Analysis of zz-www.sudokuwiki.org-0266-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=266
level: medium
position: 4..8.5..9..6.7.......4..13..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 initial
Autosolve
position: 4..8.5..9..6.7..5....4..13..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E1: 2,6 => CTR => E1: 1,3 * DIS # B5: 2,9 => CTR => B5: 4,5 * CNT 2 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E1: 2,6 => CTR => E1: 1,3 * DIS E1: 1,3 # B5: 2,9 => CTR => B5: 4,5 * DIS E1: 1,3 + B5: 4,5 # D2: 1,2 => CTR => D2: 9 * DIS E1: 1,3 + B5: 4,5 + D2: 9 # B1: 2,7 => CTR => B1: 1,3 * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # F8: 8 => CTR => F8: 1,3 * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 # G2: 2 => CTR => G2: 4,8 * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 # I8: 1,3,6 => CTR => I8: 4,8 * PRF E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 # G7: 8 => SOL * STA E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 + G7: 8 * CNT 8 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 4..8.5..9..6.7.......4..13..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 | initial |
| 4..8.5..9..6.7..5....4..13..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 | autosolve |
| 417835629326971458598426137683142795241759386759368241965214873872693514134587962 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E3: 2,6 F3: 6,9 I2: 4,8 C6: 2,9 D7: 1,2 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B2: 1.. / B1 = 1 => 5 pairs (_) / B2 = 1 => 8 pairs (_) H4,I6: 1.. / H4 = 1 => 14 pairs (_) / I6 = 1 => 8 pairs (_) B1,E1: 1.. / B1 = 1 => 5 pairs (_) / E1 = 1 => 8 pairs (_) H5,G6: 2.. / H5 = 2 => 7 pairs (_) / G6 = 2 => 0 pairs (*) H1,H5: 2.. / H1 = 2 => 0 pairs (*) / H5 = 2 => 0 pairs (X) E1,F2: 3.. / E1 = 3 => 10 pairs (_) / F2 = 3 => 5 pairs (_) A4,C4: 3.. / A4 = 3 => 14 pairs (_) / C4 = 3 => 11 pairs (_) I7,I8: 3.. / I7 = 3 => 5 pairs (_) / I8 = 3 => 11 pairs (_) F2,F8: 3.. / F2 = 3 => 5 pairs (_) / F8 = 3 => 10 pairs (_) G2,I2: 4.. / G2 = 4 => 22 pairs (_) / I2 = 4 => 8 pairs (_) C4,B5: 4.. / C4 = 4 => 14 pairs (_) / B5 = 4 => 7 pairs (_) E4,E5: 4.. / E4 = 4 => 7 pairs (_) / E5 = 4 => 14 pairs (_) I8,G9: 4.. / I8 = 4 => 22 pairs (_) / G9 = 4 => 8 pairs (_) C4,E4: 4.. / C4 = 4 => 14 pairs (_) / E4 = 4 => 7 pairs (_) B5,E5: 4.. / B5 = 4 => 7 pairs (_) / E5 = 4 => 14 pairs (_) G2,G9: 4.. / G2 = 4 => 22 pairs (_) / G9 = 4 => 8 pairs (_) I2,I8: 4.. / I2 = 4 => 8 pairs (_) / I8 = 4 => 22 pairs (_) A3,B3: 5.. / A3 = 5 => 7 pairs (_) / B3 = 5 => 19 pairs (_) E5,E6: 5.. / E5 = 5 => 7 pairs (_) / E6 = 5 => 13 pairs (_) B6,E6: 5.. / B6 = 5 => 7 pairs (_) / E6 = 5 => 13 pairs (_) A3,A5: 5.. / A3 = 5 => 7 pairs (_) / A5 = 5 => 19 pairs (_) A4,A5: 6.. / A4 = 6 => 11 pairs (_) / A5 = 6 => 13 pairs (_) D4,D5: 7.. / D4 = 7 => 7 pairs (_) / D5 = 7 => 6 pairs (_) B8,C8: 7.. / B8 = 7 => 5 pairs (_) / C8 = 7 => 6 pairs (_) * DURATION: 0:00:19.521316 START: 14:13:13.540045 END: 14:13:33.061361 2019-04-28 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D7,E3,F3,I2) * 4..8.5..9..6.7..5....4..13..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 * PAIR E3: 2,6 BLK 2 E1: 2,6,1,3 # reduction candidate for 2,6 E1: 2,6 => CTR * 413865279.26173.5.57842913638.7.2..56.19.83277.23.6.4.8652347912.7691583139587462 E1: 1,3 # 7 pairs * PAIR F3: 6,9 COL F F5: 6,9,8 # reduction candidate for 6,9 F5: 6,9 # 8 pairs F6: 6,9,1,8 # reduction candidate for 6,9 F6: 6,9 # 10 pairs * PAIR I2: 4,8 BLK 3 G2: 4,8,2 # reduction candidate for 4,8 G2: 2 # 20 pairs G2: 4,8 # 8 pairs * PAIR I2: 4,8 COL I I8: 4,8,1,3,6 # reduction candidate for 4,8 I8: 4,8 # 25 pairs I8: 1,3,6 # 8 pairs * PAIR C6: 2,9 BLK 4 A5: 2,9,5,6 # reduction candidate for 2,9 A5: 2,9 # 12 pairs B5: 2,9,4,5 # reduction candidate for 2,9 B5: 2,9 => CTR * 4..8.5..9..6.7..5..5.4..13.384..2..5..1.4.3..7..35..4..65..4.......9.5..1..5.7..2 B5: 4,5 # 6 pairs B6: 2,9,5 # reduction candidate for 2,9 B6: 2,9 # 13 pairs * PAIR C6: 2,9 ROW 6 G6: 2,9,6,8 # reduction candidate for 2,9 G6: 6,8 # 10 pairs G6: 2,9 # 8 pairs * PAIR C6: 2,9 COL C C3: 2,9,7,8 # reduction candidate for 2,9 C3: 2,9 # 12 pairs C3: 7,8 # 6 pairs * PAIR D7: 1,2 BLK 8 E7: 1,2,3,8 # reduction candidate for 1,2 E7: 1,2 # 10 pairs D8: 1,2,6 # reduction candidate for 1,2 D8: 1,2 # 23 pairs * PAIR D7: 1,2 COL D D2: 1,2,9 # reduction candidate for 1,2 D2: 1,2 # 11 pairs D2: 9 # 8 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0266-base-pr-000.dot * REASONING * DIS # E1: 2,6 => CTR => E1: 1,3 * DIS # B5: 2,9 => CTR => B5: 4,5 * CNT 2 HDP CHAINS / 20 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C6,D7,E3,F3,I2) * 4..8.5..9..6.7..5....4..13..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 * PAIR E3: 2,6 BLK 2 E1: 2,6,1,3 # reduction candidate for 2,6 E1: 2,6 => CTR * 413865279.26173.5.57842913638.7.2..56.19.83277.23.6.4.8652347912.7691583139587462 * PAIR F3: 6,9 COL F F5: 6,9,8 # reduction candidate for 6,9 F5: 6,9 # 11 pairs F6: 6,9,1,8 # reduction candidate for 6,9 F6: 6,9 # 13 pairs * PAIR I2: 4,8 BLK 3 G2: 4,8,2 # reduction candidate for 4,8 G2: 2 # 23 pairs G2: 4,8 # 11 pairs * PAIR I2: 4,8 COL I I8: 4,8,1,3,6 # reduction candidate for 4,8 I8: 4,8 # 18 pairs I8: 1,3,6 # 10 pairs * PAIR C6: 2,9 BLK 4 A5: 2,9,5,6 # reduction candidate for 2,9 A5: 2,9 # 12 pairs B5: 2,9,4,5 # reduction candidate for 2,9 B5: 2,9 => CTR * 4..8.5..9..6.7..5..5.4..13.384..2..5..1.4.3..7..35..4..65..4.......9.5..1..5.7..2 B6: 2,9,5 # reduction candidate for 2,9 B6: 2,9 # 15 pairs * PAIR C6: 2,9 ROW 6 G6: 2,9,6,8 # reduction candidate for 2,9 G6: 6,8 # 13 pairs G6: 2,9 # 10 pairs * PAIR C6: 2,9 COL C C3: 2,9,7,8 # reduction candidate for 2,9 C3: 2,9 # 14 pairs C3: 7,8 # 9 pairs * PAIR RESTART * PAIR C6: 2,9 BLK 4 A5: 2,9,5,6 # reduction candidate for 2,9 A5: 2,9 # 12 pairs B6: 2,9,5 # reduction candidate for 2,9 B6: 2,9 # 15 pairs * PAIR C6: 2,9 ROW 6 G6: 2,9,6,8 # reduction candidate for 2,9 G6: 6,8 # 13 pairs G6: 2,9 # 10 pairs * PAIR C6: 2,9 COL C C3: 2,9,7,8 # reduction candidate for 2,9 C3: 2,9 # 14 pairs C3: 7,8 # 9 pairs * PAIR D7: 1,2 BLK 8 E7: 1,2,3,8 # reduction candidate for 1,2 E7: 1,2 # 17 pairs D8: 1,2,6 # reduction candidate for 1,2 D8: 1,2 # 30 pairs * PAIR D7: 1,2 COL D D2: 1,2,9 # reduction candidate for 1,2 D2: 1,2 => CTR * 4..8.56798.6.7.254...426138.8...2915..19.83277..3.18463652.4.9.2..69.58.1..5.7462 * PAIR RESTART * PAIR D7: 1,2 BLK 8 D8: 1,2,6 # reduction candidate for 1,2 D8: 1,2 # 30 pairs D8: 6 # 19 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (B5,C6,D5,D7,E1,F2,F5,I2,I3) * 4..8.5..9..697..5....42613..8...2..5..1...3..7..3...4..65..4.......9.5..1..5.7..2 * PAIR E1: 1,3 ROW 1 B1: 1,3,2,7 # reduction candidate for 1,3 B1: 2,7 => CTR * 4.3815..9.169738545.842613738...2..56.17.93287..3...4.9652.47..8.7.915..1..5.7..2 * PAIR E1: 1,3 COL E E7: 1,3,8 # reduction candidate for 1,3 E7: 8 # 15 pairs E7: 1,3 # 15 pairs * PAIR RESTART * PAIR E1: 1,3 COL E E7: 1,3,8 # reduction candidate for 1,3 E7: 8 # 15 pairs E7: 1,3 # 15 pairs * PAIR F2: 1,3 ROW 2 B2: 1,3,2 # reduction candidate for 1,3 B2: 2 # 18 pairs B2: 1,3 # 14 pairs * PAIR F2: 1,3 COL F F8: 1,3,8 # reduction candidate for 1,3 F8: 8 => CTR * 43.8156.9.16973.54..842613738.64271564175932.7..3.1.4..65.34.......985631.3567482 * PAIR RESTART * PAIR F2: 1,3 ROW 2 B2: 1,3,2 # reduction candidate for 1,3 B2: 2 # 18 pairs B2: 1,3 # 16 pairs * PAIR I2: 4,8 BLK 3 G2: 4,8,2 # reduction candidate for 4,8 G2: 2 => CTR * 4.28.5..98.697.254...426138.8...2..5..1..832.7293..84..65..4.......9.5..1..5.74.2 * PAIR I2: 4,8 COL I I8: 4,8,1,3,6 # reduction candidate for 4,8 I8: 1,3,6 => CTR * 417835269326971854...426137.83.42..5.4175.32875231..4..65..4....74.935.61..5674.2 * PAIR RESTART * LEVEL 0 PASS 1 ROUND 3 (AUTO SOLVE) (A5,A7,A8,C6,C8,C9,F5,F6,G1,G2,G4,G6,H1,H4,H5,H9,I2,I8) * 417835..9326971.5.598426137683142..5.4175.3.675.36..41.65214..3.7.69351.13.587..2 * PAIR G4: 7,9 COL G G7: 7,9,8 # reduction candidate for 7,9 G7: 8 => SOLVED * 417835629326971458598426137683142795241759386759368241965214873872693514134587962 * DURATION: 0:00:25.006702 START: 14:13:42.154626 END: 14:14:07.161328 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0266-base-pr-001.dot * REASONING * DIS # E1: 2,6 => CTR => E1: 1,3 * DIS E1: 1,3 # B5: 2,9 => CTR => B5: 4,5 * DIS E1: 1,3 + B5: 4,5 # D2: 1,2 => CTR => D2: 9 * DIS E1: 1,3 + B5: 4,5 + D2: 9 # B1: 2,7 => CTR => B1: 1,3 * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # F8: 8 => CTR => F8: 1,3 * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 # G2: 2 => CTR => G2: 4,8 * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 # I8: 1,3,6 => CTR => I8: 4,8 * PRF E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 # G7: 8 => SOL * STA E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 + G7: 8 * CNT 8 HDP CHAINS / 43 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=266
Solution
position: 417835629326971458598426137683142795241759386759368241965214873872693514134587962 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 # E1: 2,6 => CTR => E1: 1,3 * INC # E1: 1,3 => UNS * INC # F5: 6,9 => UNS * INC # F6: 6,9 => UNS * INC # G2: 4,8 => UNS * INC # G2: 2 => UNS * INC # I8: 4,8 => UNS * INC # I8: 1,3,6 => UNS * INC # A5: 2,9 => UNS * DIS # B5: 2,9 => CTR => B5: 4,5 * INC # B5: 4,5 => UNS * INC # B6: 2,9 => UNS * INC # G6: 2,9 => UNS * INC # G6: 6,8 => UNS * INC # C3: 2,9 => UNS * INC # C3: 7,8 => UNS * INC # E7: 1,2 => UNS * INC # D8: 1,2 => UNS * INC # D2: 1,2 => UNS * INC # D2: 9 => UNS * CNT 20 HDP CHAINS / 20 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E1: 2,6 => CTR => E1: 1,3 * INC E1: 1,3 # F5: 6,9 => UNS * INC E1: 1,3 # F6: 6,9 => UNS * INC E1: 1,3 # G2: 4,8 => UNS * INC E1: 1,3 # G2: 2 => UNS * INC E1: 1,3 # I8: 4,8 => UNS * INC E1: 1,3 # I8: 1,3,6 => UNS * INC E1: 1,3 # A5: 2,9 => UNS * DIS E1: 1,3 # B5: 2,9 => CTR => B5: 4,5 * INC E1: 1,3 + B5: 4,5 # B6: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # G6: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # G6: 6,8 => UNS * INC E1: 1,3 + B5: 4,5 # C3: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # C3: 7,8 => UNS * INC E1: 1,3 + B5: 4,5 # A5: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # B6: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # G6: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # G6: 6,8 => UNS * INC E1: 1,3 + B5: 4,5 # C3: 2,9 => UNS * INC E1: 1,3 + B5: 4,5 # C3: 7,8 => UNS * INC E1: 1,3 + B5: 4,5 # E7: 1,2 => UNS * INC E1: 1,3 + B5: 4,5 # D8: 1,2 => UNS * DIS E1: 1,3 + B5: 4,5 # D2: 1,2 => CTR => D2: 9 * INC E1: 1,3 + B5: 4,5 + D2: 9 # D8: 1,2 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 # D8: 6 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 # B1: 1,3 => UNS * DIS E1: 1,3 + B5: 4,5 + D2: 9 # B1: 2,7 => CTR => B1: 1,3 * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # E7: 1,3 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # E7: 8 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # E7: 1,3 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # E7: 8 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # B2: 1,3 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # B2: 2 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # F8: 1,3 => UNS * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 # F8: 8 => CTR => F8: 1,3 * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 # B2: 1,3 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 # B2: 2 => UNS * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 # G2: 4,8 => UNS * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 # G2: 2 => CTR => G2: 4,8 * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 # I8: 4,8 => UNS * DIS E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 # I8: 1,3,6 => CTR => I8: 4,8 * INC E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 # G7: 7,9 => UNS * PRF E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 # G7: 8 => SOL * STA E1: 1,3 + B5: 4,5 + D2: 9 + B1: 1,3 + F8: 1,3 + G2: 4,8 + I8: 4,8 + G7: 8 * CNT 43 HDP CHAINS / 43 HYP OPENED