Analysis of zz-www.sudokuwiki.org-0278-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=278
level: medium
position: 5....6.29.6......7..1.94...7..1..9.2.2.....4.4.....6......2...8.....13..83...5... initial
Autosolve
position: 5....6.29.6......7..1.94...7.614.9.2.2.....4.4.....6......2...8.....13..83...52.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G2: 5,8 => SOL * DIS # H4: 3 => CTR => H4: 5,8 * DIS # D7: 6,7 => CTR => D7: 3,4,9 * DIS # H9: 6,7 => CTR => H9: 1,9 * DIS # B7: 5,7 => CTR => B7: 1,4,9 * CNT 5 HDP CHAINS / 47 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G2: 5,8 => SOL * STA G2: 5,8 * CNT 1 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 5....6.29.6......7..1.94...7..1..9.2.2.....4.4.....6......2...8.....13..83...5... | initial |
| 5....6.29.6......7..1.94...7.614.9.2.2.....4.4.....6......2...8.....13..83...52.. | autosolve |
| 583716429964238517271594836756143982329687145418952673145329768692871354837465291 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) A3: 2,3 B3: 7,8 G3: 5,8 B4: 5,8 F4: 3,8 E9: 6,7 G7: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) E1,E2: 1.. / E1 = 1 => 8 pairs (_) / E2 = 1 => 7 pairs (_) A5,B6: 1.. / A5 = 1 => 11 pairs (_) / B6 = 1 => 12 pairs (_) A7,B7: 1.. / A7 = 1 => 12 pairs (_) / B7 = 1 => 11 pairs (_) H9,I9: 1.. / H9 = 1 => 10 pairs (_) / I9 = 1 => 22 pairs (_) E1,G1: 1.. / E1 = 1 => 8 pairs (_) / G1 = 1 => 7 pairs (_) A5,A7: 1.. / A5 = 1 => 11 pairs (_) / A7 = 1 => 12 pairs (_) B6,B7: 1.. / B6 = 1 => 12 pairs (_) / B7 = 1 => 11 pairs (_) D6,F6: 2.. / D6 = 2 => 8 pairs (_) / F6 = 2 => 12 pairs (_) A8,C8: 2.. / A8 = 2 => 13 pairs (_) / C8 = 2 => 8 pairs (_) A3,D3: 2.. / A3 = 2 => 8 pairs (_) / D3 = 2 => 16 pairs (_) C2,C8: 2.. / C2 = 2 => 13 pairs (_) / C8 = 2 => 8 pairs (_) F2,F6: 2.. / F2 = 2 => 8 pairs (_) / F6 = 2 => 12 pairs (_) D7,F7: 3.. / D7 = 3 => 10 pairs (_) / F7 = 3 => 0 pairs (X) F4,H4: 3.. / F4 = 3 => 13 pairs (_) / H4 = 3 => 0 pairs (X) G1,G2: 4.. / G1 = 4 => 0 pairs (*) / G2 = 4 => 0 pairs (X) I8,I9: 4.. / I8 = 4 => 8 pairs (_) / I9 = 4 => 12 pairs (_) C2,G2: 4.. / C2 = 4 => 0 pairs (*) / G2 = 4 => 0 pairs (X) B4,H4: 5.. / B4 = 5 => 7 pairs (_) / H4 = 5 => 16 pairs (_) H3,I3: 6.. / H3 = 6 => 12 pairs (_) / I3 = 6 => 15 pairs (_) D5,E5: 6.. / D5 = 6 => 7 pairs (_) / E5 = 6 => 10 pairs (_) A7,A8: 6.. / A7 = 6 => 11 pairs (_) / A8 = 6 => 10 pairs (_) G5,H6: 7.. / G5 = 7 => 9 pairs (_) / H6 = 7 => 7 pairs (_) B3,D3: 7.. / B3 = 7 => 7 pairs (_) / D3 = 7 => 15 pairs (_) G5,G7: 7.. / G5 = 7 => 9 pairs (_) / G7 = 7 => 7 pairs (_) D8,E8: 8.. / D8 = 8 => 13 pairs (_) / E8 = 8 => 7 pairs (_) A2,C2: 9.. / A2 = 9 => 10 pairs (_) / C2 = 9 => 14 pairs (_) * DURATION: 0:00:21.433539 START: 14:42:28.493364 END: 14:42:49.926903 2019-04-28 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,B4,E9,F4,G3,G7) * 5....6.29.6......7..1.94...7.614.9.2.2.....4.4.....6......2...8.....13..83...52.. * PAIR A3: 2,3 BLK 1 A2: 2,3,9 # reduction candidate for 2,3 A2: 2,3 # 14 pairs C2: 2,3,4,8,9 # reduction candidate for 2,3 C2: 2,3 # 13 pairs * PAIR A3: 2,3 ROW 3 D3: 2,3,5,7,8 # reduction candidate for 2,3 D3: 2,3 # 16 pairs D3: 5,7,8 # 10 pairs * PAIR B3: 7,8 BLK 1 B1: 7,8,4 # reduction candidate for 7,8 B1: 7,8 # 12 pairs C1: 7,8,3,4 # reduction candidate for 7,8 C1: 7,8 # 10 pairs * PAIR B3: 7,8 ROW 3 D3: 7,8,2,3,5 # reduction candidate for 7,8 D3: 7,8 # 12 pairs D3: 2,3,5 # 8 pairs * PAIR G3: 5,8 BLK 3 G2: 5,8,1,4 # reduction candidate for 5,8 G2: 5,8 => SOLVED * 583716429964238517271594836756143982329687145418952673145329768692871354837465291 G2: 1,4 # 8 pairs H2: 5,8,1,3 # reduction candidate for 5,8 H2: 5,8 # 13 pairs H3: 5,8,3,6 # reduction candidate for 5,8 H3: 5,8 # 19 pairs * PAIR G3: 5,8 ROW 3 D3: 5,8,2,3,7 # reduction candidate for 5,8 D3: 5,8 # 11 pairs D3: 2,3,7 # 7 pairs * PAIR G3: 5,8 COL G G5: 5,8,1,7 # reduction candidate for 5,8 G5: 5,8 # 11 pairs G5: 1,7 # 8 pairs * PAIR B4: 5,8 BLK 4 C5: 5,8,3,9 # reduction candidate for 5,8 C5: 5,8 # 10 pairs B6: 5,8,1,9 # reduction candidate for 5,8 B6: 5,8 # 19 pairs C6: 5,8,3,9 # reduction candidate for 5,8 C6: 5,8 # 11 pairs * PAIR B4: 5,8 ROW 4 H4: 5,8,3 # reduction candidate for 5,8 H4: 3 => CTR * 5....6.29.6...2.872.1.94563756148932.2...784.4..2.967...5.23798.92..135.837965214 H4: 5,8 # 13 pairs * PAIR F4: 3,8 BLK 5 D5: 3,8,5,6,7,9 # reduction candidate for 3,8 D5: 3,8 # 16 pairs E5: 3,8,5,6,7 # reduction candidate for 3,8 E5: 3,8 # 11 pairs F5: 3,8,7,9 # reduction candidate for 3,8 F5: 3,8 # 20 pairs D6: 3,8,2,5,7,9 # reduction candidate for 3,8 D6: 3,8 # 19 pairs E6: 3,8,5,7 # reduction candidate for 3,8 E6: 3,8 # 9 pairs F6: 3,8,2,7,9 # reduction candidate for 3,8 F6: 3,8 # 21 pairs * PAIR F4: 3,8 ROW 4 H4: 3,8,5 # reduction candidate for 3,8 H4: 5 # 16 pairs H4: 3,8 # 7 pairs * PAIR F4: 3,8 COL F F2: 3,8,2 # reduction candidate for 3,8 F2: 3,8 # 12 pairs F2: 2 # 8 pairs * PAIR E9: 6,7 BLK 8 D7: 6,7,3,4,9 # reduction candidate for 6,7 D7: 6,7 => CTR * 5.7..6429.64..21872.1.94563756148932.2....84.4..2..67..456237986.2..135483.475216 D7: 3,4,9 # 7 pairs D8: 6,7,4,8,9 # reduction candidate for 6,7 D8: 6,7 # 11 pairs E8: 6,7,8 # reduction candidate for 6,7 E8: 6,7 # 13 pairs D9: 6,7,4,9 # reduction candidate for 6,7 D9: 6,7 # 14 pairs * PAIR E9: 6,7 ROW 9 H9: 6,7,1,9 # reduction candidate for 6,7 H9: 6,7 => CTR * 547836129962.....7..1.94..6756143982.2.....4.49....61..1432...8.75..13.48394.52.1 H9: 1,9 # 8 pairs * PAIR E9: 6,7 COL E E5: 6,7,3,5,8 # reduction candidate for 6,7 E5: 6,7 # 10 pairs E5: 3,5,8 # 7 pairs * PAIR G7: 5,7 BLK 9 H7: 5,7,6,9 # reduction candidate for 5,7 H7: 5,7 # 12 pairs H8: 5,7,6,9 # reduction candidate for 5,7 H8: 5,7 # 10 pairs * PAIR G7: 5,7 ROW 7 B7: 5,7,1,4,9 # reduction candidate for 5,7 B7: 5,7 => CTR * 54...6.29.6....417.71.94..67.614.9.2.2.....4.41....6..1...2.7.8692..1354837465291 B7: 1,4,9 # 7 pairs C7: 5,7,4,9 # reduction candidate for 5,7 C7: 5,7 # 10 pairs * PAIR G7: 5,7 COL G G5: 5,7,1,8 # reduction candidate for 5,7 G5: 5,7 # 10 pairs G5: 1,8 # 9 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0278-base-pr-000.dot * REASONING * PRF # G2: 5,8 => SOL * DIS # H4: 3 => CTR => H4: 5,8 * DIS # D7: 6,7 => CTR => D7: 3,4,9 * DIS # H9: 6,7 => CTR => H9: 1,9 * DIS # B7: 5,7 => CTR => B7: 1,4,9 * CNT 5 HDP CHAINS / 47 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,B3,B4,E9,F4,G3,G7) * 5....6.29.6......7..1.94...7.614.9.2.2.....4.4.....6......2...8.....13..83...52.. * PAIR A3: 2,3 BLK 1 A2: 2,3,9 # reduction candidate for 2,3 A2: 2,3 # 14 pairs C2: 2,3,4,8,9 # reduction candidate for 2,3 C2: 2,3 # 13 pairs * PAIR A3: 2,3 ROW 3 D3: 2,3,5,7,8 # reduction candidate for 2,3 D3: 2,3 # 16 pairs D3: 5,7,8 # 10 pairs * PAIR B3: 7,8 BLK 1 B1: 7,8,4 # reduction candidate for 7,8 B1: 7,8 # 12 pairs C1: 7,8,3,4 # reduction candidate for 7,8 C1: 7,8 # 10 pairs * PAIR B3: 7,8 ROW 3 D3: 7,8,2,3,5 # reduction candidate for 7,8 D3: 7,8 # 12 pairs D3: 2,3,5 # 8 pairs * PAIR G3: 5,8 BLK 3 G2: 5,8,1,4 # reduction candidate for 5,8 G2: 5,8 => SOLVED * 583716429964238517271594836756143982329687145418952673145329768692871354837465291 * DURATION: 0:00:05.314568 START: 14:43:12.080365 END: 14:43:17.394933 2019-04-28 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0278-base-pr-001.dot * REASONING * PRF # G2: 5,8 => SOL * STA G2: 5,8 * CNT 1 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=278
Solution
position: 583716429964238517271594836756143982329687145418952673145329768692871354837465291 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 # A2: 2,3 => UNS * INC # C2: 2,3 => UNS * INC # D3: 2,3 => UNS * INC # D3: 5,7,8 => UNS * INC # B1: 7,8 => UNS * INC # C1: 7,8 => UNS * INC # D3: 7,8 => UNS * INC # D3: 2,3,5 => UNS * PRF # G2: 5,8 => SOL * INC # G2: 1,4 => UNS * INC # H2: 5,8 => UNS * INC # H3: 5,8 => UNS * INC # D3: 5,8 => UNS * INC # D3: 2,3,7 => UNS * INC # G5: 5,8 => UNS * INC # G5: 1,7 => UNS * INC # C5: 5,8 => UNS * INC # B6: 5,8 => UNS * INC # C6: 5,8 => UNS * INC # H4: 5,8 => UNS * DIS # H4: 3 => CTR => H4: 5,8 * INC # D5: 3,8 => UNS * INC # E5: 3,8 => UNS * INC # F5: 3,8 => UNS * INC # D6: 3,8 => UNS * INC # E6: 3,8 => UNS * INC # F6: 3,8 => UNS * INC # H4: 3,8 => UNS * INC # H4: 5 => UNS * INC # F2: 3,8 => UNS * INC # F2: 2 => UNS * DIS # D7: 6,7 => CTR => D7: 3,4,9 * INC # D7: 3,4,9 => UNS * INC # D8: 6,7 => UNS * INC # E8: 6,7 => UNS * INC # D9: 6,7 => UNS * DIS # H9: 6,7 => CTR => H9: 1,9 * INC # H9: 1,9 => UNS * INC # E5: 6,7 => UNS * INC # E5: 3,5,8 => UNS * INC # H7: 5,7 => UNS * INC # H8: 5,7 => UNS * DIS # B7: 5,7 => CTR => B7: 1,4,9 * INC # B7: 1,4,9 => UNS * INC # C7: 5,7 => UNS * INC # G5: 5,7 => UNS * INC # G5: 1,8 => UNS * CNT 47 HDP CHAINS / 47 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A2: 2,3 => UNS * INC # C2: 2,3 => UNS * INC # D3: 2,3 => UNS * INC # D3: 5,7,8 => UNS * INC # B1: 7,8 => UNS * INC # C1: 7,8 => UNS * INC # D3: 7,8 => UNS * INC # D3: 2,3,5 => UNS * PRF # G2: 5,8 => SOL * STA G2: 5,8 * CNT 9 HDP CHAINS / 9 HYP OPENED