Analysis of zz-www.sudokuwiki.org-0134-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=134
level: medium
position: ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. initial
Autosolve
position: ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # H1: 4,7 => CTR => H1: 3,9 * PRF # B2: 4,7 => SOL * DIS # C2: 4,7 => CTR => C2: 3,5 * PRF # I4: 4,6 => SOL * DIS # C5: 4,6 => CTR => C5: 2,3 * DIS # D5: 4,6 => CTR => D5: 1,2,5 * PRF # C8: 5,7 => SOL * DIS # H9: 5,7 => CTR => H9: 4,8,9 * PRF # I9: 5,7 => SOL * PRF # C2: 3,4 => SOL * CNT 10 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:
* DIS # H1: 4,7 => CTR => H1: 3,9 * PRF H1: 3,9 # B2: 4,7 => SOL * STA H1: 3,9 + B2: 4,7 * CNT 2 HDP CHAINS / 6 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. | initial |
| ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. | autosolve |
| 518642937273519468694837521739256814842173659156984372321495786465728193987361245 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) G2: 4,7 G5: 4,6 C9: 5,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,A6: 1.. / B5 = 1 => 4 pairs (_) / A6 = 1 => 3 pairs (_) G8,I9: 1.. / G8 = 1 => 4 pairs (_) / I9 = 1 => 15 pairs (_) F9,I9: 1.. / F9 = 1 => 4 pairs (_) / I9 = 1 => 15 pairs (_) G1,G8: 1.. / G1 = 1 => 15 pairs (_) / G8 = 1 => 4 pairs (_) H3,I3: 2.. / H3 = 2 => 5 pairs (_) / I3 = 2 => 3 pairs (_) B7,C8: 2.. / B7 = 2 => 0 pairs (*) / C8 = 2 => 0 pairs (X) B2,C2: 3.. / B2 = 3 => 4 pairs (_) / C2 = 3 => 0 pairs (*) H1,H3: 3.. / H1 = 3 => 3 pairs (_) / H3 = 3 => 0 pairs (X) A7,B7: 3.. / A7 = 3 => 4 pairs (_) / B7 = 3 => 0 pairs (X) E1,H1: 3.. / E1 = 3 => 0 pairs (X) / H1 = 3 => 3 pairs (_) A4,A7: 3.. / A4 = 3 => 0 pairs (X) / A7 = 3 => 4 pairs (_) C2,C5: 3.. / C2 = 3 => 0 pairs (*) / C5 = 3 => 0 pairs (X) A1,C2: 5.. / A1 = 5 => 0 pairs (*) / C2 = 5 => 0 pairs (X) I4,H5: 5.. / I4 = 5 => 10 pairs (_) / H5 = 5 => 0 pairs (*) C2,D2: 5.. / C2 = 5 => 10 pairs (_) / D2 = 5 => 0 pairs (*) D5,H5: 5.. / D5 = 5 => 10 pairs (_) / H5 = 5 => 0 pairs (*) C8,H8: 5.. / C8 = 5 => 0 pairs (*) / H8 = 5 => 0 pairs (X) A1,A9: 5.. / A1 = 5 => 0 pairs (*) / A9 = 5 => 0 pairs (X) E1,E4: 5.. / E1 = 5 => 10 pairs (_) / E4 = 5 => 0 pairs (*) I4,I9: 5.. / I4 = 5 => 10 pairs (_) / I9 = 5 => 0 pairs (*) G4,H6: 8.. / G4 = 8 => 3 pairs (_) / H6 = 8 => 5 pairs (_) B7,B9: 8.. / B7 = 8 => 9 pairs (_) / B9 = 8 => 3 pairs (_) D6,E6: 9.. / D6 = 9 => 3 pairs (_) / E6 = 9 => 4 pairs (_) * DURATION: 0:00:31.563370 START: 06:01:42.651367 END: 06:02:14.214737 2017-05-01 * CP COUNT: (23) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G2,G5) * ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. * PAIR G2: 4,7 BLK 3 G1: 4,7,1,9 # reduction candidate for 4,7 G1: 4,7 # 9 pairs H1: 4,7,3,9 # reduction candidate for 4,7 H1: 4,7 => CTR * 548632971273519468.96847532.3925.81.812473659.5419832..21..5...465.2.1.3987361245 H1: 3,9 # 4 pairs I1: 4,7,1 # reduction candidate for 4,7 I1: 4,7 # 7 pairs H3: 4,7,2,3,9 # reduction candidate for 4,7 H3: 4,7 # 8 pairs I3: 4,7,1,2 # reduction candidate for 4,7 I3: 4,7 # 9 pairs * PAIR G2: 4,7 ROW 2 B2: 4,7,3 # reduction candidate for 4,7 B2: 4,7 => SOLVED * 518642937273519468694837521739256814842173659156984372321495786465728193987361245 B2: 3 # 4 pairs C2: 4,7,3,5 # reduction candidate for 4,7 C2: 4,7 => CTR * 5.8..2...234519768..68..52...9.538128.327..59.52198374321.85...465.2.1.39873.1245 C2: 3,5 # 4 pairs D2: 4,7,5 # reduction candidate for 4,7 D2: 4,7 # 10 pairs * PAIR G2: 4,7 COL G G4: 4,7,6,8 # reduction candidate for 4,7 G4: 4,7 # 5 pairs G7: 4,7,6,8,9 # reduction candidate for 4,7 G7: 4,7 # 5 pairs * PAIR G5: 4,6 BLK 6 G4: 4,6,7,8 # reduction candidate for 4,6 G4: 4,6 # 11 pairs I4: 4,6,2,5,7 # reduction candidate for 4,6 I4: 4,6 => SOLVED * 518642937273519468694837521739256814842173659156984372321495786465728193987361245 I4: 2,5,7 # 3 pairs I6: 4,6,2,7 # reduction candidate for 4,6 I6: 4,6 # 6 pairs * PAIR G5: 4,6 ROW 5 C5: 4,6,2,3 # reduction candidate for 4,6 C5: 4,6 => CTR * 5.8..2...2.3519.68...8..52...9.5..128..27..59.5219.3..321.85...465.27183987361245 C5: 2,3 # 4 pairs D5: 4,6,1,2,5 # reduction candidate for 4,6 D5: 4,6 => CTR * 5.86.2..12.3519.681.68.75...3925..1.812473659.5419.3..321..5...465.2.1.3987361245 D5: 1,2,5 # 3 pairs F5: 4,6,1,3 # reduction candidate for 4,6 F5: 4,6 # 7 pairs * PAIR G5: 4,6 COL G G7: 4,6,7,8,9 # reduction candidate for 4,6 G7: 4,6 # 8 pairs G7: 7,8,9 # 3 pairs * PAIR C9: 5,7 BLK 7 C8: 5,7,2 # reduction candidate for 5,7 C8: 5,7 => SOLVED * 518642937273519468694837521739256814842173659156984372321495786465728193987361245 C8: 2 # 10 pairs A9: 5,7,9 # reduction candidate for 5,7 A9: 5,7 # 10 pairs * PAIR C9: 5,7 ROW 9 H9: 5,7,4,8,9 # reduction candidate for 5,7 H9: 5,7 => CTR * 5.8..2...2..519.68...8..5....9.5..1.8...7..59.5....3....1..5...465.....39873..2.. H9: 4,8,9 # 3 pairs I9: 5,7,1,4,6 # reduction candidate for 5,7 I9: 5,7 => SOLVED * 518642937273519468694837521739256814842173659156984372321495786465728193987361245 I9: 1,4,6 # 10 pairs * PAIR C9: 5,7 COL C C2: 5,7,3,4 # reduction candidate for 5,7 C2: 3,4 => SOLVED * 518642937273519468694837521739256814842173659156984372321495786465728193987361245 C2: 5,7 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0134-base-pr-000.dot * REASONING * DIS # H1: 4,7 => CTR => H1: 3,9 * PRF # B2: 4,7 => SOL * DIS # C2: 4,7 => CTR => C2: 3,5 * PRF # I4: 4,6 => SOL * DIS # C5: 4,6 => CTR => C5: 2,3 * DIS # D5: 4,6 => CTR => D5: 1,2,5 * PRF # C8: 5,7 => SOL * DIS # H9: 5,7 => CTR => H9: 4,8,9 * PRF # I9: 5,7 => SOL * PRF # C2: 3,4 => SOL * CNT 10 HDP CHAINS / 33 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C9,G2,G5) * ..8..2...2...19.68...8..5....9....1.8...7...9.5....3....1..5...46......3...3..2.. * PAIR G2: 4,7 BLK 3 G1: 4,7,1,9 # reduction candidate for 4,7 G1: 4,7 # 9 pairs H1: 4,7,3,9 # reduction candidate for 4,7 H1: 4,7 => CTR * 548632971273519468.96847532.3925.81.812473659.5419832..21..5...465.2.1.3987361245 I1: 4,7,1 # reduction candidate for 4,7 I1: 4,7 # 7 pairs H3: 4,7,2,3,9 # reduction candidate for 4,7 H3: 4,7 # 8 pairs I3: 4,7,1,2 # reduction candidate for 4,7 I3: 4,7 # 9 pairs * PAIR G2: 4,7 ROW 2 B2: 4,7,3 # reduction candidate for 4,7 B2: 4,7 => SOLVED * 518642937273519468694837521739256814842173659156984372321495786465728193987361245 * DURATION: 0:00:06.126513 START: 06:02:38.988110 END: 06:02:45.114623 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0134-base-pr-001.dot * REASONING * DIS # H1: 4,7 => CTR => H1: 3,9 * PRF H1: 3,9 # B2: 4,7 => SOL * STA H1: 3,9 + B2: 4,7 * CNT 2 HDP CHAINS / 6 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=134
Solution
position: 518642937273519468694837521739256814842173659156984372321495786465728193987361245 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 # G1: 4,7 => UNS * DIS # H1: 4,7 => CTR => H1: 3,9 * INC # H1: 3,9 => UNS * INC # I1: 4,7 => UNS * INC # H3: 4,7 => UNS * INC # I3: 4,7 => UNS * PRF # B2: 4,7 => SOL * INC # B2: 3 => UNS * DIS # C2: 4,7 => CTR => C2: 3,5 * INC # C2: 3,5 => UNS * INC # D2: 4,7 => UNS * INC # G4: 4,7 => UNS * INC # G7: 4,7 => UNS * INC # G4: 4,6 => UNS * PRF # I4: 4,6 => SOL * INC # I4: 2,5,7 => UNS * INC # I6: 4,6 => UNS * DIS # C5: 4,6 => CTR => C5: 2,3 * INC # C5: 2,3 => UNS * DIS # D5: 4,6 => CTR => D5: 1,2,5 * INC # D5: 1,2,5 => UNS * INC # F5: 4,6 => UNS * INC # G7: 4,6 => UNS * INC # G7: 7,8,9 => UNS * PRF # C8: 5,7 => SOL * INC # C8: 2 => UNS * INC # A9: 5,7 => UNS * DIS # H9: 5,7 => CTR => H9: 4,8,9 * INC # H9: 4,8,9 => UNS * PRF # I9: 5,7 => SOL * INC # I9: 1,4,6 => UNS * INC # C2: 5,7 => UNS * PRF # C2: 3,4 => SOL * CNT 33 HDP CHAINS / 33 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G1: 4,7 => UNS * DIS # H1: 4,7 => CTR => H1: 3,9 * INC H1: 3,9 # I1: 4,7 => UNS * INC H1: 3,9 # H3: 4,7 => UNS * INC H1: 3,9 # I3: 4,7 => UNS * PRF H1: 3,9 # B2: 4,7 => SOL * STA H1: 3,9 + B2: 4,7 * CNT 6 HDP CHAINS / 6 HYP OPENED