Analysis of zz-www.sudokuwiki.org-0050-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=50
level: medium
position: ...7...86.28.1.7.......3...9.5.....3.7..4..5.2.....4.7...6.......4...51.53...2... initial
Autosolve
position: ...7...86.28.1.7.......3...945.....3.7..4..5.2.....4.7..265......4...51253...2... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # G1: 2,9 => SOL * DIS # G4: 2,6 => CTR => G4: 1,8 * CNT 2 HDP CHAINS / 15 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # G1: 2,9 => SOL * STA G1: 2,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...7...86.28.1.7.......3...9.5.....3.7..4..5.2.....4.7...6.......4...51.53...2... | initial |
| ...7...86.28.1.7.......3...945.....3.7..4..5.2.....4.7..265......4...51253...2... | autosolve |
| 413725986628419735759863124945271863376948251281536497192654378864397512537182649 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) E1: 2,9 H4: 2,6 H6: 6,9 F7: 1,4 D9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) F7,D9: 1.. / F7 = 1 => 13 pairs (_) / D9 = 1 => 8 pairs (_) C9,D9: 1.. / C9 = 1 => 13 pairs (_) / D9 = 1 => 8 pairs (_) I3,I5: 1.. / I3 = 1 => 8 pairs (_) / I5 = 1 => 8 pairs (_) E1,G1: 2.. / E1 = 2 => 4 pairs (_) / G1 = 2 => 0 pairs (X) D5,G5: 2.. / D5 = 2 => 7 pairs (_) / G5 = 2 => 8 pairs (_) H3,H4: 2.. / H3 = 2 => 7 pairs (_) / H4 = 2 => 7 pairs (_) G1,H2: 3.. / G1 = 3 => 22 pairs (_) / H2 = 3 => 6 pairs (_) D8,E8: 3.. / D8 = 3 => 6 pairs (_) / E8 = 3 => 6 pairs (_) G7,H7: 3.. / G7 = 3 => 6 pairs (_) / H7 = 3 => 22 pairs (_) A2,H2: 3.. / A2 = 3 => 22 pairs (_) / H2 = 3 => 6 pairs (_) E6,E8: 3.. / E6 = 3 => 6 pairs (_) / E8 = 3 => 6 pairs (_) G1,G7: 3.. / G1 = 3 => 22 pairs (_) / G7 = 3 => 6 pairs (_) H2,H7: 3.. / H2 = 3 => 6 pairs (_) / H7 = 3 => 22 pairs (_) F7,D9: 4.. / F7 = 4 => 8 pairs (_) / D9 = 4 => 13 pairs (_) A1,F1: 4.. / A1 = 4 => 7 pairs (_) / F1 = 4 => 13 pairs (_) B1,B3: 5.. / B1 = 5 => 6 pairs (_) / B3 = 5 => 8 pairs (_) I2,I3: 5.. / I2 = 5 => 6 pairs (_) / I3 = 5 => 10 pairs (_) D6,F6: 5.. / D6 = 5 => 6 pairs (_) / F6 = 5 => 6 pairs (_) B1,F1: 5.. / B1 = 5 => 6 pairs (_) / F1 = 5 => 8 pairs (_) F2,E3: 6.. / F2 = 6 => 6 pairs (_) / E3 = 6 => 14 pairs (_) A8,B8: 6.. / A8 = 6 => 11 pairs (_) / B8 = 6 => 8 pairs (_) G9,H9: 6.. / G9 = 6 => 5 pairs (_) / H9 = 6 => 12 pairs (_) A2,F2: 6.. / A2 = 6 => 14 pairs (_) / F2 = 6 => 6 pairs (_) A3,C3: 7.. / A3 = 7 => 0 pairs (*) / C3 = 7 => 0 pairs (X) E4,F4: 7.. / E4 = 7 => 8 pairs (_) / F4 = 7 => 6 pairs (_) H7,H9: 7.. / H7 = 7 => 7 pairs (_) / H9 = 7 => 9 pairs (_) A7,H7: 7.. / A7 = 7 => 9 pairs (_) / H7 = 7 => 7 pairs (_) C3,C9: 7.. / C3 = 7 => 7 pairs (_) / C9 = 7 => 0 pairs (*) F4,F8: 7.. / F4 = 7 => 6 pairs (_) / F8 = 7 => 8 pairs (_) D3,E3: 8.. / D3 = 8 => 7 pairs (_) / E3 = 8 => 11 pairs (_) A5,B6: 8.. / A5 = 8 => 15 pairs (_) / B6 = 8 => 7 pairs (_) * DURATION: 0:00:39.688546 START: 04:23:54.692704 END: 04:24:34.381250 2017-05-01 * CP COUNT: (31) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D9,E1,F7,H4,H6) * ...7...86.28.1.7.......3...945.....3.7..4..5.2.....4.7..265......4...51253...2... * PAIR E1: 2,9 BLK 2 D3: 2,9,4,5,8 # reduction candidate for 2,9 D3: 2,9 # 16 pairs E3: 2,9,6,8 # reduction candidate for 2,9 E3: 2,9 # 15 pairs * PAIR E1: 2,9 ROW 1 G1: 2,9,1,3 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 413725986628419735759863124945271863376948251281536497192654378864397512537182649 G1: 1,3 # 5 pairs * PAIR H4: 2,6 BLK 6 G4: 2,6,1,8 # reduction candidate for 2,6 G4: 2,6 => CTR * ...7...86.28.1.7.......3...945..1..3.7..4..5.281...4.7..2654.....4...51253.1.2... G4: 1,8 # 6 pairs G5: 2,6,1,8,9 # reduction candidate for 2,6 G5: 2,6 # 9 pairs * PAIR H4: 2,6 ROW 4 E4: 2,6,7,8 # reduction candidate for 2,6 E4: 2,6 # 9 pairs E4: 7,8 # 6 pairs * PAIR H6: 6,9 BLK 6 G5: 6,9,1,2,8 # reduction candidate for 6,9 G5: 6,9 # 12 pairs G5: 1,2,8 # 5 pairs * PAIR H6: 6,9 ROW 6 E6: 6,9,3,8 # reduction candidate for 6,9 E6: 6,9 # 9 pairs F6: 6,9,1,5,8 # reduction candidate for 6,9 F6: 6,9 # 11 pairs * PAIR H6: 6,9 COL H H9: 6,9,4,7 # reduction candidate for 6,9 H9: 6,9 # 10 pairs H9: 4,7 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0050-base-pr-000.dot * REASONING * PRF # G1: 2,9 => SOL * DIS # G4: 2,6 => CTR => G4: 1,8 * CNT 2 HDP CHAINS / 15 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D9,E1,F7,H4,H6) * ...7...86.28.1.7.......3...945.....3.7..4..5.2.....4.7..265......4...51253...2... * PAIR E1: 2,9 BLK 2 D3: 2,9,4,5,8 # reduction candidate for 2,9 D3: 2,9 # 16 pairs E3: 2,9,6,8 # reduction candidate for 2,9 E3: 2,9 # 15 pairs * PAIR E1: 2,9 ROW 1 G1: 2,9,1,3 # reduction candidate for 2,9 G1: 2,9 => SOLVED * 413725986628419735759863124945271863376948251281536497192654378864397512537182649 * DURATION: 0:00:04.161666 START: 04:24:45.624891 END: 04:24:49.786557 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0050-base-pr-001.dot * REASONING * PRF # G1: 2,9 => SOL * STA G1: 2,9 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=50
Solution
position: 413725986628419735759863124945271863376948251281536497192654378864397512537182649 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 # D3: 2,9 => UNS * INC # E3: 2,9 => UNS * PRF # G1: 2,9 => SOL * INC # G1: 1,3 => UNS * DIS # G4: 2,6 => CTR => G4: 1,8 * INC # G4: 1,8 => UNS * INC # G5: 2,6 => UNS * INC # E4: 2,6 => UNS * INC # E4: 7,8 => UNS * INC # G5: 6,9 => UNS * INC # G5: 1,2,8 => UNS * INC # E6: 6,9 => UNS * INC # F6: 6,9 => UNS * INC # H9: 6,9 => UNS * INC # H9: 4,7 => UNS * CNT 15 HDP CHAINS / 15 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D3: 2,9 => UNS * INC # E3: 2,9 => UNS * PRF # G1: 2,9 => SOL * STA G1: 2,9 * CNT 3 HDP CHAINS / 3 HYP OPENED