Analysis of zz-www.sudokuwiki.org-0098-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=98
level: hard
position: 7..3..6....6...38......2..7..5..7.3..6..8..9..2.4..5..5..6......41...9....2..9..4 initial
Autosolve
position: 7..3..6..2.6...38.....621.7..5..7.36.6..8..9..2.4.65..5..6......41...9....2..9..4 autosolve
Pair Reduction Variants
Deep Pair Reduction
Time used: 0:00:41.437466
The following important HDP chains were detected:
* DIS # I1: 5,9 # B1: 5,9 => CTR => B1: 1,8 * DIS # I1: 5,9 + B1: 1,8 # E1: 1 => CTR => E1: 5,9 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 # D2: 5,9 => CTR => D2: 1,7 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 # E2: 5,9 => CTR => E2: 1,4,7 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 # B2: 1 => CTR => B2: 5,9 * PRF # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 + B2: 5,9 # A4: 8,9 => SOL * STA # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 + B2: 5,9 + A4: 8,9 * CNT 6 HDP CHAINS / 38 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 7..3..6....6...38......2..7..5..7.3..6..8..9..2.4..5..5..6......41...9....2..9..4 | initial |
| 7..3..6..2.6...38.....621.7..5..7.36.6..8..9..2.4.65..5..6......41...9....2..9..4 | autosolve |
| 714358629296741385358962147985127436467583291123496578579634812841275963632819754 | solved |
Classification
level: hard
Pairing Analysis
-------------------------------------------------- * PAIRS (7) I2: 5,9 H3: 4,5 B4: 8,9 I5: 1,2 H6: 1,7 I6: 1,8 G9: 7,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B1,B2: 1.. / B1 = 1 => 12 pairs (_) / B2 = 1 => 8 pairs (_) H1,I1: 2.. / H1 = 2 => 11 pairs (_) / I1 = 2 => 18 pairs (_) F5,E6: 3.. / F5 = 3 => 13 pairs (_) / E6 = 3 => 16 pairs (_) I7,I8: 3.. / I7 = 3 => 9 pairs (_) / I8 = 3 => 16 pairs (_) E2,F2: 4.. / E2 = 4 => 8 pairs (_) / F2 = 4 => 7 pairs (_) H1,H3: 4.. / H1 = 4 => 0 pairs (X) / H3 = 4 => 8 pairs (_) G4,G5: 4.. / G4 = 4 => 8 pairs (_) / G5 = 4 => 12 pairs (_) E7,F7: 4.. / E7 = 4 => 7 pairs (_) / F7 = 4 => 8 pairs (_) C1,H1: 4.. / C1 = 4 => 8 pairs (_) / H1 = 4 => 0 pairs (X) A4,G4: 4.. / A4 = 4 => 12 pairs (_) / G4 = 4 => 8 pairs (_) E2,E7: 4.. / E2 = 4 => 8 pairs (_) / E7 = 4 => 7 pairs (_) F2,F7: 4.. / F2 = 4 => 7 pairs (_) / F7 = 4 => 8 pairs (_) D5,F5: 5.. / D5 = 5 => 10 pairs (_) / F5 = 5 => 19 pairs (_) A8,A9: 6.. / A8 = 6 => 12 pairs (_) / A9 = 6 => 8 pairs (_) H8,H9: 6.. / H8 = 6 => 8 pairs (_) / H9 = 6 => 12 pairs (_) A8,H8: 6.. / A8 = 6 => 12 pairs (_) / H8 = 6 => 8 pairs (_) A9,H9: 6.. / A9 = 6 => 8 pairs (_) / H9 = 6 => 12 pairs (_) D2,E2: 7.. / D2 = 7 => 7 pairs (_) / E2 = 7 => 7 pairs (_) C5,C6: 7.. / C5 = 7 => 8 pairs (_) / C6 = 7 => 0 pairs (X) G5,H6: 7.. / G5 = 7 => 0 pairs (X) / H6 = 7 => 8 pairs (_) B7,B9: 7.. / B7 = 7 => 11 pairs (_) / B9 = 7 => 9 pairs (_) C5,G5: 7.. / C5 = 7 => 8 pairs (_) / G5 = 7 => 0 pairs (X) C6,H6: 7.. / C6 = 7 => 0 pairs (X) / H6 = 7 => 8 pairs (_) F1,D3: 8.. / F1 = 8 => 10 pairs (_) / D3 = 8 => 10 pairs (_) G4,I6: 8.. / G4 = 8 => 0 pairs (X) / I6 = 8 => 7 pairs (_) I1,I2: 9.. / I1 = 9 => 12 pairs (_) / I2 = 9 => 8 pairs (_) B7,C7: 9.. / B7 = 9 => 11 pairs (_) / C7 = 9 => 8 pairs (_) * DURATION: 0:00:33.666825 START: 18:51:48.492908 END: 18:52:22.159733 2017-04-30 * CP COUNT: (27) * CLUE FOUND * DEEP PAIR REDUCTION * DURATION: 0:00:41.212830 START: 18:53:00.396074 END: 18:53:41.608904 2017-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0098-base-pr-002.dot * REASONING * DIS # I1: 5,9 # B1: 5,9 => CTR => B1: 1,8 * DIS # I1: 5,9 + B1: 1,8 # E1: 1 => CTR => E1: 5,9 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 # D2: 5,9 => CTR => D2: 1,7 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 # E2: 5,9 => CTR => E2: 1,4,7 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 # B2: 1 => CTR => B2: 5,9 * PRF # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 + B2: 5,9 # A4: 8,9 => SOL * STA # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 + B2: 5,9 + A4: 8,9 * CNT 6 HDP CHAINS / 38 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=98
Solution
position: 714358629296741385358962147985127436467583291123496578579634812841275963632819754 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 # I1: 5,9 => UNS * INC # I1: 2 => UNS * INC # B2: 5,9 => UNS * INC # D2: 5,9 => UNS * INC # E2: 5,9 => UNS * INC # H1: 4,5 => UNS * INC # H1: 2 => UNS * INC # A4: 8,9 => UNS * INC # A6: 8,9 => UNS * INC # C6: 8,9 => UNS * INC # B1: 8,9 => UNS * INC # B3: 8,9 => UNS * INC # B7: 8,9 => UNS * INC # D5: 1,2 => UNS * INC # D5: 5 => UNS * INC # I7: 1,2 => UNS * INC # I7: 3,8 => UNS * INC # H7: 1,7 => UNS * INC # H9: 1,7 => UNS * INC # A6: 1,8 => UNS * INC # A6: 3,9 => UNS * INC # I7: 1,8 => UNS * INC # I7: 2,3 => UNS * INC # G7: 7,8 => UNS * INC # G7: 2 => UNS * INC # B9: 7,8 => UNS * INC # D9: 7,8 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # I1: 5,9 => UNS * INC # I1: 2 => UNS * INC # B2: 5,9 => UNS * INC # D2: 5,9 => UNS * INC # E2: 5,9 => UNS * INC # H1: 4,5 => UNS * INC # H1: 2 => UNS * INC # A4: 8,9 => UNS * INC # A6: 8,9 => UNS * INC # C6: 8,9 => UNS * INC # B1: 8,9 => UNS * INC # B3: 8,9 => UNS * INC # B7: 8,9 => UNS * INC # D5: 1,2 => UNS * INC # D5: 5 => UNS * INC # I7: 1,2 => UNS * INC # I7: 3,8 => UNS * INC # H7: 1,7 => UNS * INC # H9: 1,7 => UNS * INC # A6: 1,8 => UNS * INC # A6: 3,9 => UNS * INC # I7: 1,8 => UNS * INC # I7: 2,3 => UNS * INC # G7: 7,8 => UNS * INC # G7: 2 => UNS * INC # B9: 7,8 => UNS * INC # D9: 7,8 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A3. Deep Pair Reduction
Full list of HDP chains traversed:
* INC # I1: 5,9 => UNS * INC # I1: 2 => UNS * INC # B2: 5,9 => UNS * INC # D2: 5,9 => UNS * INC # E2: 5,9 => UNS * INC # H1: 4,5 => UNS * INC # H1: 2 => UNS * INC # A4: 8,9 => UNS * INC # A6: 8,9 => UNS * INC # C6: 8,9 => UNS * INC # B1: 8,9 => UNS * INC # B3: 8,9 => UNS * INC # B7: 8,9 => UNS * INC # D5: 1,2 => UNS * INC # D5: 5 => UNS * INC # I7: 1,2 => UNS * INC # I7: 3,8 => UNS * INC # H7: 1,7 => UNS * INC # H9: 1,7 => UNS * INC # A6: 1,8 => UNS * INC # A6: 3,9 => UNS * INC # I7: 1,8 => UNS * INC # I7: 2,3 => UNS * INC # G7: 7,8 => UNS * INC # G7: 2 => UNS * INC # B9: 7,8 => UNS * INC # D9: 7,8 => UNS * DIS # I1: 5,9 # B1: 5,9 => CTR => B1: 1,8 * INC # I1: 5,9 + B1: 1,8 # E1: 5,9 => UNS * INC # I1: 5,9 + B1: 1,8 # E1: 5,9 => UNS * DIS # I1: 5,9 + B1: 1,8 # E1: 1 => CTR => E1: 5,9 * INC # I1: 5,9 + B1: 1,8 + E1: 5,9 # B2: 5,9 => UNS * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 # D2: 5,9 => CTR => D2: 1,7 * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 # E2: 5,9 => CTR => E2: 1,4,7 * INC # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 # B2: 5,9 => UNS * DIS # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 # B2: 1 => CTR => B2: 5,9 * PRF # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 + B2: 5,9 # A4: 8,9 => SOL * STA # I1: 5,9 + B1: 1,8 + E1: 5,9 + D2: 1,7 + E2: 1,4,7 + B2: 5,9 + A4: 8,9 * CNT 37 HDP CHAINS / 38 HYP OPENED