..1482.......4..9.. * PAIR B9: 2,7 BLK 7 A9: 2,7,3,6 # reduction candidate for 2,7 A9: 2,7 => CTR * 83.....614..6....36..3......6....83.143.86....8....61.358.6..7.914827356..64..9.8 C9: 2,7,6 # reduction candidate for 2,7 C9: 2,7 => CTR * 8.......14..6........3......6....138143.86....8....6...58....7..1482.......4..9.. * RESTART * PAIR B9: 2,7 COL B B2: 2,7,9 # reduction candidate for 2,7 B2: 2,7 # 12 pairs B3: 2,7,9 # reduction candidate for 2,7 B3: 2,7 # 10 pairs * PAIR D7: 1,9 COL D D4: 1,9,2,5,7 # reduction candidate for 1,9 D4: 1,9 # 9 pairs D6: 1,9,2,5,7 # reduction candidate for 1,9 D6: 1,9 # 9 pairs * PAIR F8: 7,9 COL F F1: 7,9,2,4,5 # reduction candidate for 7,9 F1: 7,9 # 10 pairs F4: 7,9,1,2,4,5 # reduction candidate for 7,9 F4: 7,9 # 10 pairs F6: 7,9,1,2,4,5 # reduction candidate for 7,9 F6: 7,9 # 10 pairs * PAIR I7: 2,4 BLK 9 G7: 2,4,1 # reduction candidate for 2,4 G7: 2,4 => CTR * 83.....614..6....36..3......6....138143.86....8..3.6...58163.7..148293563.64..9.. G7: 1 => SOLVED * 837549261425618793691372845762195438143786529589234617258963174914827356376451982 * DURATION: 0:00:11.743155 START: 16:17:39.881125 END: 16:17:51.624280 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-393-base-pr-001.dot * REASONING * DIS # A9: 2,7 => CTR => A9: 3,6 * DIS A9: 3,6 # C9: 2,7 => CTR => C9: 6 * DIS A9: 3,6 + C9: 6 # G7: 2,4 => CTR => G7: 1 * PRF A9: 3,6 + C9: 6 + G7: 1 => SOL * STA A9: 3,6 + C9: 6 + G7: 1 * CNT 4 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 393 solution: 837549261425618793691372845762195438143786529589234617258963174914827356376451982 info: 58462 FNBHK S8.f 44590 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 837549261425618793691372845762195438143786529589234617258963174914827356376451982 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 # A9: 2,7 => CTR => A9: 3,6 * INC # A9: 3,6 => UNS * DIS # C9: 2,7 => CTR => C9: 6 * INC # C9: 6 => UNS * DIS # B1: 2,7 => CTR => B1: 3,9 * INC # B1: 3,9 => UNS * INC # B2: 2,7 => UNS * INC # B3: 2,7 => UNS * DIS # E7: 1,9 => CTR => E7: 3,6 * INC # E7: 3,6 => UNS * DIS # F7: 1,9 => CTR => F7: 3 * INC # F7: 3 => UNS * INC # D4: 1,9 => UNS * INC # D6: 1,9 => UNS * INC # F1: 7,9 => UNS * INC # F2: 7,9 => UNS * INC # F3: 7,9 => UNS * INC # F4: 7,9 => UNS * INC # F6: 7,9 => UNS * DIS # G7: 2,4 => CTR => G7: 1 * PRF # G7: 1 => SOL * DIS # I3: 2,4 => CTR => I3: 5,6,7,8,9 * INC # I3: 5,6,7,8,9 => UNS * DIS # I4: 2,4 => CTR => I4: 5,7,8,9 * INC # I4: 5,7,8,9 => UNS * DIS # I6: 2,4 => CTR => I6: 5,7,9 * INC # I6: 5,7,9 => UNS * DIS # I8: 3,5 => CTR => I8: 6 * INC # I8: 6 => UNS * INC # G1: 3,5 => UNS * INC # G2: 3,5 => UNS * INC # I8: 5,6 => UNS * DIS # I8: 3 => CTR => I8: 5,6 * INC # H1: 5,6 => UNS * DIS # H3: 5,6 => CTR => H3: 2,4,8,9 * INC # H3: 2,4,8,9 => UNS * PRF # H9: 2,8 => SOL * DIS # H9: 1 => CTR => H9: 2,8 * DIS # I2: 2,8 => CTR => I2: 3,5,7,9 * INC # I2: 3,5,7,9 => UNS * DIS # I3: 2,8 => CTR => I3: 4,5,6,7,9 * INC # I3: 4,5,6,7,9 => UNS * PRF # I4: 2,8 => SOL * DIS # I4: 4,5,7,9 => CTR => I4: 2,8 * CNT 44 HDP CHAINS / 44 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # A9: 2,7 => CTR => A9: 3,6 * DIS A9: 3,6 # C9: 2,7 => CTR => C9: 6 * INC A9: 3,6 + C9: 6 # B2: 2,7 => UNS * INC A9: 3,6 + C9: 6 # B3: 2,7 => UNS * INC A9: 3,6 + C9: 6 # D4: 1,9 => UNS * INC A9: 3,6 + C9: 6 # D6: 1,9 => UNS * INC A9: 3,6 + C9: 6 # F1: 7,9 => UNS * INC A9: 3,6 + C9: 6 # F4: 7,9 => UNS * INC A9: 3,6 + C9: 6 # F6: 7,9 => UNS * DIS A9: 3,6 + C9: 6 # G7: 2,4 => CTR => G7: 1 * PRF A9: 3,6 + C9: 6 + G7: 1 => SOL * STA A9: 3,6 + C9: 6 + G7: 1 * CNT 11 HDP CHAINS / 10 HYP OPENED