Analysis of zz-www.sudokuwiki.org-0147-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=147
level: medium
position: ...3..4..1...5.7.8.8.......5....8...4.6.2.5.9...4....2.......6.2.9.1...7..5..23.. initial
Autosolve
position: .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # D3: 1,7 => SOL * DIS # H4: 7 => CTR => H4: 3,4 * DIS # B6: 3,7 => CTR => B6: 1,9 * PRF # I7: 1 => SOL * CNT 4 HDP CHAINS / 39 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # D3: 1,7 => SOL * STA D3: 1,7 * CNT 1 HDP CHAINS / 21 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3..4..1...5.7.8.8.......5....8...4.6.2.5.9...4....2.......6.2.9.1...7..5..23.. | initial |
| .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239. | autosolve |
| 952387416164259738783146925527968143436721589891435672378594261249613857615872394 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (13) A1: 7,9 C1: 2,7 H1: 1,2 H2: 2,3 I3: 3,5 D5: 1,7 G4: 1,6 I4: 3,4 G6: 1,6 H6: 3,7 D8: 5,6 H8: 4,5 I9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H1,H3: 1.. / H1 = 1 => 13 pairs (_) / H3 = 1 => 19 pairs (_) G4,G6: 1.. / G4 = 1 => 14 pairs (_) / G6 = 1 => 15 pairs (_) I7,I9: 1.. / I7 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) F1,H1: 1.. / F1 = 1 => 19 pairs (_) / H1 = 1 => 13 pairs (_) B9,I9: 1.. / B9 = 1 => 0 pairs (*) / I9 = 1 => 0 pairs (X) D2,D3: 2.. / D2 = 2 => 0 pairs (*) / D3 = 2 => 0 pairs (X) B4,C4: 2.. / B4 = 2 => 13 pairs (_) / C4 = 2 => 0 pairs (X) C1,H1: 2.. / C1 = 2 => 13 pairs (_) / H1 = 2 => 19 pairs (_) B2,B4: 2.. / B2 = 2 => 0 pairs (X) / B4 = 2 => 13 pairs (_) B5,F5: 3.. / B5 = 3 => 18 pairs (_) / F5 = 3 => 18 pairs (_) B8,F8: 3.. / B8 = 3 => 18 pairs (_) / F8 = 3 => 18 pairs (_) I3,I4: 3.. / I3 = 3 => 14 pairs (_) / I4 = 3 => 17 pairs (_) H4,I4: 4.. / H4 = 4 => 17 pairs (_) / I4 = 4 => 14 pairs (_) H4,H8: 4.. / H4 = 4 => 17 pairs (_) / H8 = 4 => 14 pairs (_) H3,I3: 5.. / H3 = 5 => 14 pairs (_) / I3 = 5 => 17 pairs (_) D7,D8: 5.. / D7 = 5 => 17 pairs (_) / D8 = 5 => 14 pairs (_) I7,H8: 5.. / I7 = 5 => 14 pairs (_) / H8 = 5 => 17 pairs (_) D7,I7: 5.. / D7 = 5 => 17 pairs (_) / I7 = 5 => 14 pairs (_) D8,H8: 5.. / D8 = 5 => 14 pairs (_) / H8 = 5 => 17 pairs (_) H3,H8: 5.. / H3 = 5 => 14 pairs (_) / H8 = 5 => 17 pairs (_) I3,I7: 5.. / I3 = 5 => 17 pairs (_) / I7 = 5 => 14 pairs (_) B2,A3: 6.. / B2 = 6 => 18 pairs (_) / A3 = 6 => 15 pairs (_) G4,G6: 6.. / G4 = 6 => 15 pairs (_) / G6 = 6 => 14 pairs (_) E6,G6: 6.. / E6 = 6 => 15 pairs (_) / G6 = 6 => 14 pairs (_) A3,A9: 6.. / A3 = 6 => 15 pairs (_) / A9 = 6 => 18 pairs (_) H4,H6: 7.. / H4 = 7 => 0 pairs (X) / H6 = 7 => 13 pairs (_) A6,C6: 8.. / A6 = 8 => 16 pairs (_) / C6 = 8 => 13 pairs (_) D7,D9: 8.. / D7 = 8 => 16 pairs (_) / D9 = 8 => 14 pairs (_) A9,D9: 8.. / A9 = 8 => 16 pairs (_) / D9 = 8 => 14 pairs (_) C6,C7: 8.. / C6 = 8 => 13 pairs (_) / C7 = 8 => 16 pairs (_) A1,B2: 9.. / A1 = 9 => 13 pairs (_) / B2 = 9 => 0 pairs (X) A1,F1: 9.. / A1 = 9 => 13 pairs (_) / F1 = 9 => 0 pairs (X) A1,A6: 9.. / A1 = 9 => 13 pairs (_) / A6 = 9 => 0 pairs (X) * DURATION: 0:00:46.566191 START: 06:10:29.570190 END: 06:11:16.136381 2017-05-01 * CP COUNT: (33) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C1,D5,D8,G4,G6,H1,H2,H6,H8,I3,I4,I9) * .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239. * PAIR A1: 7,9 ROW 1 F1: 7,9,1 # reduction candidate for 7,9 F1: 1 # 19 pairs F1: 7,9 # 13 pairs * PAIR A1: 7,9 COL A A6: 7,9,3,8 # reduction candidate for 7,9 A6: 7,9 # 17 pairs A6: 3,8 # 14 pairs * PAIR C1: 2,7 BLK 1 C3: 2,7,3,4 # reduction candidate for 2,7 C3: 2,7 # 18 pairs C3: 3,4 # 14 pairs * PAIR C1: 2,7 COL C C4: 2,7,1,3 # reduction candidate for 2,7 C4: 2,7 # 19 pairs C4: 1,3 # 14 pairs * PAIR H1: 1,2 BLK 3 H3: 1,2,3,5 # reduction candidate for 1,2 H3: 1,2 # 18 pairs H3: 3,5 # 17 pairs * PAIR H2: 2,3 BLK 3 H3: 2,3,1,5 # reduction candidate for 2,3 H3: 2,3 # 20 pairs H3: 1,5 # 14 pairs * PAIR H2: 2,3 ROW 2 B2: 2,3,4,6,9 # reduction candidate for 2,3 B2: 2,3 # 20 pairs C2: 2,3,4 # reduction candidate for 2,3 C2: 2,3 # 16 pairs * PAIR I3: 3,5 BLK 3 H3: 3,5,1,2 # reduction candidate for 3,5 H3: 1,2 # 18 pairs H3: 3,5 # 17 pairs * PAIR D5: 1,7 BLK 5 D4: 1,7,6,9 # reduction candidate for 1,7 D4: 1,7 # 24 pairs F5: 1,7,3 # reduction candidate for 1,7 F5: 1,7 # 18 pairs * PAIR D5: 1,7 ROW 5 B5: 1,7,3 # reduction candidate for 1,7 B5: 3 # 18 pairs B5: 1,7 # 18 pairs * PAIR D5: 1,7 COL D D3: 1,7,2,6 # reduction candidate for 1,7 D3: 1,7 => SOLVED * 952387416164259738783146925527968143436721589891435672378594261249613857615872394 D3: 2,6 # 15 pairs * PAIR G4: 1,6 ROW 4 D4: 1,6,7,9 # reduction candidate for 1,6 D4: 7,9 # 18 pairs D4: 1,6 # 16 pairs * PAIR I4: 3,4 BLK 6 H4: 3,4,7 # reduction candidate for 3,4 H4: 7 => CTR * 75238941619365.72868.2.195352..38.74436127589...4.5.323.....265269513847..5..2391 H4: 3,4 # 13 pairs * PAIR H6: 3,7 BLK 6 H4: 3,7,4 # reduction candidate for 3,7 H4: 4 # 17 pairs H4: 3,7 # 14 pairs * PAIR H6: 3,7 ROW 6 A6: 3,7,8,9 # reduction candidate for 3,7 A6: 3,7 # 16 pairs B6: 3,7,1,9 # reduction candidate for 3,7 B6: 3,7 => CTR * .5.38.4.61...567.868....9..5...38..4436.2.589.7.4.5.323.....26.2.9.13847..5..2391 B6: 1,9 # 14 pairs C6: 3,7,1,8 # reduction candidate for 3,7 C6: 3,7 # 22 pairs E6: 3,7,6,9 # reduction candidate for 3,7 E6: 3,7 # 19 pairs * PAIR H8: 4,5 BLK 9 I7: 4,5,1 # reduction candidate for 4,5 I7: 1 => SOLVED * 952387416164259738783146925527968143436721589891435672378594261249613857615872394 I7: 4,5 # 13 pairs * PAIR I9: 1,4 BLK 9 I7: 1,4,5 # reduction candidate for 1,4 I7: 1,4 # 17 pairs I7: 5 # 14 pairs * PAIR I9: 1,4 ROW 9 B9: 1,4,6,7 # reduction candidate for 1,4 B9: 6,7 # 16 pairs B9: 1,4 # 15 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0147-base-pr-000.dot * REASONING * PRF # D3: 1,7 => SOL * DIS # H4: 7 => CTR => H4: 3,4 * DIS # B6: 3,7 => CTR => B6: 1,9 * PRF # I7: 1 => SOL * CNT 4 HDP CHAINS / 39 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,C1,D5,D8,G4,G6,H1,H2,H6,H8,I3,I4,I9) * .5.38.4.61...5.7.8.8....9..5....8...4.6.2.589...4.5..2......26.2.9.1.8.7..5..239. * PAIR A1: 7,9 ROW 1 F1: 7,9,1 # reduction candidate for 7,9 F1: 1 # 19 pairs F1: 7,9 # 13 pairs * PAIR A1: 7,9 COL A A6: 7,9,3,8 # reduction candidate for 7,9 A6: 7,9 # 17 pairs A6: 3,8 # 14 pairs * PAIR C1: 2,7 BLK 1 C3: 2,7,3,4 # reduction candidate for 2,7 C3: 2,7 # 18 pairs C3: 3,4 # 14 pairs * PAIR C1: 2,7 COL C C4: 2,7,1,3 # reduction candidate for 2,7 C4: 2,7 # 19 pairs C4: 1,3 # 14 pairs * PAIR H1: 1,2 BLK 3 H3: 1,2,3,5 # reduction candidate for 1,2 H3: 1,2 # 18 pairs H3: 3,5 # 17 pairs * PAIR H2: 2,3 BLK 3 H3: 2,3,1,5 # reduction candidate for 2,3 H3: 2,3 # 20 pairs H3: 1,5 # 14 pairs * PAIR H2: 2,3 ROW 2 B2: 2,3,4,6,9 # reduction candidate for 2,3 B2: 2,3 # 20 pairs C2: 2,3,4 # reduction candidate for 2,3 C2: 2,3 # 16 pairs * PAIR I3: 3,5 BLK 3 H3: 3,5,1,2 # reduction candidate for 3,5 H3: 1,2 # 18 pairs H3: 3,5 # 17 pairs * PAIR D5: 1,7 BLK 5 D4: 1,7,6,9 # reduction candidate for 1,7 D4: 1,7 # 24 pairs F5: 1,7,3 # reduction candidate for 1,7 F5: 1,7 # 18 pairs * PAIR D5: 1,7 ROW 5 B5: 1,7,3 # reduction candidate for 1,7 B5: 3 # 18 pairs B5: 1,7 # 18 pairs * PAIR D5: 1,7 COL D D3: 1,7,2,6 # reduction candidate for 1,7 D3: 1,7 => SOLVED * 952387416164259738783146925527968143436721589891435672378594261249613857615872394 * DURATION: 0:00:16.378859 START: 06:11:45.801690 END: 06:12:02.180549 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0147-base-pr-001.dot * REASONING * PRF # D3: 1,7 => SOL * STA D3: 1,7 * CNT 1 HDP CHAINS / 21 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=147
Solution
position: 952387416164259738783146925527968143436721589891435672378594261249613857615872394 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 # F1: 7,9 => UNS * INC # F1: 1 => UNS * INC # A6: 7,9 => UNS * INC # A6: 3,8 => UNS * INC # C3: 2,7 => UNS * INC # C3: 3,4 => UNS * INC # C4: 2,7 => UNS * INC # C4: 1,3 => UNS * INC # H3: 1,2 => UNS * INC # H3: 3,5 => UNS * INC # H3: 2,3 => UNS * INC # H3: 1,5 => UNS * INC # B2: 2,3 => UNS * INC # C2: 2,3 => UNS * INC # H3: 3,5 => UNS * INC # H3: 1,2 => UNS * INC # D4: 1,7 => UNS * INC # F5: 1,7 => UNS * INC # B5: 1,7 => UNS * INC # B5: 3 => UNS * PRF # D3: 1,7 => SOL * INC # D3: 2,6 => UNS * INC # D4: 1,6 => UNS * INC # D4: 7,9 => UNS * INC # H4: 3,4 => UNS * DIS # H4: 7 => CTR => H4: 3,4 * INC # H4: 3,7 => UNS * INC # H4: 4 => UNS * INC # A6: 3,7 => UNS * DIS # B6: 3,7 => CTR => B6: 1,9 * INC # B6: 1,9 => UNS * INC # C6: 3,7 => UNS * INC # E6: 3,7 => UNS * INC # I7: 4,5 => UNS * PRF # I7: 1 => SOL * INC # I7: 1,4 => UNS * INC # I7: 5 => UNS * INC # B9: 1,4 => UNS * INC # B9: 6,7 => UNS * CNT 39 HDP CHAINS / 39 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # F1: 7,9 => UNS * INC # F1: 1 => UNS * INC # A6: 7,9 => UNS * INC # A6: 3,8 => UNS * INC # C3: 2,7 => UNS * INC # C3: 3,4 => UNS * INC # C4: 2,7 => UNS * INC # C4: 1,3 => UNS * INC # H3: 1,2 => UNS * INC # H3: 3,5 => UNS * INC # H3: 2,3 => UNS * INC # H3: 1,5 => UNS * INC # B2: 2,3 => UNS * INC # C2: 2,3 => UNS * INC # H3: 3,5 => UNS * INC # H3: 1,2 => UNS * INC # D4: 1,7 => UNS * INC # F5: 1,7 => UNS * INC # B5: 1,7 => UNS * INC # B5: 3 => UNS * PRF # D3: 1,7 => SOL * STA D3: 1,7 * CNT 21 HDP CHAINS / 21 HYP OPENED