Analysis of zz-www.sudokuwiki.org-0076-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=76
level: medium
position: ....792...5.8....37......6.2....1.9...8...1...6.3....4.7......29....7.3...614.... initial
Autosolve
position: ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614.... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C6: 1,9 => CTR => C6: 5,7 * DIS # C6: 1,5 => CTR => C6: 7,9 * CNT 2 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C6: 1,9 => CTR => C6: 5,7 * DIS C6: 5,7 # A1: 8 => CTR => A1: 4,6 * PRF C6: 5,7 + A1: 4,6 # F2: 2 => SOL * STA C6: 5,7 + A1: 4,6 + F2: 2 * CNT 3 HDP CHAINS / 8 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....792...5.8....37......6.2....1.9...8...1...6.3....4.7......29....7.3...614.... | initial |
| ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614.... | autosolve |
| 431679285659812743782534961245781396398426157167395824573968412914257638826143579 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) C4: 5,7 A5: 3,5 B5: 3,9 A6: 1,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E2,E3: 1.. / E2 = 1 => 6 pairs (_) / E3 = 1 => 8 pairs (_) A6,C6: 1.. / A6 = 1 => 4 pairs (_) / C6 = 1 => 0 pairs (X) H7,I8: 1.. / H7 = 1 => 9 pairs (_) / I8 = 1 => 8 pairs (_) H5,H6: 2.. / H5 = 2 => 4 pairs (_) / H6 = 2 => 6 pairs (_) B9,F9: 2.. / B9 = 2 => 5 pairs (_) / F9 = 2 => 9 pairs (_) E3,F3: 3.. / E3 = 3 => 6 pairs (_) / F3 = 3 => 5 pairs (_) A5,B5: 3.. / A5 = 3 => 5 pairs (_) / B5 = 3 => 0 pairs (X) C1,C7: 3.. / C1 = 3 => 5 pairs (_) / C7 = 3 => 9 pairs (_) E3,E7: 3.. / E3 = 3 => 6 pairs (_) / E7 = 3 => 5 pairs (_) D5,F5: 4.. / D5 = 4 => 9 pairs (_) / F5 = 4 => 5 pairs (_) C8,G8: 4.. / C8 = 4 => 9 pairs (_) / G8 = 4 => 6 pairs (_) A1,A2: 6.. / A1 = 6 => 8 pairs (_) / A2 = 6 => 11 pairs (_) I4,I5: 6.. / I4 = 6 => 7 pairs (_) / I5 = 6 => 4 pairs (_) G7,G8: 6.. / G7 = 6 => 5 pairs (_) / G8 = 6 => 10 pairs (_) A1,D1: 6.. / A1 = 6 => 8 pairs (_) / D1 = 6 => 11 pairs (_) G2,H2: 7.. / G2 = 7 => 8 pairs (_) / H2 = 7 => 11 pairs (_) C4,C6: 7.. / C4 = 7 => 0 pairs (X) / C6 = 7 => 7 pairs (_) D4,D5: 7.. / D4 = 7 => 7 pairs (_) / D5 = 7 => 8 pairs (_) E4,I4: 8.. / E4 = 8 => 5 pairs (_) / I4 = 8 => 14 pairs (_) B5,C6: 9.. / B5 = 9 => 5 pairs (_) / C6 = 9 => 0 pairs (X) D7,E7: 9.. / D7 = 9 => 4 pairs (_) / E7 = 9 => 0 pairs (X) G9,I9: 9.. / G9 = 9 => 7 pairs (_) / I9 = 9 => 11 pairs (_) C2,G2: 9.. / C2 = 9 => 7 pairs (_) / G2 = 9 => 14 pairs (_) C6,E6: 9.. / C6 = 9 => 0 pairs (X) / E6 = 9 => 5 pairs (_) B3,B5: 9.. / B3 = 9 => 0 pairs (X) / B5 = 9 => 5 pairs (_) D5,D7: 9.. / D5 = 9 => 0 pairs (X) / D7 = 9 => 4 pairs (_) I3,I9: 9.. / I3 = 9 => 7 pairs (_) / I9 = 9 => 11 pairs (_) * DURATION: 0:00:28.768385 START: 04:47:49.580147 END: 04:48:18.348532 2017-05-01 * CP COUNT: (27) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B5,C4) * ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614.... * PAIR C4: 5,7 BLK 4 C6: 5,7,1,9 # reduction candidate for 5,7 C6: 1,9 => CTR * ....792...598....37.....569247..139.3987.412.561392..4.7.9....29....7.3.8.614.957 C6: 5,7 # 6 pairs * PAIR C4: 5,7 ROW 4 D4: 5,7,6 # reduction candidate for 5,7 D4: 5,7 # 7 pairs I4: 5,7,6,8 # reduction candidate for 5,7 I4: 5,7 # 18 pairs * PAIR A5: 3,5 COL A A7: 3,5,1,4,8 # reduction candidate for 3,5 A7: 3,5 # 12 pairs A9: 3,5,8 # reduction candidate for 3,5 A9: 3,5 # 6 pairs * PAIR A6: 1,5 BLK 4 C6: 1,5,7,9 # reduction candidate for 1,5 C6: 1,5 => CTR * .3.6792..659812..37124358692475.139.398724156.6.398724.739.6..298.257631526143987 C6: 7,9 # 5 pairs * PAIR A6: 1,5 COL A A7: 1,5,3,4,8 # reduction candidate for 1,5 A7: 1,5 # 11 pairs A7: 3,4,8 # 4 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0076-base-pr-000.dot * REASONING * DIS # C6: 1,9 => CTR => C6: 5,7 * DIS # C6: 1,5 => CTR => C6: 7,9 * CNT 2 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,A6,B5,C4) * ....792...5.8....37......6.24...139...8...1...6.3....4.7......29....7.3...614.... * PAIR C4: 5,7 BLK 4 C6: 5,7,1,9 # reduction candidate for 5,7 C6: 1,9 => CTR * ....792...598....37.....569247..139.3987.412.561392..4.7.9....29....7.3.8.614.957 * PAIR C4: 5,7 ROW 4 D4: 5,7,6 # reduction candidate for 5,7 D4: 5,7 # 9 pairs I4: 5,7,6,8 # reduction candidate for 5,7 I4: 5,7 # 20 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A9,B9,C4,C6,F9) * ....792...5.8....37......6.24...139.398...1..16.39...4.7.9....29....7.3...614.... * PAIR A2: 4,6 BLK 1 A1: 4,6,8 # reduction candidate for 4,6 A1: 8 => CTR * 8..6792..65.8....37......6.24578139639845612716739258447.9386.298..6743.5.614.... * PAIR A2: 4,6 ROW 2 F2: 4,6,2 # reduction candidate for 4,6 F2: 2 => SOLVED * 431679285659812743782534961245781396398426157167395824573968412914257638826143579 * DURATION: 0:00:07.968592 START: 04:48:25.246592 END: 04:48:33.215184 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0076-base-pr-001.dot * REASONING * DIS # C6: 1,9 => CTR => C6: 5,7 * DIS C6: 5,7 # A1: 8 => CTR => A1: 4,6 * PRF C6: 5,7 + A1: 4,6 # F2: 2 => SOL * STA C6: 5,7 + A1: 4,6 + F2: 2 * CNT 3 HDP CHAINS / 8 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=76
Solution
position: 431679285659812743782534961245781396398426157167395824573968412914257638826143579 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 # C6: 5,7 => UNS * DIS # C6: 1,9 => CTR => C6: 5,7 * INC # D4: 5,7 => UNS * INC # I4: 5,7 => UNS * INC # A7: 3,5 => UNS * INC # A9: 3,5 => UNS * DIS # C6: 1,5 => CTR => C6: 7,9 * INC # C6: 7,9 => UNS * INC # A7: 1,5 => UNS * INC # A7: 3,4,8 => UNS * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # C6: 5,7 => UNS * DIS # C6: 1,9 => CTR => C6: 5,7 * INC C6: 5,7 # D4: 5,7 => UNS * INC C6: 5,7 # I4: 5,7 => UNS * INC C6: 5,7 # A1: 4,6 => UNS * DIS C6: 5,7 # A1: 8 => CTR => A1: 4,6 * INC C6: 5,7 + A1: 4,6 # F2: 4,6 => UNS * PRF C6: 5,7 + A1: 4,6 # F2: 2 => SOL * STA C6: 5,7 + A1: 4,6 + F2: 2 * CNT 8 HDP CHAINS / 8 HYP OPENED