Analysis of xx-top500-098-base.sdk
Contents
Original Sudoku
level: medium
position: 3.7.9..........2..1...........1.3.....4....9..2....8.....24..3.65......1......... initial
Autosolve
position: 387.9261.4.5...2..1.2...3..976183542834.2.19.521...8.371824.93.65....42124....7.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 4,5 => CTR => D3: 6,7,8 * DIS # I3: 4,5 => CTR => I3: 7,8,9 * DIS # I2: 7,8 => CTR => I2: 9 * DIS # H3: 7,8 => CTR => H3: 5 * DIS # D2: 7,8 => CTR => D2: 3,6 * DIS # F5: 6,7 => CTR => F5: 5 * DIS # E2: 6,7 => CTR => E2: 1,3 * DIS # F5: 6,7 => CTR => F5: 5 * DIS # D8: 3,9 => CTR => D8: 7,8 * DIS # D9: 5,6 => CTR => D9: 3,9 * DIS # D9: 5,6 => CTR => D9: 3,9 * DIS # F9: 5,6 => CTR => F9: 1,9 * DIS # F3: 5,6 => CTR => F3: 4,7,8 * DIS # E2: 3,7 => CTR => E2: 1,6 * PRF # I9: 5,6 => SOL * CNT 15 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 # D3: 4,5 => CTR => D3: 6,7,8 * DIS D3: 6,7,8 # F3: 6,7,8 => CTR => F3: 4,5 * PRF D3: 6,7,8 + F3: 4,5 # D3: 7,8 => SOL * STA D3: 6,7,8 + F3: 4,5 + D3: 7,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 3.7.9..........2..1...........1.3.....4....9..2....8.....24..3.65......1......... | initial |
| 387.9261.4.5...2..1.2...3..976183542834.2.19.521...8.371824.93.65....42124....7.. | autosolve |
| 387592614465318279192764358976183542834625197521479863718246935659837421243951786 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) B2: 6,9 B3: 6,9 D1: 4,5 I1: 4,5 H2: 7,8 D6: 4,9 E6: 6,7 F6: 4,9 I5: 6,7 H6: 6,7 C8: 3,9 C9: 3,9 F7: 5,6 E8: 3,7 I7: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,F2: 1.. / E2 = 1 => 15 pairs (_) / F2 = 1 => 0 pairs (X) E9,F9: 1.. / E9 = 1 => 0 pairs (X) / F9 = 1 => 15 pairs (_) E2,E9: 1.. / E2 = 1 => 15 pairs (_) / E9 = 1 => 0 pairs (X) F2,F9: 1.. / F2 = 1 => 0 pairs (X) / F9 = 1 => 15 pairs (_) D2,E2: 3.. / D2 = 3 => 15 pairs (_) / E2 = 3 => 0 pairs (X) C8,C9: 3.. / C8 = 3 => 0 pairs (X) / C9 = 3 => 14 pairs (_) I1,I3: 4.. / I1 = 4 => 12 pairs (_) / I3 = 4 => 0 pairs (X) D6,F6: 4.. / D6 = 4 => 12 pairs (_) / F6 = 4 => 13 pairs (_) D1,I1: 4.. / D1 = 4 => 0 pairs (X) / I1 = 4 => 12 pairs (_) F3,F6: 4.. / F3 = 4 => 12 pairs (_) / F6 = 4 => 13 pairs (_) D5,F5: 5.. / D5 = 5 => 0 pairs (X) / F5 = 5 => 12 pairs (_) D1,I1: 5.. / D1 = 5 => 12 pairs (_) / I1 = 5 => 0 pairs (X) F7,I7: 5.. / F7 = 5 => 0 pairs (X) / I7 = 5 => 12 pairs (_) E3,E9: 5.. / E3 = 5 => 0 pairs (X) / E9 = 5 => 12 pairs (_) H3,H9: 5.. / H3 = 5 => 12 pairs (_) / H9 = 5 => 0 pairs (X) B2,B3: 6.. / B2 = 6 => 13 pairs (_) / B3 = 6 => 0 pairs (X) I5,H6: 6.. / I5 = 6 => 0 pairs (X) / H6 = 6 => 20 pairs (_) E6,H6: 6.. / E6 = 6 => 0 pairs (X) / H6 = 6 => 20 pairs (_) F7,I7: 6.. / F7 = 6 => 12 pairs (_) / I7 = 6 => 0 pairs (X) H6,H9: 6.. / H6 = 6 => 20 pairs (_) / H9 = 6 => 0 pairs (X) I5,H6: 7.. / I5 = 7 => 20 pairs (_) / H6 = 7 => 0 pairs (X) E6,H6: 7.. / E6 = 7 => 20 pairs (_) / H6 = 7 => 0 pairs (X) D8,F8: 8.. / D8 = 8 => 16 pairs (_) / F8 = 8 => 15 pairs (_) H9,I9: 8.. / H9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) B2,B3: 9.. / B2 = 9 => 0 pairs (X) / B3 = 9 => 13 pairs (_) I2,I3: 9.. / I2 = 9 => 13 pairs (_) / I3 = 9 => 0 pairs (X) D6,F6: 9.. / D6 = 9 => 13 pairs (_) / F6 = 9 => 12 pairs (_) C8,C9: 9.. / C8 = 9 => 14 pairs (_) / C9 = 9 => 0 pairs (X) B2,I2: 9.. / B2 = 9 => 0 pairs (X) / I2 = 9 => 13 pairs (_) B3,I3: 9.. / B3 = 9 => 13 pairs (_) / I3 = 9 => 0 pairs (X) * DURATION: 0:00:53.297003 START: 06:07:19.235139 END: 06:08:12.532142 2017-05-04 * CP COUNT: (30) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,C8,C9,D1,D6,E6,E8,F6,F7,H2,H6,I1,I5,I7) * 387.9261.4.5...2..1.2...3..976183542834.2.19.521...8.371824.93.65....42124....7.. * PAIR D1: 4,5 BLK 2 D3: 4,5,6,7,8 # reduction candidate for 4,5 D3: 4,5 => CTR * 387.9261.4.5...2..1.2...3..976183542834.2519.5219.48.371824693565..3.42124....7.. D3: 6,7,8 # 15 pairs F3: 4,5,6,7,8 # reduction candidate for 4,5 F3: 4,5 # 12 pairs * PAIR I1: 4,5 BLK 3 I3: 4,5,7,8,9 # reduction candidate for 4,5 I3: 4,5 => CTR * 387.9261.46531.2.9192.5.3.497618354283452.197521.7.86371824.936659.3.421243..1758 I3: 7,8,9 # 12 pairs * PAIR H2: 7,8 BLK 3 I2: 7,8,9 # reduction candidate for 7,8 I2: 7,8 => CTR * 387592614495.1.2..162.7.359976183542834.2519.521.6.87371824693565..374212439517.. I2: 9 # 13 pairs H3: 7,8,5 # reduction candidate for 7,8 H3: 7,8 => CTR * 3874926154.5...2..1.2.5.3.497618354283452619752197486371824593665..3.421243619758 H3: 5 # 12 pairs I3: 7,8,4,5,9 # reduction candidate for 7,8 I3: 7,8 # 12 pairs * PAIR H2: 7,8 ROW 2 D2: 7,8,3,6 # reduction candidate for 7,8 D2: 7,8 => CTR * 387.9261.465.312.9192.5.3..976183542834.2.19.521.6.87371824.93.65..7.42124..1.7.. D2: 3,6 # 16 pairs F2: 7,8,1,6 # reduction candidate for 7,8 F2: 7,8 # 14 pairs * PAIR E6: 6,7 BLK 5 D5: 6,7,5 # reduction candidate for 6,7 D5: 6,7 # 12 pairs F5: 6,7,5 # reduction candidate for 6,7 F5: 6,7 => CTR * 3874926154.5...2.9192.5.3.497618354283452619752197486371824593665..3.421243619758 F5: 5 # 12 pairs * PAIR E6: 6,7 COL E E2: 6,7,1,3 # reduction candidate for 6,7 E2: 6,7 => CTR * 3874926154.53.128.1.2.5.37497618354283452.197521974863718245936659738421243619758 E2: 1,3 # 16 pairs E3: 6,7,5 # reduction candidate for 6,7 E3: 6,7 # 12 pairs * PAIR I5: 6,7 ROW 5 D5: 6,7,5 # reduction candidate for 6,7 D5: 6,7 # 12 pairs F5: 6,7,5 # reduction candidate for 6,7 F5: 6,7 => CTR * 3874926154.5...2.9192.5.3.497618354283452619752197486371824593665..3.421243619758 F5: 5 # 12 pairs * PAIR C8: 3,9 ROW 8 D8: 3,9,7,8 # reduction candidate for 3,9 D8: 3,9 => CTR * 387.9261.4.5...28.1.285.3..976183542834.2.19.521.6.87371824.93.65..7842124....768 D8: 7,8 # 16 pairs * PAIR C9: 3,9 ROW 9 D9: 3,9,5,6 # reduction candidate for 3,9 D9: 5,6 => CTR * 3874926154.5.612.91.2.5.3.497618354283452.19.5219.486371824593665....42124.6..758 D9: 3,9 # 16 pairs * PAIR F7: 5,6 BLK 8 D9: 5,6,3,9 # reduction candidate for 5,6 D9: 5,6 => CTR * 3874926154.5.612.91.2.5.3.497618354283452.19.5219.486371824593665....42124.6..758 D9: 3,9 # 16 pairs E9: 5,6,1,3 # reduction candidate for 5,6 E9: 5,6 # 12 pairs F9: 5,6,1,9 # reduction candidate for 5,6 F9: 5,6 => CTR * 3874926154.5..12..1.2.5.3.497618354283452.19.5219.486371824593665...9421249316758 F9: 1,9 # 16 pairs * PAIR F7: 5,6 COL F F3: 5,6,4,7,8 # reduction candidate for 5,6 F3: 5,6 => CTR * 387.9261.4.5...2..1.2...3..97618354283452719652196487371824693565....42124.351768 F3: 4,7,8 # 15 pairs F5: 5,6,7 # reduction candidate for 5,6 F5: 5,6 # 17 pairs * PAIR E8: 3,7 BLK 8 D8: 3,7,8,9 # reduction candidate for 3,7 D8: 8,9 # 16 pairs D8: 3,7 # 14 pairs * PAIR E8: 3,7 COL E E2: 3,7,1,6 # reduction candidate for 3,7 E2: 3,7 => CTR * 387.9261.4.5..12..1.2.5.3..976183542834.2.19.521.6.87371824.93.65....42124..1.7.. E2: 1,6 # 16 pairs * PAIR I7: 5,6 BLK 9 H9: 5,6,8 # reduction candidate for 5,6 H9: 5,6 # 17 pairs I9: 5,6,8 # reduction candidate for 5,6 I9: 5,6 => SOLVED * 387592614465318279192764358976183542834625197521479863718246935659837421243951786 I9: 8 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-098-base-pr-000.dot * REASONING * DIS # D3: 4,5 => CTR => D3: 6,7,8 * DIS # I3: 4,5 => CTR => I3: 7,8,9 * DIS # I2: 7,8 => CTR => I2: 9 * DIS # H3: 7,8 => CTR => H3: 5 * DIS # D2: 7,8 => CTR => D2: 3,6 * DIS # F5: 6,7 => CTR => F5: 5 * DIS # E2: 6,7 => CTR => E2: 1,3 * DIS # F5: 6,7 => CTR => F5: 5 * DIS # D8: 3,9 => CTR => D8: 7,8 * DIS # D9: 5,6 => CTR => D9: 3,9 * DIS # D9: 5,6 => CTR => D9: 3,9 * DIS # F9: 5,6 => CTR => F9: 1,9 * DIS # F3: 5,6 => CTR => F3: 4,7,8 * DIS # E2: 3,7 => CTR => E2: 1,6 * PRF # I9: 5,6 => SOL * CNT 15 HDP CHAINS / 41 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,C8,C9,D1,D6,E6,E8,F6,F7,H2,H6,I1,I5,I7) * 387.9261.4.5...2..1.2...3..976183542834.2.19.521...8.371824.93.65....42124....7.. * PAIR D1: 4,5 BLK 2 D3: 4,5,6,7,8 # reduction candidate for 4,5 D3: 4,5 => CTR * 387.9261.4.5...2..1.2...3..976183542834.2519.5219.48.371824693565..3.42124....7.. F3: 4,5,6,7,8 # reduction candidate for 4,5 F3: 4,5 # 12 pairs * RESTART * PAIR D1: 4,5 BLK 2 F3: 4,5,6,7,8 # reduction candidate for 4,5 F3: 6,7,8 => CTR * 3874926154.5...2.9192.5.3.497618354283452619752197486371824593665..3.421243619758 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (D5,D8,E3,E6,F2,F8,H2,H6,H9,I3,I5,I9) * 38759261446531.2.9192..435.976183542834.2519.5214.98.3718246935659.3.4212439517.. * PAIR F2: 7,8 BLK 2 D3: 7,8,6 # reduction candidate for 7,8 D3: 7,8 => SOLVED * 387592614465318279192764358976183542834625197521479863718246935659837421243951786 * DURATION: 0:00:07.116046 START: 06:08:52.049314 END: 06:08:59.165360 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-098-base-pr-001.dot * REASONING * DIS # D3: 4,5 => CTR => D3: 6,7,8 * DIS D3: 6,7,8 # F3: 6,7,8 => CTR => F3: 4,5 * PRF D3: 6,7,8 + F3: 4,5 # D3: 7,8 => SOL * STA D3: 6,7,8 + F3: 4,5 + D3: 7,8 * CNT 3 HDP CHAINS / 5 HYP OPENED
Header Info
Top 500 Minimum 17 098 solution: 387592614465318279192764358976183542834625197521479863718246935659837421243951786 info: 1575 FNBTWXY S8.f 44954 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 387592614465318279192764358976183542834625197521479863718246935659837421243951786 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 # D3: 4,5 => CTR => D3: 6,7,8 * INC # D3: 6,7,8 => UNS * INC # F3: 4,5 => UNS * DIS # I3: 4,5 => CTR => I3: 7,8,9 * INC # I3: 7,8,9 => UNS * DIS # I2: 7,8 => CTR => I2: 9 * INC # I2: 9 => UNS * DIS # H3: 7,8 => CTR => H3: 5 * INC # H3: 5 => UNS * INC # I3: 7,8 => UNS * DIS # D2: 7,8 => CTR => D2: 3,6 * INC # D2: 3,6 => UNS * INC # F2: 7,8 => UNS * INC # D5: 6,7 => UNS * DIS # F5: 6,7 => CTR => F5: 5 * INC # F5: 5 => UNS * DIS # E2: 6,7 => CTR => E2: 1,3 * INC # E2: 1,3 => UNS * INC # E3: 6,7 => UNS * INC # D5: 6,7 => UNS * DIS # F5: 6,7 => CTR => F5: 5 * INC # F5: 5 => UNS * DIS # D8: 3,9 => CTR => D8: 7,8 * INC # D8: 7,8 => UNS * INC # D9: 3,9 => UNS * DIS # D9: 5,6 => CTR => D9: 3,9 * DIS # D9: 5,6 => CTR => D9: 3,9 * INC # D9: 3,9 => UNS * INC # E9: 5,6 => UNS * DIS # F9: 5,6 => CTR => F9: 1,9 * INC # F9: 1,9 => UNS * DIS # F3: 5,6 => CTR => F3: 4,7,8 * INC # F3: 4,7,8 => UNS * INC # F5: 5,6 => UNS * INC # D8: 3,7 => UNS * INC # D8: 8,9 => UNS * DIS # E2: 3,7 => CTR => E2: 1,6 * INC # E2: 1,6 => UNS * INC # H9: 5,6 => UNS * PRF # I9: 5,6 => SOL * INC # I9: 8 => UNS * CNT 41 HDP CHAINS / 41 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # D3: 4,5 => CTR => D3: 6,7,8 * INC D3: 6,7,8 # F3: 4,5 => UNS * INC D3: 6,7,8 # F3: 4,5 => UNS * DIS D3: 6,7,8 # F3: 6,7,8 => CTR => F3: 4,5 * PRF D3: 6,7,8 + F3: 4,5 # D3: 7,8 => SOL * STA D3: 6,7,8 + F3: 4,5 + D3: 7,8 * CNT 5 HDP CHAINS / 5 HYP OPENED