Analysis of zz-www.sudokuwiki.org-0095-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=95
level: medium
position: ..47...2.....9.4.......6.186....98.5.........8.72....313.9.......5.2.....4...71.. initial
Autosolve
position: ..47...2.....924.......6.186....98.54.....2.18.72....313.9.......5.2.....4...71.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # G1: 6,9 => CTR => G1: 3,5 * DIS # I8: 6,9 => CTR => I8: 4 * DIS # G1: 6,9 => CTR => G1: 3,5 * CNT 3 HDP CHAINS / 32 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # G1: 6,9 => CTR => G1: 3,5 * DIS G1: 3,5 # I8: 6,9 => CTR => I8: 4 * DIS G1: 3,5 + I8: 4 # I9: 2 => CTR => I9: 6,9 * DIS G1: 3,5 + I8: 4 + I9: 6,9 # G8: 6,9 => CTR => G8: 3 * PRF G1: 3,5 + I8: 4 + I9: 6,9 + G8: 3 => SOL * STA G1: 3,5 + I8: 4 + I9: 6,9 + G8: 3 * CNT 5 HDP CHAINS / 18 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..47...2.....9.4.......6.186....98.5.........8.72....313.9.......5.2.....4...71.. | initial |
| ..47...2.....924.......6.186....98.54.....2.18.72....313.9.......5.2.....4...71.. | autosolve |
| 984713526561892437372456918623179845459368271817245693136984752795621384248537169 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) C3: 2,9 I1: 6,9 I2: 6,7 B4: 1,2 B5: 5,9 C5: 3,9 H4: 4,7 G6: 6,9 A8: 7,9 A9: 2,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D8,F8: 1.. / D8 = 1 => 12 pairs (_) / F8 = 1 => 11 pairs (_) C2,C4: 1.. / C2 = 1 => 18 pairs (_) / C4 = 1 => 14 pairs (_) B4,C4: 2.. / B4 = 2 => 11 pairs (_) / C4 = 2 => 0 pairs (X) I7,I9: 2.. / I7 = 2 => 13 pairs (_) / I9 = 2 => 15 pairs (_) C7,I7: 2.. / C7 = 2 => 15 pairs (_) / I7 = 2 => 13 pairs (_) A3,A9: 2.. / A3 = 2 => 14 pairs (_) / A9 = 2 => 12 pairs (_) B3,B4: 2.. / B3 = 2 => 0 pairs (X) / B4 = 2 => 11 pairs (_) C4,C5: 3.. / C4 = 3 => 18 pairs (_) / C5 = 3 => 14 pairs (_) D3,E3: 4.. / D3 = 4 => 13 pairs (_) / E3 = 4 => 11 pairs (_) H4,H6: 4.. / H4 = 4 => 12 pairs (_) / H6 = 4 => 11 pairs (_) I7,I8: 4.. / I7 = 4 => 0 pairs (X) / I8 = 4 => 10 pairs (_) B5,B6: 5.. / B5 = 5 => 11 pairs (_) / B6 = 5 => 14 pairs (_) I2,G3: 7.. / I2 = 7 => 11 pairs (_) / G3 = 7 => 0 pairs (X) E4,E5: 7.. / E4 = 7 => 12 pairs (_) / E5 = 7 => 11 pairs (_) H4,H5: 7.. / H4 = 7 => 11 pairs (_) / H5 = 7 => 12 pairs (_) A8,B8: 7.. / A8 = 7 => 10 pairs (_) / B8 = 7 => 19 pairs (_) G7,I7: 7.. / G7 = 7 => 11 pairs (_) / I7 = 7 => 0 pairs (X) A2,I2: 7.. / A2 = 7 => 0 pairs (X) / I2 = 7 => 11 pairs (_) E4,H4: 7.. / E4 = 7 => 12 pairs (_) / H4 = 7 => 11 pairs (_) E5,H5: 7.. / E5 = 7 => 11 pairs (_) / H5 = 7 => 12 pairs (_) B3,B8: 7.. / B3 = 7 => 10 pairs (_) / B8 = 7 => 19 pairs (_) G3,G7: 7.. / G3 = 7 => 0 pairs (X) / G7 = 7 => 11 pairs (_) I2,I7: 7.. / I2 = 7 => 11 pairs (_) / I7 = 7 => 0 pairs (X) * DURATION: 0:00:30.715375 START: 05:11:06.647606 END: 05:11:37.362981 2017-05-01 * CP COUNT: (23) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B4,B5,C3,C5,G6,H4,I1,I2) * ..47...2.....924.......6.186....98.54.....2.18.72....313.9.......5.2.....4...71.. * PAIR C3: 2,9 BLK 1 A3: 2,9,3,5,7 # reduction candidate for 2,9 A3: 2,9 # 13 pairs B3: 2,9,7 # reduction candidate for 2,9 B3: 2,9 # 19 pairs * PAIR C3: 2,9 COL C C9: 2,9,6,8 # reduction candidate for 2,9 C9: 2,9 # 19 pairs C9: 6,8 # 11 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,3,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 3847...2.561892437..23465186234.98.54596832718172....313.9..7.2..5.2.3.424.5371.. G1: 3,5 # 11 pairs * PAIR I1: 6,9 COL I I8: 6,9,4 # reduction candidate for 6,9 I8: 6,9 => CTR * ..47.3.2.3..592467279..6.18621..98.54.3...2.18.72....31329..7.47.5.2....94...71.2 I8: 4 # 10 pairs I9: 6,9,2 # reduction candidate for 6,9 I9: 6,9 # 13 pairs * PAIR I2: 6,7 COL I I7: 6,7,2,4 # reduction candidate for 6,7 I7: 6,7 # 15 pairs I7: 2,4 # 12 pairs * PAIR B4: 1,2 BLK 4 C4: 1,2,3 # reduction candidate for 1,2 C4: 3 # 18 pairs C4: 1,2 # 14 pairs * PAIR B5: 5,9 BLK 4 B6: 5,9,1 # reduction candidate for 5,9 B6: 1 # 18 pairs B6: 5,9 # 14 pairs * PAIR H4: 4,7 ROW 4 E4: 4,7,1,3 # reduction candidate for 4,7 E4: 1,3 # 13 pairs E4: 4,7 # 12 pairs * PAIR G6: 6,9 BLK 6 H5: 6,9,7 # reduction candidate for 6,9 H5: 6,9 # 11 pairs H6: 6,9,4 # reduction candidate for 6,9 H6: 6,9 # 12 pairs * PAIR G6: 6,9 COL G G1: 6,9,3,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 3847...2.561892437..23465186234.98.54596832718172....313.9..7.2..5.2.3.424.5371.. G1: 3,5 # 11 pairs G8: 6,9,3 # reduction candidate for 6,9 G8: 6,9 # 21 pairs * PAIR A8: 7,9 BLK 7 B8: 7,9,6,8 # reduction candidate for 7,9 B8: 7,9 # 18 pairs B8: 6,8 # 14 pairs * PAIR A8: 7,9 COL A A3: 7,9,2,3,5 # reduction candidate for 7,9 A3: 7,9 # 15 pairs A3: 2,3,5 # 10 pairs * PAIR A9: 2,9 BLK 7 C9: 2,9,6,8 # reduction candidate for 2,9 C9: 2,9 # 19 pairs C9: 6,8 # 11 pairs * PAIR A9: 2,9 ROW 9 I9: 2,9,6 # reduction candidate for 2,9 I9: 6 # 15 pairs I9: 2,9 # 12 pairs * PAIR A9: 2,9 COL A A3: 2,9,3,5,7 # reduction candidate for 2,9 A3: 2,9 # 13 pairs A3: 3,5,7 # 12 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0095-base-pr-000.dot * REASONING * DIS # G1: 6,9 => CTR => G1: 3,5 * DIS # I8: 6,9 => CTR => I8: 4 * DIS # G1: 6,9 => CTR => G1: 3,5 * CNT 3 HDP CHAINS / 32 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A8,A9,B4,B5,C3,C5,G6,H4,I1,I2) * ..47...2.....924.......6.186....98.54.....2.18.72....313.9.......5.2.....4...71.. * PAIR C3: 2,9 BLK 1 A3: 2,9,3,5,7 # reduction candidate for 2,9 A3: 2,9 # 13 pairs B3: 2,9,7 # reduction candidate for 2,9 B3: 2,9 # 19 pairs * PAIR C3: 2,9 COL C C9: 2,9,6,8 # reduction candidate for 2,9 C9: 2,9 # 19 pairs C9: 6,8 # 11 pairs * PAIR I1: 6,9 BLK 3 G1: 6,9,3,5 # reduction candidate for 6,9 G1: 6,9 => CTR * 3847...2.561892437..23465186234.98.54596832718172....313.9..7.2..5.2.3.424.5371.. * PAIR I1: 6,9 COL I I8: 6,9,4 # reduction candidate for 6,9 I8: 6,9 => CTR * .647.3529.18.92467279..6.18621..98.54.36..2.18.72..6.313296.7.4785124936946837152 I9: 6,9,2 # reduction candidate for 6,9 I9: 6,9 # 14 pairs * RESTART * PAIR I1: 6,9 COL I I9: 6,9,2 # reduction candidate for 6,9 I9: 2 => CTR * .6471..29..8.924..279..6.18621..98.54.3...2.18.72....31329..7.6785621..4946..71.2 * PAIR RESTART * PAIR B4: 1,2 BLK 4 C4: 1,2,3 # reduction candidate for 1,2 C4: 3 # 19 pairs C4: 1,2 # 18 pairs * PAIR B5: 5,9 BLK 4 B6: 5,9,1 # reduction candidate for 5,9 B6: 1 # 19 pairs B6: 5,9 # 18 pairs * PAIR H4: 4,7 ROW 4 E4: 4,7,1,3 # reduction candidate for 4,7 E4: 4,7 # 17 pairs E4: 1,3 # 17 pairs * PAIR G6: 6,9 BLK 6 H5: 6,9,7 # reduction candidate for 6,9 H5: 6,9 # 15 pairs H6: 6,9,4 # reduction candidate for 6,9 H6: 6,9 # 17 pairs * PAIR G6: 6,9 COL G G8: 6,9,3 # reduction candidate for 6,9 G8: 6,9 => CTR * .64718.29.18.92467.7...6.18621..98.54.3.6527185724.6.31369..7.2785621934.4...71.6 G8: 3 => SOLVED * 984713526561892437372456918623179845459368271817245693136984752795621384248537169 * DURATION: 0:00:18.878248 START: 05:12:02.685824 END: 05:12:21.564072 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0095-base-pr-001.dot * REASONING * DIS # G1: 6,9 => CTR => G1: 3,5 * DIS G1: 3,5 # I8: 6,9 => CTR => I8: 4 * DIS G1: 3,5 + I8: 4 # I9: 2 => CTR => I9: 6,9 * DIS G1: 3,5 + I8: 4 + I9: 6,9 # G8: 6,9 => CTR => G8: 3 * PRF G1: 3,5 + I8: 4 + I9: 6,9 + G8: 3 => SOL * STA G1: 3,5 + I8: 4 + I9: 6,9 + G8: 3 * CNT 5 HDP CHAINS / 18 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=95
Solution
position: 984713526561892437372456918623179845459368271817245693136984752795621384248537169 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 # A3: 2,9 => UNS * INC # B3: 2,9 => UNS * INC # C9: 2,9 => UNS * INC # C9: 6,8 => UNS * DIS # G1: 6,9 => CTR => G1: 3,5 * INC # G1: 3,5 => UNS * DIS # I8: 6,9 => CTR => I8: 4 * INC # I8: 4 => UNS * INC # I9: 6,9 => UNS * INC # I7: 6,7 => UNS * INC # I7: 2,4 => UNS * INC # C4: 1,2 => UNS * INC # C4: 3 => UNS * INC # B6: 5,9 => UNS * INC # B6: 1 => UNS * INC # E4: 4,7 => UNS * INC # E4: 1,3 => UNS * INC # H5: 6,9 => UNS * INC # H6: 6,9 => UNS * DIS # G1: 6,9 => CTR => G1: 3,5 * INC # G1: 3,5 => UNS * INC # G8: 6,9 => UNS * INC # B8: 7,9 => UNS * INC # B8: 6,8 => UNS * INC # A3: 7,9 => UNS * INC # A3: 2,3,5 => UNS * INC # C9: 2,9 => UNS * INC # C9: 6,8 => UNS * INC # I9: 2,9 => UNS * INC # I9: 6 => UNS * INC # A3: 2,9 => UNS * INC # A3: 3,5,7 => UNS * CNT 32 HDP CHAINS / 32 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A3: 2,9 => UNS * INC # B3: 2,9 => UNS * INC # C9: 2,9 => UNS * INC # C9: 6,8 => UNS * DIS # G1: 6,9 => CTR => G1: 3,5 * DIS G1: 3,5 # I8: 6,9 => CTR => I8: 4 * INC G1: 3,5 + I8: 4 # I9: 6,9 => UNS * INC G1: 3,5 + I8: 4 # I9: 6,9 => UNS * DIS G1: 3,5 + I8: 4 # I9: 2 => CTR => I9: 6,9 * INC G1: 3,5 + I8: 4 + I9: 6,9 # C4: 1,2 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # C4: 3 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # B6: 5,9 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # B6: 1 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # E4: 4,7 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # E4: 1,3 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # H5: 6,9 => UNS * INC G1: 3,5 + I8: 4 + I9: 6,9 # H6: 6,9 => UNS * DIS G1: 3,5 + I8: 4 + I9: 6,9 # G8: 6,9 => CTR => G8: 3 * PRF G1: 3,5 + I8: 4 + I9: 6,9 + G8: 3 => SOL * STA G1: 3,5 + I8: 4 + I9: 6,9 + G8: 3 * CNT 19 HDP CHAINS / 18 HYP OPENED