Analysis of xx-top500-167-base.sdk
Contents
Original Sudoku
level: medium
position: 2.....1.3...5.6...............73...2.61.............8.3...2.4...4....65.......... initial
Autosolve
position: 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.41.8421.365.61..5423. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I7: 7,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 8 => CTR => I9: 7,9 * PRF # I7: 7,8 => SOL * DIS # I7: 9 => CTR => I7: 7,8 * PRF # I9: 8,9 => SOL * DIS # I9: 7 => CTR => I9: 8,9 * DIS # I7: 7,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 8 => CTR => I9: 7,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I7: 7,9 => CTR => I7: 8 * PRF I7: 8 => SOL * STA I7: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2.....1.3...5.6...............73...2.61.............8.3...2.4...4....65.......... | initial |
| 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.41.8421.365.61..5423. | autosolve |
| 256948173139576824478312596584731962761289345923465781395627418842193657617854239 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) C2: 7,9 B3: 7,9 D1: 8,9 F1: 7,8 E2: 7,9 H1: 7,9 H3: 7,9 B7: 7,9 C9: 7,9 F7: 7,8 E8: 7,9 D9: 8,9 I8: 7,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C2,B3: 7.. / C2 = 7 => 0 pairs (X) / B3 = 7 => 0 pairs (_) F1,E2: 7.. / F1 = 7 => 0 pairs (X) / E2 = 7 => 0 pairs (_) H1,H3: 7.. / H1 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) B7,C9: 7.. / B7 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) F7,E8: 7.. / F7 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) F1,H1: 7.. / F1 = 7 => 0 pairs (X) / H1 = 7 => 0 pairs (_) C2,E2: 7.. / C2 = 7 => 0 pairs (X) / E2 = 7 => 0 pairs (_) B3,H3: 7.. / B3 = 7 => 0 pairs (*) / H3 = 7 => 0 pairs (X) E8,I8: 7.. / E8 = 7 => 0 pairs (X) / I8 = 7 => 0 pairs (_) C9,I9: 7.. / C9 = 7 => 0 pairs (*) / I9 = 7 => 0 pairs (X) B3,B7: 7.. / B3 = 7 => 0 pairs (*) / B7 = 7 => 0 pairs (X) C2,C9: 7.. / C2 = 7 => 0 pairs (X) / C9 = 7 => 0 pairs (_) E2,E8: 7.. / E2 = 7 => 0 pairs (*) / E8 = 7 => 0 pairs (X) F1,F7: 7.. / F1 = 7 => 0 pairs (X) / F7 = 7 => 0 pairs (_) D1,F1: 8.. / D1 = 8 => 0 pairs (X) / F1 = 8 => 0 pairs (_) F7,D9: 8.. / F7 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) I7,I9: 8.. / I7 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) F7,I7: 8.. / F7 = 8 => 0 pairs (X) / I7 = 8 => 0 pairs (_) D9,I9: 8.. / D9 = 8 => 0 pairs (*) / I9 = 8 => 0 pairs (X) D1,D9: 8.. / D1 = 8 => 0 pairs (X) / D9 = 8 => 0 pairs (_) F1,F7: 8.. / F1 = 8 => 0 pairs (*) / F7 = 8 => 0 pairs (X) C2,B3: 9.. / C2 = 9 => 0 pairs (*) / B3 = 9 => 0 pairs (X) D1,E2: 9.. / D1 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) H1,H3: 9.. / H1 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B7,C9: 9.. / B7 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) E8,D9: 9.. / E8 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) D1,H1: 9.. / D1 = 9 => 0 pairs (*) / H1 = 9 => 0 pairs (X) C2,E2: 9.. / C2 = 9 => 0 pairs (*) / E2 = 9 => 0 pairs (X) B3,H3: 9.. / B3 = 9 => 0 pairs (X) / H3 = 9 => 0 pairs (_) B7,I7: 9.. / B7 = 9 => 0 pairs (*) / I7 = 9 => 0 pairs (X) E8,I8: 9.. / E8 = 9 => 0 pairs (*) / I8 = 9 => 0 pairs (X) B3,B7: 9.. / B3 = 9 => 0 pairs (X) / B7 = 9 => 0 pairs (_) C2,C9: 9.. / C2 = 9 => 0 pairs (*) / C9 = 9 => 0 pairs (X) D1,D9: 9.. / D1 = 9 => 0 pairs (*) / D9 = 9 => 0 pairs (X) E2,E8: 9.. / E2 = 9 => 0 pairs (X) / E8 = 9 => 0 pairs (_) * DURATION: 0:01:01.624090 START: 08:27:25.488852 END: 08:28:27.112942 2017-05-04 * CP COUNT: (35) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B7,C2,C9,D1,D9,E2,E8,F1,F7,H1,H3,I8) * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.41.8421.365.61..5423. * PAIR B7: 7,9 ROW 7 I7: 7,9,8 # reduction candidate for 7,9 I7: 7,9 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562841.84217365961.954238 I7: 8 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 * PAIR C9: 7,9 ROW 9 I9: 7,9,8 # reduction candidate for 7,9 I9: 7,9 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 I9: 8 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.41.8421.365.617954238 * PAIR F7: 7,8 ROW 7 I7: 7,8,9 # reduction candidate for 7,8 I7: 7,8 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 I7: 9 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.56284198421.365.61..5423. * PAIR D9: 8,9 ROW 9 I9: 8,9,7 # reduction candidate for 8,9 I9: 8,9 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 I9: 7 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.4188421.365961..5423. * PAIR I8: 7,9 BLK 9 I7: 7,9,8 # reduction candidate for 7,9 I7: 7,9 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562841.84217365961.954238 I7: 8 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 I9: 7,9,8 # reduction candidate for 7,9 I9: 7,9 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 I9: 8 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.41.8421.365.617954238 * INCONCLUSIVE * SAVE PR GRAPH xx-top500-167-base-pr-000.dot * REASONING * DIS # I7: 7,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 8 => CTR => I9: 7,9 * PRF # I7: 7,8 => SOL * DIS # I7: 9 => CTR => I7: 7,8 * PRF # I9: 8,9 => SOL * DIS # I9: 7 => CTR => I9: 8,9 * DIS # I7: 7,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 8 => CTR => I9: 7,9 * CNT 12 HDP CHAINS / 12 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B3,B7,C2,C9,D1,D9,E2,E8,F1,F7,H1,H3,I8) * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562.41.8421.365.61..5423. * PAIR B7: 7,9 ROW 7 I7: 7,9,8 # reduction candidate for 7,9 I7: 7,9 => CTR * 256.4.1.313.5.68244.83125.65847319627612893459234657813.562841.84217365961.954238 I7: 8 => SOLVED * 256948173139576824478312596584731962761289345923465781395627418842193657617854239 * DURATION: 0:00:03.179718 START: 08:28:42.683411 END: 08:28:45.863129 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-167-base-pr-001.dot * REASONING * DIS # I7: 7,9 => CTR => I7: 8 * PRF I7: 8 => SOL * STA I7: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 500 Minimum 17 167 solution: 256948173139576824478312596584731962761289345923465781395627418842193657617854239 info: 1824 FNTWX S8.f 26886 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 256948173139576824478312596584731962761289345923465781395627418842193657617854239 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 # I7: 7,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 8 => CTR => I9: 7,9 * PRF # I7: 7,8 => SOL * DIS # I7: 9 => CTR => I7: 7,8 * PRF # I9: 8,9 => SOL * DIS # I9: 7 => CTR => I9: 8,9 * DIS # I7: 7,9 => CTR => I7: 8 * PRF # I7: 8 => SOL * PRF # I9: 7,9 => SOL * DIS # I9: 8 => CTR => I9: 7,9 * CNT 12 HDP CHAINS / 12 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I7: 7,9 => CTR => I7: 8 * PRF I7: 8 => SOL * STA I7: 8 * CNT 2 HDP CHAINS / 1 HYP OPENED