Analysis of zz-www.sudokuwiki.org-0092-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=92
level: medium
position: ...8....2.....4.5..63...9....2.9...1..1...6..3...5.7....4...23..7.1.....5....7... initial
Autosolve
position: ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 7 => CTR => D3: 2,5 * DIS # H3: 4,8 => CTR => H3: 1,7 * DIS # A3: 1 => CTR => A3: 4,8 * DIS # I8: 4,8 => CTR => I8: 5,6,9 * DIS # H6: 4,8 => CTR => H6: 2,9 * DIS # B4: 5 => CTR => B4: 4,8 * DIS # H3: 4,8 => CTR => H3: 1,7 * CNT 7 HDP CHAINS / 24 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 7 => CTR => D3: 2,5 * DIS D3: 2,5 # H3: 4,8 => CTR => H3: 1,7 * DIS D3: 2,5 + H3: 1,7 # I8: 4,8 => CTR => I8: 5,6,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H6: 4,8 => CTR => H6: 2,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 5 => CTR => B4: 4,8 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 9 => CTR => I6: 4,8 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # F7: 6,8 => CTR => F7: 5,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 # E8: 6,8 => CTR => E8: 3,4 * PRF D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 # F8: 6,8 => SOL * STA D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 + F8: 6,8 * CNT 9 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...8....2.....4.5..63...9....2.9...1..1...6..3...5.7....4...23..7.1.....5....7... | initial |
| ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7... | autosolve |
| 145869372927314856863572914782693541451728693396451728614985237279136485538247169 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (6) F3: 2,5 I3: 4,8 G4: 3,5 H4: 4,8 I5: 3,5 E7: 6,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A7,B7: 1.. / A7 = 1 => 19 pairs (_) / B7 = 1 => 9 pairs (_) G9,H9: 1.. / G9 = 1 => 16 pairs (_) / H9 = 1 => 7 pairs (_) B1,B7: 1.. / B1 = 1 => 19 pairs (_) / B7 = 1 => 9 pairs (_) H5,H6: 2.. / H5 = 2 => 0 pairs (X) / H6 = 2 => 7 pairs (_) D9,E9: 2.. / D9 = 2 => 8 pairs (_) / E9 = 2 => 8 pairs (_) D6,H6: 2.. / D6 = 2 => 0 pairs (X) / H6 = 2 => 7 pairs (_) F3,F5: 2.. / F3 = 2 => 8 pairs (_) / F5 = 2 => 7 pairs (_) G4,I5: 3.. / G4 = 3 => 0 pairs (X) / I5 = 3 => 10 pairs (_) E8,F8: 3.. / E8 = 3 => 16 pairs (_) / F8 = 3 => 9 pairs (_) I2,I5: 3.. / I2 = 3 => 0 pairs (X) / I5 = 3 => 10 pairs (_) D3,F3: 5.. / D3 = 5 => 8 pairs (_) / F3 = 5 => 7 pairs (_) B4,B5: 5.. / B4 = 5 => 0 pairs (X) / B5 = 5 => 10 pairs (_) G4,I5: 5.. / G4 = 5 => 10 pairs (_) / I5 = 5 => 0 pairs (X) D7,F7: 5.. / D7 = 5 => 7 pairs (_) / F7 = 5 => 8 pairs (_) G8,I8: 5.. / G8 = 5 => 0 pairs (X) / I8 = 5 => 10 pairs (_) B4,G4: 5.. / B4 = 5 => 0 pairs (X) / G4 = 5 => 10 pairs (_) B5,I5: 5.. / B5 = 5 => 10 pairs (_) / I5 = 5 => 0 pairs (X) D3,D7: 5.. / D3 = 5 => 8 pairs (_) / D7 = 5 => 7 pairs (_) F3,F7: 5.. / F3 = 5 => 7 pairs (_) / F7 = 5 => 8 pairs (_) G4,G8: 5.. / G4 = 5 => 10 pairs (_) / G8 = 5 => 0 pairs (X) I5,I8: 5.. / I5 = 5 => 0 pairs (X) / I8 = 5 => 10 pairs (_) H1,I2: 6.. / H1 = 6 => 12 pairs (_) / I2 = 6 => 11 pairs (_) A4,C6: 6.. / A4 = 6 => 15 pairs (_) / C6 = 6 => 13 pairs (_) C6,D6: 6.. / C6 = 6 => 13 pairs (_) / D6 = 6 => 15 pairs (_) A4,A7: 6.. / A4 = 6 => 15 pairs (_) / A7 = 6 => 13 pairs (_) H1,H3: 7.. / H1 = 7 => 12 pairs (_) / H3 = 7 => 9 pairs (_) A4,A5: 7.. / A4 = 7 => 13 pairs (_) / A5 = 7 => 9 pairs (_) E1,H1: 7.. / E1 = 7 => 9 pairs (_) / H1 = 7 => 12 pairs (_) A4,D4: 7.. / A4 = 7 => 13 pairs (_) / D4 = 7 => 9 pairs (_) A2,A3: 8.. / A2 = 8 => 13 pairs (_) / A3 = 8 => 9 pairs (_) F1,D2: 9.. / F1 = 9 => 0 pairs (*) / D2 = 9 => 0 pairs (X) A2,D2: 9.. / A2 = 9 => 0 pairs (*) / D2 = 9 => 0 pairs (X) * DURATION: 0:00:43.276404 START: 05:07:49.005216 END: 05:08:32.281620 2017-05-01 * CP COUNT: (32) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E7,F3,G4,H4,I3,I5) * ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7... * PAIR F3: 2,5 BLK 2 D3: 2,5,7 # reduction candidate for 2,5 D3: 7 => CTR * ..58...72.279.4.56.637259..7.2698341..13726.53.645172.61458923727.1..5..53.2.7... D3: 2,5 # 8 pairs * PAIR I3: 4,8 BLK 3 H3: 4,8,1,7 # reduction candidate for 4,8 H3: 4,8 => CTR * ..58...728279.4.56.63...9..7.23965.1.51...6.33.6.517..6145892372791.3.6553...7.19 H3: 1,7 # 8 pairs * PAIR I3: 4,8 ROW 3 A3: 4,8,1 # reduction candidate for 4,8 A3: 1 => CTR * ..58...728279.4.56163...9..7.23965.1.51...6.33.6.517..6145892372791.3.6553...7.19 A3: 4,8 # 8 pairs * PAIR I3: 4,8 COL I I6: 4,8,9 # reduction candidate for 4,8 I6: 4,8 # 11 pairs I8: 4,8,5,6,9 # reduction candidate for 4,8 I8: 4,8 => CTR * 9.5873462827964153463.1.97865279.3.17913..6.53...517.9..4.8.23727.13.594539..7816 I8: 5,6,9 # 6 pairs I9: 4,8,6,9 # reduction candidate for 4,8 I9: 4,8 # 18 pairs * PAIR H4: 4,8 BLK 6 H5: 4,8,2,9 # reduction candidate for 4,8 H5: 4,8 # 18 pairs H6: 4,8,2,9 # reduction candidate for 4,8 H6: 4,8 => CTR * 1458.93.2927..4.5.8635.29.4..2.9...1.91..86253.62517.961498523727.1..5..53..2741. H6: 2,9 # 7 pairs I6: 4,8,9 # reduction candidate for 4,8 I6: 4,8 # 11 pairs * PAIR H4: 4,8 ROW 4 B4: 4,8,5 # reduction candidate for 4,8 B4: 5 => CTR * ..5873462.27964153463.1.9786527983417.13.26.53.9.517....4.8.23727.13.5..53...7.1. B4: 4,8 # 10 pairs * PAIR H4: 4,8 COL H H3: 4,8,1,7 # reduction candidate for 4,8 H3: 4,8 => CTR * ..58...728279.4.56.63...9..7.23965.1.51...6.33.6.517..6145892372791.3.6553...7.19 H3: 1,7 # 8 pairs H8: 4,8,6,9 # reduction candidate for 4,8 H8: 4,8 # 15 pairs H9: 4,8,1,6,9 # reduction candidate for 4,8 H9: 4,8 # 22 pairs * PAIR E7: 6,8 BLK 8 F7: 6,8,5,9 # reduction candidate for 6,8 F7: 6,8 # 23 pairs E8: 6,8,3,4 # reduction candidate for 6,8 E8: 6,8 # 20 pairs F8: 6,8,3,9 # reduction candidate for 6,8 F8: 6,8 # 26 pairs E9: 6,8,2,4 # reduction candidate for 6,8 E9: 6,8 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0092-base-pr-000.dot * REASONING * DIS # D3: 7 => CTR => D3: 2,5 * DIS # H3: 4,8 => CTR => H3: 1,7 * DIS # A3: 1 => CTR => A3: 4,8 * DIS # I8: 4,8 => CTR => I8: 5,6,9 * DIS # H6: 4,8 => CTR => H6: 2,9 * DIS # B4: 5 => CTR => B4: 4,8 * DIS # H3: 4,8 => CTR => H3: 1,7 * CNT 7 HDP CHAINS / 24 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (E7,F3,G4,H4,I3,I5) * ..58....2.27..4.5..63...9....2.9...1..1...6..3...517....4...23727.1.....53...7... * PAIR F3: 2,5 BLK 2 D3: 2,5,7 # reduction candidate for 2,5 D3: 7 => CTR * ..58...72.279.4.56.637259..7.2698341..13726.53.645172.61458923727.1..5..53.2.7... * PAIR I3: 4,8 BLK 3 H3: 4,8,1,7 # reduction candidate for 4,8 H3: 4,8 => CTR * ..58...728279.4.56163.7.9..7.23965.1.517..6.33.6.517..6145892372791.3.6553...7.19 * PAIR I3: 4,8 COL I I6: 4,8,9 # reduction candidate for 4,8 I6: 4,8 # 15 pairs I8: 4,8,5,6,9 # reduction candidate for 4,8 I8: 4,8 => CTR * 9.5873462827964153463.1.97865279.3.17913..6.53...517.9..4.8.23727.13.594539..7816 I9: 4,8,6,9 # reduction candidate for 4,8 I9: 4,8 # 20 pairs * PAIR RESTART * PAIR I3: 4,8 COL I I6: 4,8,9 # reduction candidate for 4,8 I6: 4,8 # 15 pairs I9: 4,8,6,9 # reduction candidate for 4,8 I9: 4,8 # 20 pairs * PAIR H4: 4,8 BLK 6 H5: 4,8,2,9 # reduction candidate for 4,8 H5: 4,8 # 21 pairs H6: 4,8,2,9 # reduction candidate for 4,8 H6: 4,8 => CTR * ..58.9..2927..4.5.8635.29.4..2.9...1.91..86253.62517.961498523727.1..5.653.627418 I6: 4,8,9 # reduction candidate for 4,8 I6: 4,8 # 15 pairs * PAIR H4: 4,8 ROW 4 B4: 4,8,5 # reduction candidate for 4,8 B4: 5 => CTR * ..5873462827964153463.1.9786527983.17.13..6.53...517....4.8.23727.13.54.53...781. * PAIR H4: 4,8 COL H H8: 4,8,6,9 # reduction candidate for 4,8 H8: 4,8 # 26 pairs H9: 4,8,1,6,9 # reduction candidate for 4,8 H9: 4,8 # 24 pairs * PAIR RESTART * PAIR H4: 4,8 BLK 6 I6: 4,8,9 # reduction candidate for 4,8 I6: 9 => CTR * .958....2.279.4.5..63...9..74239658195172864338645172961458.23727.1....553...7... * PAIR H4: 4,8 COL H H8: 4,8,6 # reduction candidate for 4,8 H8: 4,8 # 26 pairs H9: 4,8,1,6 # reduction candidate for 4,8 H9: 4,8 # 24 pairs * PAIR E7: 6,8 BLK 8 F7: 6,8,5,9 # reduction candidate for 6,8 F7: 6,8 => CTR * ..58....2.279.4.56.632.59....23965.1.517826933...5172...45..23727.1.9..553..27..9 E8: 6,8,3,4 # reduction candidate for 6,8 E8: 6,8 => CTR * ..58....2.27..4.56.63...9....23965.1.517.86.33.6.517..614.8.237279163..5538..7.69 F8: 6,8,3,9 # reduction candidate for 6,8 F8: 6,8 => SOLVED * 145869372927314856863572914782693541451728693396451728614985237279136485538247169 * DURATION: 0:00:22.635944 START: 05:08:51.798170 END: 05:09:14.434114 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0092-base-pr-001.dot * REASONING * DIS # D3: 7 => CTR => D3: 2,5 * DIS D3: 2,5 # H3: 4,8 => CTR => H3: 1,7 * DIS D3: 2,5 + H3: 1,7 # I8: 4,8 => CTR => I8: 5,6,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H6: 4,8 => CTR => H6: 2,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 5 => CTR => B4: 4,8 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 9 => CTR => I6: 4,8 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # F7: 6,8 => CTR => F7: 5,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 # E8: 6,8 => CTR => E8: 3,4 * PRF D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 # F8: 6,8 => SOL * STA D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 + F8: 6,8 * CNT 9 HDP CHAINS / 22 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=92
Solution
position: 145869372927314856863572914782693541451728693396451728614985237279136485538247169 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 # D3: 2,5 => UNS * DIS # D3: 7 => CTR => D3: 2,5 * DIS # H3: 4,8 => CTR => H3: 1,7 * INC # H3: 1,7 => UNS * INC # A3: 4,8 => UNS * DIS # A3: 1 => CTR => A3: 4,8 * INC # I6: 4,8 => UNS * DIS # I8: 4,8 => CTR => I8: 5,6,9 * INC # I8: 5,6,9 => UNS * INC # I9: 4,8 => UNS * INC # H5: 4,8 => UNS * DIS # H6: 4,8 => CTR => H6: 2,9 * INC # H6: 2,9 => UNS * INC # I6: 4,8 => UNS * INC # B4: 4,8 => UNS * DIS # B4: 5 => CTR => B4: 4,8 * DIS # H3: 4,8 => CTR => H3: 1,7 * INC # H3: 1,7 => UNS * INC # H8: 4,8 => UNS * INC # H9: 4,8 => UNS * INC # F7: 6,8 => UNS * INC # E8: 6,8 => UNS * INC # F8: 6,8 => UNS * INC # E9: 6,8 => UNS * CNT 24 HDP CHAINS / 24 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 2,5 => UNS * DIS # D3: 7 => CTR => D3: 2,5 * DIS D3: 2,5 # H3: 4,8 => CTR => H3: 1,7 * INC D3: 2,5 + H3: 1,7 # I6: 4,8 => UNS * DIS D3: 2,5 + H3: 1,7 # I8: 4,8 => CTR => I8: 5,6,9 * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # I9: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # I6: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # I9: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H5: 4,8 => UNS * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 # H6: 4,8 => CTR => H6: 2,9 * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # I6: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 4,8 => UNS * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 # B4: 5 => CTR => B4: 4,8 * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # H8: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # H9: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 4,8 => UNS * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 # I6: 9 => CTR => I6: 4,8 * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # H8: 4,8 => UNS * INC D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # H9: 4,8 => UNS * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 # F7: 6,8 => CTR => F7: 5,9 * DIS D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 # E8: 6,8 => CTR => E8: 3,4 * PRF D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 # F8: 6,8 => SOL * STA D3: 2,5 + H3: 1,7 + I8: 5,6,9 + H6: 2,9 + B4: 4,8 + I6: 4,8 + F7: 5,9 + E8: 3,4 + F8: 6,8 * CNT 22 HDP CHAINS / 22 HYP OPENED