Analysis of zz-www.sudokuwiki.org-0003-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=3
level: medium
position: .3...5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. initial
Autosolve
position: .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 2,9 => CTR => C1: 1,7,8 * DIS # G1: 2,9 => CTR => G1: 1,7,8 * DIS # B7: 6,7 => CTR => B7: 2,8 * DIS # B4: 2,4 => CTR => B4: 6,7 * PRF # I7: 1,6 => SOL * CNT 5 HDP CHAINS / 22 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 2,9 => CTR => C1: 1,7,8 * DIS C1: 1,7,8 # G1: 2,9 => CTR => G1: 1,7,8 * DIS C1: 1,7,8 + G1: 1,7,8 # B7: 6,7 => CTR => B7: 2,8 * DIS C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 2,4 => CTR => B4: 6,7 * PRF C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # I7: 1,6 => SOL * STA C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 + I7: 1,6 * CNT 5 HDP CHAINS / 35 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .3...5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. | initial |
| .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. | autosolve |
| 938625147547819623216347985863291754725468319491753268689532471174986532352174896 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) E1: 2,9 B8: 6,7 I9: 1,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,B3: 1.. / C1 = 1 => 6 pairs (_) / B3 = 1 => 5 pairs (_) D7,D9: 1.. / D7 = 1 => 3 pairs (_) / D9 = 1 => 18 pairs (_) B3,B5: 1.. / B3 = 1 => 5 pairs (_) / B5 = 1 => 6 pairs (_) I4,I5: 4.. / I4 = 4 => 7 pairs (_) / I5 = 4 => 5 pairs (_) D9,F9: 4.. / D9 = 4 => 3 pairs (_) / F9 = 4 => 4 pairs (_) G3,I3: 5.. / G3 = 5 => 6 pairs (_) / I3 = 5 => 4 pairs (_) C5,C6: 5.. / C5 = 5 => 4 pairs (_) / C6 = 5 => 4 pairs (_) D5,E6: 5.. / D5 = 5 => 4 pairs (_) / E6 = 5 => 4 pairs (_) I7,G8: 5.. / I7 = 5 => 6 pairs (_) / G8 = 5 => 4 pairs (_) C5,D5: 5.. / C5 = 5 => 4 pairs (_) / D5 = 5 => 4 pairs (_) C6,E6: 5.. / C6 = 5 => 4 pairs (_) / E6 = 5 => 4 pairs (_) D8,G8: 5.. / D8 = 5 => 6 pairs (_) / G8 = 5 => 4 pairs (_) E6,E7: 5.. / E6 = 5 => 4 pairs (_) / E7 = 5 => 4 pairs (_) G3,G8: 5.. / G3 = 5 => 6 pairs (_) / G8 = 5 => 4 pairs (_) I3,I7: 5.. / I3 = 5 => 4 pairs (_) / I7 = 5 => 6 pairs (_) B4,A6: 6.. / B4 = 6 => 6 pairs (_) / A6 = 6 => 0 pairs (X) I4,H6: 6.. / I4 = 6 => 0 pairs (X) / H6 = 6 => 6 pairs (_) B4,I4: 6.. / B4 = 6 => 6 pairs (_) / I4 = 6 => 0 pairs (X) A6,H6: 6.. / A6 = 6 => 0 pairs (X) / H6 = 6 => 6 pairs (_) F2,F3: 7.. / F2 = 7 => 4 pairs (_) / F3 = 7 => 3 pairs (_) D5,F5: 8.. / D5 = 8 => 6 pairs (_) / F5 = 8 => 3 pairs (_) H7,G9: 8.. / H7 = 8 => 5 pairs (_) / G9 = 8 => 6 pairs (_) C1,G1: 8.. / C1 = 8 => 6 pairs (_) / G1 = 8 => 5 pairs (_) C9,G9: 8.. / C9 = 8 => 5 pairs (_) / G9 = 8 => 6 pairs (_) A7,C7: 9.. / A7 = 9 => 4 pairs (_) / C7 = 9 => 5 pairs (_) D8,F8: 9.. / D8 = 9 => 5 pairs (_) / F8 = 9 => 4 pairs (_) * DURATION: 0:00:29.287567 START: 03:23:18.985309 END: 03:23:48.272876 2017-05-01 * CP COUNT: (26) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E1,I9) * .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. * PAIR E1: 2,9 BLK 2 D2: 2,9,4,8 # reduction candidate for 2,9 D2: 2,9 # 5 pairs F2: 2,9,4,7,8 # reduction candidate for 2,9 F2: 2,9 # 6 pairs D3: 2,9,3,4,8 # reduction candidate for 2,9 D3: 2,9 # 7 pairs E3: 2,9,3,4 # reduction candidate for 2,9 E3: 2,9 # 9 pairs F3: 2,9,3,4,7,8 # reduction candidate for 2,9 F3: 2,9 # 8 pairs * PAIR E1: 2,9 ROW 1 A1: 2,9,7 # reduction candidate for 2,9 A1: 2,9 # 7 pairs C1: 2,9,1,7,8 # reduction candidate for 2,9 C1: 2,9 => CTR * 73.6.584158..1.6.3416......86...1.5..4..6.....9.7...68......48.1.4.8...2.58.7.196 C1: 1,7,8 # 3 pairs G1: 2,9,1,7,8 # reduction candidate for 2,9 G1: 2,9 => CTR * 7386.5.415.2.1.6.3916.....586...1.5..2..6..7..9.7...68689...417174986532253174896 G1: 1,7,8 # 3 pairs * PAIR E1: 2,9 COL E E4: 2,9,3,4 # reduction candidate for 2,9 E4: 2,9 # 6 pairs E4: 3,4 # 5 pairs * PAIR B8: 6,7 BLK 7 A7: 6,7,2,3,9 # reduction candidate for 6,7 A7: 6,7 # 9 pairs B7: 6,7,2,8 # reduction candidate for 6,7 B7: 6,7 => CTR * 731625849529814673486..7..584.2.1.56.1.5689.469574...8963152487174.89562258476391 B7: 2,8 # 4 pairs * PAIR B8: 6,7 ROW 8 H8: 6,7,3 # reduction candidate for 6,7 H8: 3 # 7 pairs H8: 6,7 # 6 pairs * PAIR B8: 6,7 COL B B4: 6,7,2,4 # reduction candidate for 6,7 B4: 2,4 => CTR * .3.625.49529814673486..7..584.291756.1.5689.4695743..896.152487174389562.58476391 B4: 6,7 # 5 pairs * PAIR I9: 1,6 BLK 9 H7: 1,6,3,7,8 # reduction candidate for 1,6 H7: 1,6 # 11 pairs I7: 1,6,5,7 # reduction candidate for 1,6 I7: 1,6 => SOLVED * 938625147547819623216347985863291754725468319491753268689532471174986532352174896 I7: 5,7 # 4 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0003-base-pr-000.dot * REASONING * DIS # C1: 2,9 => CTR => C1: 1,7,8 * DIS # G1: 2,9 => CTR => G1: 1,7,8 * DIS # B7: 6,7 => CTR => B7: 2,8 * DIS # B4: 2,4 => CTR => B4: 6,7 * PRF # I7: 1,6 => SOL * CNT 5 HDP CHAINS / 22 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E1,I9) * .3.6.5.4.5...1.6.3..6......8....1.5.....6.....9.7....8......4..1.4.8...2.5..7..9. * PAIR E1: 2,9 BLK 2 D2: 2,9,4,8 # reduction candidate for 2,9 D2: 2,9 # 5 pairs F2: 2,9,4,7,8 # reduction candidate for 2,9 F2: 2,9 # 6 pairs D3: 2,9,3,4,8 # reduction candidate for 2,9 D3: 2,9 # 7 pairs E3: 2,9,3,4 # reduction candidate for 2,9 E3: 2,9 # 9 pairs F3: 2,9,3,4,7,8 # reduction candidate for 2,9 F3: 2,9 # 8 pairs * PAIR E1: 2,9 ROW 1 A1: 2,9,7 # reduction candidate for 2,9 A1: 2,9 # 7 pairs C1: 2,9,1,7,8 # reduction candidate for 2,9 C1: 2,9 => CTR * 73.6.584158..1.6.3416......86...1.5..4..6.....9.7...68......48.1.4.8...2.58.7.196 G1: 2,9,1,7,8 # reduction candidate for 2,9 G1: 2,9 => CTR * 7386.5.415.2.1.6.3916.....586...1.5..2..6..7..9.7...68689...417174986532253174896 * RESTART * PAIR E1: 2,9 ROW 1 A1: 2,9,7 # reduction candidate for 2,9 A1: 2,9 # 7 pairs A1: 7 # 5 pairs * PAIR E1: 2,9 COL E E4: 2,9,3,4 # reduction candidate for 2,9 E4: 2,9 # 6 pairs E4: 3,4 # 5 pairs * PAIR RESTART * PAIR E1: 2,9 BLK 2 D2: 2,9,4,8 # reduction candidate for 2,9 D2: 2,9 # 5 pairs F2: 2,9,4,7,8 # reduction candidate for 2,9 F2: 2,9 # 6 pairs D3: 2,9,3,4,8 # reduction candidate for 2,9 D3: 2,9 # 7 pairs E3: 2,9,3,4 # reduction candidate for 2,9 E3: 2,9 # 9 pairs F3: 2,9,3,4,7,8 # reduction candidate for 2,9 F3: 2,9 # 8 pairs * PAIR E1: 2,9 ROW 1 A1: 2,9,7 # reduction candidate for 2,9 A1: 2,9 # 7 pairs A1: 7 # 5 pairs * PAIR E1: 2,9 COL E E4: 2,9,3,4 # reduction candidate for 2,9 E4: 2,9 # 6 pairs E4: 3,4 # 5 pairs * PAIR B8: 6,7 BLK 7 A7: 6,7,2,3,9 # reduction candidate for 6,7 A7: 6,7 # 9 pairs B7: 6,7,2,8 # reduction candidate for 6,7 B7: 6,7 => CTR * 731625849529814673486..7..584.2.1.56.1.5689.469574...8963152487174.89562258476391 * RESTART * PAIR B8: 6,7 BLK 7 A7: 6,7,2,3,9 # reduction candidate for 6,7 A7: 6,7 # 9 pairs A7: 2,3,9 # 4 pairs * PAIR B8: 6,7 ROW 8 H8: 6,7,3 # reduction candidate for 6,7 H8: 3 # 8 pairs H8: 6,7 # 7 pairs * PAIR B8: 6,7 COL B B4: 6,7,2,4 # reduction candidate for 6,7 B4: 2,4 => CTR * .3.6.5.4.5...1.6.34.6......84...1.56....6...469.74...8...15.467164.8.532.5.476891 * PAIR RESTART * PAIR B8: 6,7 BLK 7 A7: 6,7,2,3,9 # reduction candidate for 6,7 A7: 6,7 # 10 pairs A7: 2,3,9 # 5 pairs * PAIR B8: 6,7 ROW 8 H8: 6,7,3 # reduction candidate for 6,7 H8: 3 # 9 pairs H8: 6,7 # 8 pairs * PAIR I9: 1,6 BLK 9 H7: 1,6,3,7,8 # reduction candidate for 1,6 H7: 1,6 # 15 pairs I7: 1,6,5,7 # reduction candidate for 1,6 I7: 1,6 => SOLVED * 938625147547819623216347985863291754725468319491753268689532471174986532352174896 * DURATION: 0:00:23.940118 START: 03:24:03.174129 END: 03:24:27.114247 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0003-base-pr-001.dot * REASONING * DIS # C1: 2,9 => CTR => C1: 1,7,8 * DIS C1: 1,7,8 # G1: 2,9 => CTR => G1: 1,7,8 * DIS C1: 1,7,8 + G1: 1,7,8 # B7: 6,7 => CTR => B7: 2,8 * DIS C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 2,4 => CTR => B4: 6,7 * PRF C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # I7: 1,6 => SOL * STA C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 + I7: 1,6 * CNT 5 HDP CHAINS / 35 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=3
Solution
position: 938625147547819623216347985863291754725468319491753268689532471174986532352174896 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 # D2: 2,9 => UNS * INC # F2: 2,9 => UNS * INC # D3: 2,9 => UNS * INC # E3: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # A1: 2,9 => UNS * DIS # C1: 2,9 => CTR => C1: 1,7,8 * INC # C1: 1,7,8 => UNS * DIS # G1: 2,9 => CTR => G1: 1,7,8 * INC # G1: 1,7,8 => UNS * INC # E4: 2,9 => UNS * INC # E4: 3,4 => UNS * INC # A7: 6,7 => UNS * DIS # B7: 6,7 => CTR => B7: 2,8 * INC # B7: 2,8 => UNS * INC # H8: 6,7 => UNS * INC # H8: 3 => UNS * INC # B4: 6,7 => UNS * DIS # B4: 2,4 => CTR => B4: 6,7 * INC # H7: 1,6 => UNS * PRF # I7: 1,6 => SOL * INC # I7: 5,7 => UNS * CNT 22 HDP CHAINS / 22 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D2: 2,9 => UNS * INC # F2: 2,9 => UNS * INC # D3: 2,9 => UNS * INC # E3: 2,9 => UNS * INC # F3: 2,9 => UNS * INC # A1: 2,9 => UNS * DIS # C1: 2,9 => CTR => C1: 1,7,8 * DIS C1: 1,7,8 # G1: 2,9 => CTR => G1: 1,7,8 * INC C1: 1,7,8 + G1: 1,7,8 # A1: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # A1: 7 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # E4: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # E4: 3,4 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # D2: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # F2: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # D3: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # E3: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # F3: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # A1: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # A1: 7 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # E4: 2,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # E4: 3,4 => UNS * INC C1: 1,7,8 + G1: 1,7,8 # A7: 6,7 => UNS * DIS C1: 1,7,8 + G1: 1,7,8 # B7: 6,7 => CTR => B7: 2,8 * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # A7: 6,7 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # A7: 2,3,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # H8: 6,7 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # H8: 3 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 6,7 => UNS * DIS C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 # B4: 2,4 => CTR => B4: 6,7 * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # A7: 6,7 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # A7: 2,3,9 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # H8: 6,7 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # H8: 3 => UNS * INC C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # H7: 1,6 => UNS * PRF C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 # I7: 1,6 => SOL * STA C1: 1,7,8 + G1: 1,7,8 + B7: 2,8 + B4: 6,7 + I7: 1,6 * CNT 35 HDP CHAINS / 35 HYP OPENED