Analysis of xx-top500-396-base.sdk
Contents
Original Sudoku
level: medium
position: 34...2....1.....7.....8.6..2...5.......7...1..3.......5.....2..6.......5...1..... initial
Autosolve
position: 347612.5.8165...72952.876.127..51...46.72.51.135...72.5.1...2.76..27.1.572.1.5... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F2: 3,4 => CTR => F2: 9 * DIS # D7: 3,4 => CTR => D7: 8,9 * DIS # I4: 8,9 => CTR => I4: 3,4,6 * DIS # I5: 8,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * PRF # I6: 8,9 => SOL * DIS # I6: 4 => CTR => I6: 8,9 * DIS # I9: 8,9 => CTR => I9: 3,4,6 * DIS # F2: 3,4 => CTR => F2: 9 * DIS # H4: 3,4 => CTR => H4: 6,8,9 * DIS # H9: 3,4 => CTR => H9: 6,8,9 * DIS # D4: 8,9 => CTR => D4: 3,4 * DIS # I4: 8,9 => CTR => I4: 3,4,6 * PRF # F5: 8,9 => SOL * DIS # F5: 3 => CTR => F5: 8,9 * DIS # I5: 8,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * DIS # F7: 8,9 => CTR => F7: 3,4,6 * DIS # E9: 3,4 => CTR => E9: 6,9 * DIS # H9: 3,4 => CTR => H9: 6,8,9 * CNT 20 HDP CHAINS / 50 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F2: 3,4 => CTR => F2: 9 * DIS F2: 9 # D7: 3,4 => CTR => D7: 8,9 * DIS F2: 9 + D7: 8,9 # D4: 8,9 => CTR => D4: 3,4 * DIS F2: 9 + D7: 8,9 + D4: 3,4 # I4: 8,9 => CTR => I4: 3,4,6 * DIS F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 # I5: 8,9 => CTR => I5: 3 * PRF F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 + I5: 3 => SOL * STA F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 + I5: 3 * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 34...2....1.....7.....8.6..2...5.......7...1..3.......5.....2..6.......5...1..... | initial |
| 347612.5.8165...72952.876.127..51...46.72.51.135...72.5.1...2.76..27.1.572.1.5... | autosolve |
| 347612859816539472952487631278351964469728513135946728591863247683274195724195386 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) D3: 3,4 G1: 8,9 I1: 8,9 G2: 3,4 H3: 3,4 C4: 8,9 C5: 8,9 B7: 8,9 B8: 8,9 C8: 3,4 C9: 3,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,H3: 3.. / G2 = 3 => 0 pairs (X) / H3 = 3 => 0 pairs (_) D4,F5: 3.. / D4 = 3 => 0 pairs (*) / F5 = 3 => 0 pairs (X) C8,C9: 3.. / C8 = 3 => 0 pairs (*) / C9 = 3 => 0 pairs (X) D3,H3: 3.. / D3 = 3 => 0 pairs (X) / H3 = 3 => 0 pairs (_) F5,I5: 3.. / F5 = 3 => 0 pairs (X) / I5 = 3 => 0 pairs (_) G2,H3: 4.. / G2 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) C8,C9: 4.. / C8 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) D3,H3: 4.. / D3 = 4 => 0 pairs (*) / H3 = 4 => 0 pairs (X) E6,F6: 6.. / E6 = 6 => 17 pairs (_) / F6 = 6 => 12 pairs (_) H4,I4: 6.. / H4 = 6 => 19 pairs (_) / I4 = 6 => 11 pairs (_) F6,F7: 6.. / F6 = 6 => 12 pairs (_) / F7 = 6 => 17 pairs (_) I4,I9: 6.. / I4 = 6 => 11 pairs (_) / I9 = 6 => 19 pairs (_) G1,I1: 8.. / G1 = 8 => 13 pairs (_) / I1 = 8 => 13 pairs (_) C4,C5: 8.. / C4 = 8 => 13 pairs (_) / C5 = 8 => 13 pairs (_) B7,B8: 8.. / B7 = 8 => 13 pairs (_) / B8 = 8 => 11 pairs (_) B8,F8: 8.. / B8 = 8 => 11 pairs (_) / F8 = 8 => 13 pairs (_) H4,H9: 8.. / H4 = 8 => 17 pairs (_) / H9 = 8 => 11 pairs (_) E2,F2: 9.. / E2 = 9 => 0 pairs (X) / F2 = 9 => 13 pairs (_) G1,I1: 9.. / G1 = 9 => 13 pairs (_) / I1 = 9 => 13 pairs (_) C4,C5: 9.. / C4 = 9 => 13 pairs (_) / C5 = 9 => 13 pairs (_) B7,B8: 9.. / B7 = 9 => 11 pairs (_) / B8 = 9 => 13 pairs (_) * DURATION: 0:00:38.378449 START: 16:21:50.756307 END: 16:22:29.134756 2017-05-04 * CP COUNT: (21) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,C4,C5,C8,C9,D3,G1,G2,H3,I1) * 347612.5.8165...72952.876.127..51...46.72.51.135...72.5.1...2.76..27.1.572.1.5... * PAIR D3: 3,4 BLK 2 E2: 3,4,9 # reduction candidate for 3,4 E2: 3,4 # 13 pairs F2: 3,4,9 # reduction candidate for 3,4 F2: 3,4 => CTR * 347612.5.81659..72952.8764127..514.646.72.513135.4672.5.143.2676.427.135723165..4 F2: 9 # 13 pairs * PAIR D3: 3,4 COL D D4: 3,4,8,9 # reduction candidate for 3,4 D4: 3,4 # 14 pairs D7: 3,4,8,9 # reduction candidate for 3,4 D7: 3,4 => CTR * 347612.5.8165...72952.876.127..51...46.72351.135...72.5.1...2.76..27.1.572.1.5... D7: 8,9 # 12 pairs * PAIR G1: 8,9 COL G G4: 8,9,3,4 # reduction candidate for 8,9 G4: 8,9 # 19 pairs G9: 8,9,3,4 # reduction candidate for 8,9 G9: 8,9 # 13 pairs * PAIR I1: 8,9 COL I I4: 8,9,3,4,6 # reduction candidate for 8,9 I4: 8,9 => CTR * 347612.5.8165...72952.876.127..51.6.46.72.513135...7245.1...2.76..27.1.572.1.5.86 I4: 3,4,6 # 11 pairs I5: 8,9,3 # reduction candidate for 8,9 I5: 8,9 => CTR * 347612.5.8165..37295238764127.451...46.72351.135...7245.1...2.76.427.135723195486 I5: 3 => SOLVED * 347612859816539472952487631278351964469728513135946728591863247683274195724195386 I6: 8,9,4 # reduction candidate for 8,9 I6: 8,9 => SOLVED * 347612859816539472952487631278351964469728513135946728591863247683274195724195386 I6: 4 => CTR * 347612.5.8165..37295238764127.451..346.72351.135...7245.1.342676.427.1357231654.. I9: 8,9,3,4,6 # reduction candidate for 8,9 I9: 8,9 => CTR * 347612.5.8165...72952.876.127..51..646.72.513135...7245.1...2.76..27.1.572.1.5... I9: 3,4,6 # 11 pairs * PAIR G2: 3,4 ROW 2 E2: 3,4,9 # reduction candidate for 3,4 E2: 3,4 # 13 pairs F2: 3,4,9 # reduction candidate for 3,4 F2: 3,4 => CTR * 347612.5.81659..72952.8764127..514.646.72.513135.4672.5.143.2676.427.135723165..4 F2: 9 # 13 pairs * PAIR G2: 3,4 COL G G4: 3,4,8,9 # reduction candidate for 3,4 G4: 3,4 # 13 pairs G9: 3,4,8,9 # reduction candidate for 3,4 G9: 3,4 # 19 pairs * PAIR H3: 3,4 COL H H4: 3,4,6,8,9 # reduction candidate for 3,4 H4: 3,4 => CTR * 347612.5.8165...72952.876.127..51..646.72.51.135...72.5.1...2676..27.19572.1.5.8. H4: 6,8,9 # 11 pairs H7: 3,4,6,9 # reduction candidate for 3,4 H7: 3,4 # 16 pairs H8: 3,4,9 # reduction candidate for 3,4 H8: 3,4 # 15 pairs H9: 3,4,6,8,9 # reduction candidate for 3,4 H9: 3,4 => CTR * 347612.5.8165...72952.876.127..51.8646872.51.135...72.5.1...2676..27.19572.1.5... H9: 6,8,9 # 11 pairs * PAIR C4: 8,9 ROW 4 D4: 8,9,3,4 # reduction candidate for 8,9 D4: 8,9 => CTR * 347612.5.8165...72952.876.127..51...46.72351.135...72.5.1...2.76..27.1.572.1.5... D4: 3,4 # 14 pairs G4: 8,9,3,4 # reduction candidate for 8,9 G4: 8,9 # 19 pairs H4: 8,9,3,4,6 # reduction candidate for 8,9 H4: 8,9 # 17 pairs I4: 8,9,3,4,6 # reduction candidate for 8,9 I4: 8,9 => CTR * 347612.5.8165...72952.876.127..51.6.46.72.513135...7245.1...2.76..27.1.572.1.5.86 I4: 3,4,6 # 11 pairs * PAIR C5: 8,9 ROW 5 F5: 8,9,3 # reduction candidate for 8,9 F5: 8,9 => SOLVED * 347612859816539472952487631278351964469728513135946728591863247683274195724195386 F5: 3 => CTR * 347612.5.8165..37295238764127.451...46.72351.135...7245.1...2.76.427.135723195486 I5: 8,9,3 # reduction candidate for 8,9 I5: 8,9 => CTR * 347612.5.8165..37295238764127.451...46.72351.135...7245.1...2.76.427.135723195486 I5: 3 => SOLVED * 347612859816539472952487631278351964469728513135946728591863247683274195724195386 * PAIR B7: 8,9 ROW 7 D7: 8,9,3,4 # reduction candidate for 8,9 D7: 8,9 # 12 pairs F7: 8,9,3,4,6 # reduction candidate for 8,9 F7: 8,9 => CTR * 347612.5.8165...72952.876.127..51...46.72351.135.4672.5.1...2.76..27.1.572.1.5... F7: 3,4,6 # 11 pairs * PAIR B8: 8,9 ROW 8 F8: 8,9,3,4 # reduction candidate for 8,9 F8: 3,4 # 16 pairs F8: 8,9 # 15 pairs * PAIR C8: 3,4 ROW 8 F8: 3,4,8,9 # reduction candidate for 3,4 F8: 3,4 # 16 pairs H8: 3,4,9 # reduction candidate for 3,4 H8: 3,4 # 15 pairs * PAIR C9: 3,4 ROW 9 E9: 3,4,6,9 # reduction candidate for 3,4 E9: 3,4 => CTR * 347612.5.8165...72952.876.127..51...46.72.51.135...72.5.1...2.76..27.1.572.1.5... E9: 6,9 # 12 pairs G9: 3,4,8,9 # reduction candidate for 3,4 G9: 3,4 # 19 pairs H9: 3,4,6,8,9 # reduction candidate for 3,4 H9: 3,4 => CTR * 347612.5.8165...72952.876.127..51.8646872.51.135...72.5.1...2676..27.19572.1.5... H9: 6,8,9 # 11 pairs I9: 3,4,6,8,9 # reduction candidate for 3,4 I9: 3,4 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top500-396-base-pr-000.dot * REASONING * DIS # F2: 3,4 => CTR => F2: 9 * DIS # D7: 3,4 => CTR => D7: 8,9 * DIS # I4: 8,9 => CTR => I4: 3,4,6 * DIS # I5: 8,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * PRF # I6: 8,9 => SOL * DIS # I6: 4 => CTR => I6: 8,9 * DIS # I9: 8,9 => CTR => I9: 3,4,6 * DIS # F2: 3,4 => CTR => F2: 9 * DIS # H4: 3,4 => CTR => H4: 6,8,9 * DIS # H9: 3,4 => CTR => H9: 6,8,9 * DIS # D4: 8,9 => CTR => D4: 3,4 * DIS # I4: 8,9 => CTR => I4: 3,4,6 * PRF # F5: 8,9 => SOL * DIS # F5: 3 => CTR => F5: 8,9 * DIS # I5: 8,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * DIS # F7: 8,9 => CTR => F7: 3,4,6 * DIS # E9: 3,4 => CTR => E9: 6,9 * DIS # H9: 3,4 => CTR => H9: 6,8,9 * CNT 20 HDP CHAINS / 50 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B8,C4,C5,C8,C9,D3,G1,G2,H3,I1) * 347612.5.8165...72952.876.127..51...46.72.51.135...72.5.1...2.76..27.1.572.1.5... * PAIR D3: 3,4 BLK 2 E2: 3,4,9 # reduction candidate for 3,4 E2: 3,4 # 13 pairs F2: 3,4,9 # reduction candidate for 3,4 F2: 3,4 => CTR * 347612.5.81659..72952.8764127..514.646.72.513135.4672.5.143.2676.427.135723165..4 * RESTART * PAIR D3: 3,4 COL D D4: 3,4,8,9 # reduction candidate for 3,4 D4: 3,4 # 17 pairs D7: 3,4,8,9 # reduction candidate for 3,4 D7: 3,4 => CTR * 347612.5.8165.9.72952.876.127..51...46.72351.135...72.5.1...2.76..27.1.572.1.5... * RESTART * PAIR D3: 3,4 COL D D4: 3,4,8,9 # reduction candidate for 3,4 D4: 8,9 => CTR * 347612.5.81654937295238764127.851..34687235191354..72.5.1..42.76.42781357231.5... * PAIR RESTART * PAIR G1: 8,9 COL G G4: 8,9,3,4 # reduction candidate for 8,9 G4: 8,9 # 19 pairs G9: 8,9,3,4 # reduction candidate for 8,9 G9: 8,9 # 19 pairs * PAIR I1: 8,9 COL I I4: 8,9,3,4,6 # reduction candidate for 8,9 I4: 8,9 => CTR * 347612.5.8165.9.72952.876.127..51.6.46.72.513135...7245.1...2.76..27.19572.195.86 I5: 8,9,3 # reduction candidate for 8,9 I5: 8,9 => CTR * 347612.5.81654937295238764127.451..346.72351.1358967245819342676942781357231654.. I5: 3 => SOLVED * 347612859816539472952487631278351964469728513135946728591863247683274195724195386 * DURATION: 0:00:11.532183 START: 16:23:16.679128 END: 16:23:28.211311 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top500-396-base-pr-001.dot * REASONING * DIS # F2: 3,4 => CTR => F2: 9 * DIS F2: 9 # D7: 3,4 => CTR => D7: 8,9 * DIS F2: 9 + D7: 8,9 # D4: 8,9 => CTR => D4: 3,4 * DIS F2: 9 + D7: 8,9 + D4: 3,4 # I4: 8,9 => CTR => I4: 3,4,6 * DIS F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 # I5: 8,9 => CTR => I5: 3 * PRF F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 + I5: 3 => SOL * STA F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 + I5: 3 * CNT 6 HDP CHAINS / 10 HYP OPENED
Header Info
Top 500 Minimum 17 396 solution: 347612859816539472952487631278351964469728513135946728591863247683274195724195386 info: 67103 FNBXYK S8.f 29984 http://www.sfsudoku.com/su17ExtremeDiff500.txt from http://www.minimumsudoku.com/
Solution
position: 347612859816539472952487631278351964469728513135946728591863247683274195724195386 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 # E2: 3,4 => UNS * DIS # F2: 3,4 => CTR => F2: 9 * INC # F2: 9 => UNS * INC # D4: 3,4 => UNS * DIS # D7: 3,4 => CTR => D7: 8,9 * INC # D7: 8,9 => UNS * INC # G4: 8,9 => UNS * INC # G9: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 3,4,6 * INC # I4: 3,4,6 => UNS * DIS # I5: 8,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * PRF # I6: 8,9 => SOL * DIS # I6: 4 => CTR => I6: 8,9 * DIS # I9: 8,9 => CTR => I9: 3,4,6 * INC # I9: 3,4,6 => UNS * INC # E2: 3,4 => UNS * DIS # F2: 3,4 => CTR => F2: 9 * INC # F2: 9 => UNS * INC # G4: 3,4 => UNS * INC # G9: 3,4 => UNS * DIS # H4: 3,4 => CTR => H4: 6,8,9 * INC # H4: 6,8,9 => UNS * INC # H7: 3,4 => UNS * INC # H8: 3,4 => UNS * DIS # H9: 3,4 => CTR => H9: 6,8,9 * INC # H9: 6,8,9 => UNS * DIS # D4: 8,9 => CTR => D4: 3,4 * INC # D4: 3,4 => UNS * INC # G4: 8,9 => UNS * INC # H4: 8,9 => UNS * DIS # I4: 8,9 => CTR => I4: 3,4,6 * INC # I4: 3,4,6 => UNS * PRF # F5: 8,9 => SOL * DIS # F5: 3 => CTR => F5: 8,9 * DIS # I5: 8,9 => CTR => I5: 3 * PRF # I5: 3 => SOL * INC # D7: 8,9 => UNS * DIS # F7: 8,9 => CTR => F7: 3,4,6 * INC # F7: 3,4,6 => UNS * INC # F8: 8,9 => UNS * INC # F8: 3,4 => UNS * INC # F8: 3,4 => UNS * INC # H8: 3,4 => UNS * DIS # E9: 3,4 => CTR => E9: 6,9 * INC # E9: 6,9 => UNS * INC # G9: 3,4 => UNS * DIS # H9: 3,4 => CTR => H9: 6,8,9 * INC # H9: 6,8,9 => UNS * INC # I9: 3,4 => UNS * CNT 50 HDP CHAINS / 50 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E2: 3,4 => UNS * DIS # F2: 3,4 => CTR => F2: 9 * INC F2: 9 # D4: 3,4 => UNS * DIS F2: 9 # D7: 3,4 => CTR => D7: 8,9 * INC F2: 9 + D7: 8,9 # D4: 3,4 => UNS * DIS F2: 9 + D7: 8,9 # D4: 8,9 => CTR => D4: 3,4 * INC F2: 9 + D7: 8,9 + D4: 3,4 # G4: 8,9 => UNS * INC F2: 9 + D7: 8,9 + D4: 3,4 # G9: 8,9 => UNS * DIS F2: 9 + D7: 8,9 + D4: 3,4 # I4: 8,9 => CTR => I4: 3,4,6 * DIS F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 # I5: 8,9 => CTR => I5: 3 * PRF F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 + I5: 3 => SOL * STA F2: 9 + D7: 8,9 + D4: 3,4 + I4: 3,4,6 + I5: 3 * CNT 11 HDP CHAINS / 10 HYP OPENED