Analysis of zz-www.sudokuwiki.org-0135-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=135
level: medium
position: 1.5.....4.....13...8.3.4.....6....49.9..6..3.84....7.......7.6...28.....9.....1.5 initial
Autosolve
position: 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # C2: 7,9 => SOL * DIS # H3: 7,9 => CTR => H3: 1,2,5 * DIS # C7: 1,3 => CTR => C7: 4,8 * DIS # H3: 7,9 => CTR => H3: 1,2,5 * CNT 4 HDP CHAINS / 33 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # C2: 7,9 => SOL * STA C2: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 1.5.....4.....13...8.3.4.....6....49.9..6..3.84....7.......7.6...28.....9.....1.5 | initial |
| 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5 | autosolve |
| 135789624429651378687324951256173849791468532843592716518947263362815497974236185 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (9) C3: 7,9 C5: 1,7 C6: 1,3 B7: 1,5 B9: 6,7 D9: 2,6 G8: 4,9 H8: 7,9 I8: 3,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H3,I3: 1.. / H3 = 1 => 11 pairs (_) / I3 = 1 => 0 pairs (*) I5,H6: 1.. / I5 = 1 => 11 pairs (_) / H6 = 1 => 0 pairs (*) C5,I5: 1.. / C5 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) B8,E8: 1.. / B8 = 1 => 15 pairs (_) / E8 = 1 => 9 pairs (_) H3,H6: 1.. / H3 = 1 => 11 pairs (_) / H6 = 1 => 0 pairs (*) I3,I5: 1.. / I3 = 1 => 0 pairs (*) / I5 = 1 => 0 pairs (X) B2,B4: 2.. / B2 = 2 => 13 pairs (_) / B4 = 2 => 17 pairs (_) A4,C6: 3.. / A4 = 3 => 15 pairs (_) / C6 = 3 => 9 pairs (_) I7,I8: 3.. / I7 = 3 => 15 pairs (_) / I8 = 3 => 9 pairs (_) A2,C2: 4.. / A2 = 4 => 0 pairs (*) / C2 = 4 => 0 pairs (X) G7,G8: 4.. / G7 = 4 => 10 pairs (_) / G8 = 4 => 8 pairs (_) C9,E9: 4.. / C9 = 4 => 0 pairs (*) / E9 = 4 => 0 pairs (X) G1,G3: 6.. / G1 = 6 => 14 pairs (_) / G3 = 6 => 12 pairs (_) A3,G3: 6.. / A3 = 6 => 14 pairs (_) / G3 = 6 => 12 pairs (_) A5,C5: 7.. / A5 = 7 => 0 pairs (*) / C5 = 7 => 0 pairs (X) D4,E4: 7.. / D4 = 7 => 9 pairs (_) / E4 = 7 => 9 pairs (_) C7,C9: 8.. / C7 = 8 => 13 pairs (_) / C9 = 8 => 11 pairs (_) C9,H9: 8.. / C9 = 8 => 11 pairs (_) / H9 = 8 => 13 pairs (_) C2,C3: 9.. / C2 = 9 => 0 pairs (*) / C3 = 9 => 0 pairs (X) * DURATION: 0:00:24.673022 START: 06:02:59.770792 END: 06:03:24.443814 2017-05-01 * CP COUNT: (19) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,C3,C5,C6,D9,G8,H8,I8) * 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5 * PAIR C3: 7,9 BLK 1 C2: 7,9,4 # reduction candidate for 7,9 C2: 7,9 => SOLVED * 135789624429651378687324951256173849791468532843592716518947263362815497974236185 C2: 4 # 8 pairs * PAIR C3: 7,9 ROW 3 E3: 7,9,2,5 # reduction candidate for 7,9 E3: 7,9 # 15 pairs H3: 7,9,1,2,5 # reduction candidate for 7,9 H3: 7,9 => CTR * 135.8..244....135828.354671526..3849791468532843...7163....7.6...28.....9.4.3.185 H3: 1,2,5 # 9 pairs * PAIR C6: 1,3 ROW 6 E6: 1,3,2,5,9 # reduction candidate for 1,3 E6: 1,3 # 12 pairs E6: 2,5,9 # 9 pairs * PAIR C6: 1,3 COL C C7: 1,3,4,8 # reduction candidate for 1,3 C7: 1,3 => CTR * 1356729846.498135..8935461.3.672..49.9746..3184...97264.3.97268..2816493968243175 C7: 4,8 # 13 pairs * PAIR B7: 1,5 BLK 7 B8: 1,5,6,7 # reduction candidate for 1,5 B8: 1,5 # 17 pairs B8: 6,7 # 13 pairs * PAIR B7: 1,5 ROW 7 D7: 1,5,2,9 # reduction candidate for 1,5 D7: 1,5 # 14 pairs E7: 1,5,2,3,4,9 # reduction candidate for 1,5 E7: 1,5 # 13 pairs * PAIR B7: 1,5 COL B B4: 1,5,2 # reduction candidate for 1,5 B4: 2 # 17 pairs B4: 1,5 # 13 pairs * PAIR B9: 6,7 BLK 7 A8: 6,7,3,4,5 # reduction candidate for 6,7 A8: 6,7 # 18 pairs B8: 6,7,1,5 # reduction candidate for 6,7 B8: 6,7 # 13 pairs * PAIR B9: 6,7 COL B B2: 6,7,2 # reduction candidate for 6,7 B2: 6,7 # 17 pairs B2: 2 # 13 pairs * PAIR D9: 2,6 BLK 8 F9: 2,6,3 # reduction candidate for 2,6 F9: 2,6 # 16 pairs F9: 3 # 10 pairs * PAIR D9: 2,6 COL D D1: 2,6,7,9 # reduction candidate for 2,6 D1: 2,6 # 14 pairs D2: 2,6,5,7,9 # reduction candidate for 2,6 D2: 2,6 # 11 pairs * PAIR G8: 4,9 BLK 9 G7: 4,9,2,8 # reduction candidate for 4,9 G7: 2,8 # 12 pairs G7: 4,9 # 10 pairs * PAIR G8: 4,9 ROW 8 E8: 4,9,1,3,5 # reduction candidate for 4,9 E8: 4,9 # 20 pairs E8: 1,3,5 # 9 pairs * PAIR H8: 7,9 COL H H1: 7,9,2,8 # reduction candidate for 7,9 H1: 7,9 # 11 pairs H2: 7,9,2,5,8 # reduction candidate for 7,9 H2: 7,9 # 16 pairs H3: 7,9,1,2,5 # reduction candidate for 7,9 H3: 7,9 => CTR * 135.8..244....135828.354671526..3849791468532843...7163....7.6...28.....9.4.3.185 H3: 1,2,5 # 9 pairs * PAIR I8: 3,7 ROW 8 A8: 3,7,4,5,6 # reduction candidate for 3,7 A8: 3,7 # 16 pairs A8: 4,5,6 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0135-base-pr-000.dot * REASONING * PRF # C2: 7,9 => SOL * DIS # H3: 7,9 => CTR => H3: 1,2,5 * DIS # C7: 1,3 => CTR => C7: 4,8 * DIS # H3: 7,9 => CTR => H3: 1,2,5 * CNT 4 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,B9,C3,C5,C6,D9,G8,H8,I8) * 135.....4.....13...8.3.4.....6....49.9.46..3.84....7.6.....7.6...28.....9.....1.5 * PAIR C3: 7,9 BLK 1 C2: 7,9,4 # reduction candidate for 7,9 C2: 7,9 => SOLVED * 135789624429651378687324951256173849791468532843592716518947263362815497974236185 * DURATION: 0:00:02.592881 START: 06:03:46.510108 END: 06:03:49.102989 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0135-base-pr-001.dot * REASONING * PRF # C2: 7,9 => SOL * STA C2: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=135
Solution
position: 135789624429651378687324951256173849791468532843592716518947263362815497974236185 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:
* PRF # C2: 7,9 => SOL * INC # C2: 4 => UNS * INC # E3: 7,9 => UNS * DIS # H3: 7,9 => CTR => H3: 1,2,5 * INC # H3: 1,2,5 => UNS * INC # E6: 1,3 => UNS * INC # E6: 2,5,9 => UNS * DIS # C7: 1,3 => CTR => C7: 4,8 * INC # C7: 4,8 => UNS * INC # B8: 1,5 => UNS * INC # B8: 6,7 => UNS * INC # D7: 1,5 => UNS * INC # E7: 1,5 => UNS * INC # B4: 1,5 => UNS * INC # B4: 2 => UNS * INC # A8: 6,7 => UNS * INC # B8: 6,7 => UNS * INC # B2: 6,7 => UNS * INC # B2: 2 => UNS * INC # F9: 2,6 => UNS * INC # F9: 3 => UNS * INC # D1: 2,6 => UNS * INC # D2: 2,6 => UNS * INC # G7: 4,9 => UNS * INC # G7: 2,8 => UNS * INC # E8: 4,9 => UNS * INC # E8: 1,3,5 => UNS * INC # H1: 7,9 => UNS * INC # H2: 7,9 => UNS * DIS # H3: 7,9 => CTR => H3: 1,2,5 * INC # H3: 1,2,5 => UNS * INC # A8: 3,7 => UNS * INC # A8: 4,5,6 => UNS * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # C2: 7,9 => SOL * STA C2: 7,9 * CNT 1 HDP CHAINS / 1 HYP OPENED