Analysis of zz-www.sudokuwiki.org-0099-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=99
level: hard
position: .5.......9...8..14.....4..7..1..6...83..7..49...2..6..3..9.....54..1...3.......5. initial
Autosolve
position: .54......9...8..14.....4..7..1..6..5836.7.249..52..6.13..9.....54..1...3..9....5. autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:29.735597
The following important HDP chains were detected:
* DIS # G3: 3,5 # H1: 8,9 => CTR => H1: 2,6 * DIS # G3: 3,5 + H1: 2,6 # G8: 7 => CTR => G8: 8,9 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 6 => CTR => D3: 1,5 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 # D1: 6,7 => CTR => D1: 3 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 + D1: 3 => CTR => G3: 9 * DIS G3: 9 # A1: 7 => CTR => A1: 1,2 * DIS G3: 9 + A1: 1,2 # H1: 3,8 => CTR => H1: 2 * PRF G3: 9 + A1: 1,2 + H1: 2 => SOL * STA G3: 9 + A1: 1,2 + H1: 2 * CNT 8 HDP CHAINS / 20 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .5.......9...8..14.....4..7..1..6...83..7..49...2..6..3..9.....54..1...3.......5. | initial |
| .54......9...8..14.....4..7..1..6..5836.7.249..52..6.13..9.....54..1...3..9....5. | autosolve |
| 154769328967382514283154967421896735836571249795243681318925476542617893679438152 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (7) G2: 3,5 A6: 4,7 B6: 7,9 D5: 1,5 F5: 1,5 G7: 1,4 G9: 1,4 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) D5,F5: 1.. / D5 = 1 => 0 pairs (X) / F5 = 1 => 5 pairs (_) G7,G9: 1.. / G7 = 1 => 0 pairs (X) / G9 = 1 => 6 pairs (_) B7,G7: 1.. / B7 = 1 => 6 pairs (_) / G7 = 1 => 0 pairs (X) F1,F5: 1.. / F1 = 1 => 0 pairs (X) / F5 = 1 => 5 pairs (_) A4,B4: 2.. / A4 = 2 => 10 pairs (_) / B4 = 2 => 14 pairs (_) C2,C3: 3.. / C2 = 3 => 12 pairs (_) / C3 = 3 => 9 pairs (_) A4,A6: 4.. / A4 = 4 => 13 pairs (_) / A6 = 4 => 8 pairs (_) G7,G9: 4.. / G7 = 4 => 6 pairs (_) / G9 = 4 => 0 pairs (X) A6,E6: 4.. / A6 = 4 => 8 pairs (_) / E6 = 4 => 13 pairs (_) E7,G7: 4.. / E7 = 4 => 0 pairs (X) / G7 = 4 => 6 pairs (_) D4,D9: 4.. / D4 = 4 => 0 pairs (X) / D9 = 4 => 12 pairs (_) G2,G3: 5.. / G2 = 5 => 7 pairs (_) / G3 = 5 => 0 pairs (X) D5,F5: 5.. / D5 = 5 => 5 pairs (_) / F5 = 5 => 0 pairs (X) E7,F7: 5.. / E7 = 5 => 11 pairs (_) / F7 = 5 => 6 pairs (_) E3,E7: 5.. / E3 = 5 => 6 pairs (_) / E7 = 5 => 11 pairs (_) B2,D2: 6.. / B2 = 6 => 10 pairs (_) / D2 = 6 => 0 pairs (X) D8,H8: 6.. / D8 = 6 => 13 pairs (_) / H8 = 6 => 0 pairs (X) G4,G8: 7.. / G4 = 7 => 12 pairs (_) / G8 = 7 => 16 pairs (_) B3,C3: 8.. / B3 = 8 => 8 pairs (_) / C3 = 8 => 14 pairs (_) D4,F6: 8.. / D4 = 8 => 14 pairs (_) / F6 = 8 => 11 pairs (_) F6,H6: 8.. / F6 = 8 => 11 pairs (_) / H6 = 8 => 14 pairs (_) B4,B6: 9.. / B4 = 9 => 10 pairs (_) / B6 = 9 => 10 pairs (_) G8,H8: 9.. / G8 = 9 => 13 pairs (_) / H8 = 9 => 14 pairs (_) B4,E4: 9.. / B4 = 9 => 10 pairs (_) / E4 = 9 => 10 pairs (_) F1,F6: 9.. / F1 = 9 => 9 pairs (_) / F6 = 9 => 0 pairs (X) * DURATION: 0:00:35.568661 START: 18:53:57.143118 END: 18:54:32.711779 2017-04-30 * CP COUNT: (25) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:29.538472 START: 18:54:47.848675 END: 18:55:17.387147 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0099-base-pr-002.dot * REASONING * DIS # G3: 3,5 # H1: 8,9 => CTR => H1: 2,6 * DIS # G3: 3,5 + H1: 2,6 # G8: 7 => CTR => G8: 8,9 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 6 => CTR => D3: 1,5 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 # D1: 6,7 => CTR => D1: 3 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 + D1: 3 => CTR => G3: 9 * DIS G3: 9 # A1: 7 => CTR => A1: 1,2 * DIS G3: 9 + A1: 1,2 # H1: 3,8 => CTR => H1: 2 * PRF G3: 9 + A1: 1,2 + H1: 2 => SOL * STA G3: 9 + A1: 1,2 + H1: 2 * CNT 8 HDP CHAINS / 20 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=99
Solution
position: 154769328967382514283154967421896735836571249795243681318925476542617893679438152 solved
See section Deep 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 # G3: 3,5 => UNS * INC # G3: 9 => UNS * INC # D2: 3,5 => UNS * INC # F2: 3,5 => UNS * INC # A4: 4,7 => UNS * INC # A4: 2 => UNS * INC # B4: 7,9 => UNS * INC # B4: 2 => UNS * INC # D3: 1,5 => UNS * INC # D3: 3,6 => UNS * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 3,5 => UNS * INC # G3: 9 => UNS * INC # D2: 3,5 => UNS * INC # F2: 3,5 => UNS * INC # A4: 4,7 => UNS * INC # A4: 2 => UNS * INC # B4: 7,9 => UNS * INC # B4: 2 => UNS * INC # D3: 1,5 => UNS * INC # D3: 3,6 => UNS * CNT 10 HDP CHAINS / 10 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # G3: 3,5 => UNS * INC # G3: 9 => UNS * INC # D2: 3,5 => UNS * INC # F2: 3,5 => UNS * INC # A4: 4,7 => UNS * INC # A4: 2 => UNS * INC # B4: 7,9 => UNS * INC # B4: 2 => UNS * INC # D3: 1,5 => UNS * INC # D3: 3,6 => UNS * DIS # G3: 3,5 # H1: 8,9 => CTR => H1: 2,6 * INC # G3: 3,5 + H1: 2,6 # G8: 8,9 => UNS * DIS # G3: 3,5 + H1: 2,6 # G8: 7 => CTR => G8: 8,9 * INC # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 1,5 => UNS * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 6 => CTR => D3: 1,5 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 # D1: 6,7 => CTR => D1: 3 * DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 + D1: 3 => CTR => G3: 9 * INC G3: 9 # A1: 1,2 => UNS * DIS G3: 9 # A1: 7 => CTR => A1: 1,2 * DIS G3: 9 + A1: 1,2 # H1: 3,8 => CTR => H1: 2 * PRF G3: 9 + A1: 1,2 + H1: 2 => SOL * STA G3: 9 + A1: 1,2 + H1: 2 * CNT 21 HDP CHAINS / 20 HYP OPENED