Analysis of zz-www.sudokuwiki.org-0008-base.sdk
Contents
Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=8
level: medium
position: .1...9.4...3...5..9....38..5..1...3....652....6...8..7..8.....3..6...4...2.4...6. initial
Autosolve
position: .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # I2: 2,6 => CTR => I2: 1,9 * DIS # I3: 2,6 => CTR => I3: 1 * PRF # E1: 2,6 => SOL * DIS # H5: 1,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * DIS # I5: 1,9 => CTR => I5: 4,8 * PRF # G6: 1,9 => SOL * DIS # G6: 2 => CTR => G6: 1,9 * DIS # C5: 1,9 => CTR => C5: 4,7 * DIS # G7: 1,9 => CTR => G7: 2,7 * DIS # G9: 1,9 => CTR => G9: 7 * CNT 11 HDP CHAINS / 27 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # I2: 2,6 => CTR => I2: 1,9 * DIS I2: 1,9 # I3: 2,6 => CTR => I3: 1 * DIS I2: 1,9 + I3: 1 # H5: 1,9 => CTR => H5: 8 * PRF I2: 1,9 + I3: 1 + H5: 8 => SOL * STA I2: 1,9 + I3: 1 + H5: 8 * CNT 4 HDP CHAINS / 9 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1...9.4...3...5..9....38..5..1...3....652....6...8..7..8.....3..6...4...2.4...6. | initial |
| .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6. | autosolve |
| 815729346673814529942563871584197632397652184261348957458976213736281495129435768 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (4) I1: 2,6 F4: 4,7 D6: 3,9 G5: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) I4,G6: 2.. / I4 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) C4,I4: 2.. / C4 = 2 => 0 pairs (X) / I4 = 2 => 0 pairs (_) G6,G7: 2.. / G6 = 2 => 0 pairs (X) / G7 = 2 => 0 pairs (_) A5,B5: 3.. / A5 = 3 => 0 pairs (*) / B5 = 3 => 0 pairs (X) D6,E6: 3.. / D6 = 3 => 4 pairs (_) / E6 = 3 => 9 pairs (_) A9,E9: 3.. / A9 = 3 => 5 pairs (_) / E9 = 3 => 0 pairs (*) B5,B8: 3.. / B5 = 3 => 4 pairs (_) / B8 = 3 => 0 pairs (*) D6,D8: 3.. / D6 = 3 => 4 pairs (_) / D8 = 3 => 9 pairs (_) I4,I5: 4.. / I4 = 4 => 0 pairs (X) / I5 = 4 => 4 pairs (_) A7,B7: 4.. / A7 = 4 => 5 pairs (_) / B7 = 4 => 0 pairs (X) F2,F4: 4.. / F2 = 4 => 10 pairs (_) / F4 = 4 => 7 pairs (_) D1,D3: 5.. / D1 = 5 => 6 pairs (_) / D3 = 5 => 5 pairs (_) I8,I9: 5.. / I8 = 5 => 5 pairs (_) / I9 = 5 => 7 pairs (_) C1,D1: 5.. / C1 = 5 => 5 pairs (_) / D1 = 5 => 6 pairs (_) B7,F7: 5.. / B7 = 5 => 6 pairs (_) / F7 = 5 => 0 pairs (X) A1,A2: 6.. / A1 = 6 => 0 pairs (X) / A2 = 6 => 6 pairs (_) E7,F7: 6.. / E7 = 6 => 0 pairs (X) / F7 = 6 => 6 pairs (_) E3,I3: 6.. / E3 = 6 => 10 pairs (_) / I3 = 6 => 0 pairs (X) F2,F7: 6.. / F2 = 6 => 0 pairs (X) / F7 = 6 => 6 pairs (_) H2,H3: 7.. / H2 = 7 => 7 pairs (_) / H3 = 7 => 9 pairs (_) E4,F4: 7.. / E4 = 7 => 7 pairs (_) / F4 = 7 => 10 pairs (_) G7,G9: 7.. / G7 = 7 => 0 pairs (X) / G9 = 7 => 6 pairs (_) B4,I4: 8.. / B4 = 8 => 0 pairs (*) / I4 = 8 => 0 pairs (X) E9,I9: 8.. / E9 = 8 => 5 pairs (_) / I9 = 8 => 0 pairs (*) H5,H8: 8.. / H5 = 8 => 0 pairs (*) / H8 = 8 => 0 pairs (X) H2,I2: 9.. / H2 = 9 => 0 pairs (X) / I2 = 9 => 4 pairs (_) * DURATION: 0:00:37.664623 START: 03:29:36.992560 END: 03:30:14.657183 2017-05-01 * CP COUNT: (26) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,F4,G5,I1) * .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6. * PAIR I1: 2,6 BLK 3 I2: 2,6,1,9 # reduction candidate for 2,6 I2: 2,6 => CTR * .1758934..83...59.9452638715.21..63....652...16...8257458..6..3.96...4...214...6. I2: 1,9 # 5 pairs I3: 2,6,1 # reduction candidate for 2,6 I3: 2,6 => CTR * 2158793466832.45799745638125.21.7638837652194.6..38257..8..6923..6.2.48.32.48.76. I3: 1 # 10 pairs * PAIR I1: 2,6 ROW 1 A1: 2,6,7,8 # reduction candidate for 2,6 A1: 2,6 # 9 pairs E1: 2,6,7,8 # reduction candidate for 2,6 E1: 2,6 => SOLVED * 815729346673814529942563871584197632397652184261348957458976213736281495129435768 E1: 7,8 # 6 pairs * PAIR F4: 4,7 BLK 5 E4: 4,7,9 # reduction candidate for 4,7 E4: 9 # 21 pairs E4: 4,7 # 9 pairs * PAIR F4: 4,7 COL F F2: 4,7,1,6 # reduction candidate for 4,7 F2: 4,7 # 10 pairs F2: 1,6 # 9 pairs * PAIR D6: 3,9 BLK 5 E6: 3,9,4 # reduction candidate for 3,9 E6: 4 # 21 pairs E6: 3,9 # 9 pairs * PAIR D6: 3,9 COL D D8: 3,9,2,7,8 # reduction candidate for 3,9 D8: 3,9 # 6 pairs D8: 2,7,8 # 5 pairs * PAIR G5: 1,9 BLK 6 H5: 1,9,8 # reduction candidate for 1,9 H5: 1,9 => CTR * 2158793466832145799745638..592147638837652..4461..8257..8..6..3..6...48.32948.76. H5: 8 => SOLVED * 815729346673814529942563871584197632397652184261348957458976213736281495129435768 I5: 1,9,4,8 # reduction candidate for 1,9 I5: 1,9 => CTR * .15..934..73..45..94...387.582197634..7652.8.169348257.58..6..3.96..1425.214.5.68 I5: 4,8 # 5 pairs G6: 1,9,2 # reduction candidate for 1,9 G6: 1,9 => SOLVED * 815729346673814529942563871584197632397652184261348957458976213736281495129435768 G6: 2 => CTR * 2158793466832145799745638..592147638837652..4461..8257..8..6..3..6...48.32948.76. * PAIR G5: 1,9 ROW 5 C5: 1,9,4,7 # reduction candidate for 1,9 C5: 1,9 => CTR * 81...93466.3...5.99...638.158.1..632...652.8426...8.57458..62.3.96...41.12.4..76. C5: 4,7 # 5 pairs * PAIR G5: 1,9 COL G G7: 1,9,2,7 # reduction candidate for 1,9 G7: 1,9 => CTR * 2158793466832.45799745638..592147638837652..4461..8257.48.....3..6...48.32948.76. G7: 2,7 # 5 pairs G9: 1,9,7 # reduction candidate for 1,9 G9: 1,9 => CTR * .1587934..832..5799745.38..5.21.7638837652..4.6...8257..89..7.3.96...48..2.48..6. G9: 7 # 6 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuwiki.org-0008-base-pr-000.dot * REASONING * DIS # I2: 2,6 => CTR => I2: 1,9 * DIS # I3: 2,6 => CTR => I3: 1 * PRF # E1: 2,6 => SOL * DIS # H5: 1,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * DIS # I5: 1,9 => CTR => I5: 4,8 * PRF # G6: 1,9 => SOL * DIS # G6: 2 => CTR => G6: 1,9 * DIS # C5: 1,9 => CTR => C5: 4,7 * DIS # G7: 1,9 => CTR => G7: 2,7 * DIS # G9: 1,9 => CTR => G9: 7 * CNT 11 HDP CHAINS / 27 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,F4,G5,I1) * .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6. * PAIR I1: 2,6 BLK 3 I2: 2,6,1,9 # reduction candidate for 2,6 I2: 2,6 => CTR * .1758934..83...59.9452638715.21..63....652...16...8257458..6..3.96...4...214...6. I3: 2,6,1 # reduction candidate for 2,6 I3: 2,6 => CTR * 2158793466832.45799745638125.21.7638837652194.6..38257..8..6923..6.2.48.32.48.76. * PAIR F4: 4,7 BLK 5 E4: 4,7,9 # reduction candidate for 4,7 E4: 9 # 23 pairs E4: 4,7 # 18 pairs * PAIR D6: 3,9 BLK 5 E6: 3,9,4 # reduction candidate for 3,9 E6: 4 # 23 pairs E6: 3,9 # 18 pairs * PAIR D6: 3,9 COL D D8: 3,9,2,7,8 # reduction candidate for 3,9 D8: 2,7,8 # 17 pairs D8: 3,9 # 16 pairs * PAIR G5: 1,9 BLK 6 H5: 1,9,8 # reduction candidate for 1,9 H5: 1,9 => CTR * .1...93466.3...5.99...638.15.21..63..3.652...16...8257458..6..3796315482321487965 H5: 8 => SOLVED * 815729346673814529942563871584197632397652184261348957458976213736281495129435768 * DURATION: 0:00:09.965329 START: 03:30:37.704778 END: 03:30:47.670107 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuwiki.org-0008-base-pr-001.dot * REASONING * DIS # I2: 2,6 => CTR => I2: 1,9 * DIS I2: 1,9 # I3: 2,6 => CTR => I3: 1 * DIS I2: 1,9 + I3: 1 # H5: 1,9 => CTR => H5: 8 * PRF I2: 1,9 + I3: 1 + H5: 8 => SOL * STA I2: 1,9 + I3: 1 + H5: 8 * CNT 4 HDP CHAINS / 9 HYP OPENED
Header Info
http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=8
Solution
position: 815729346673814529942563871584197632397652184261348957458976213736281495129435768 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:
* DIS # I2: 2,6 => CTR => I2: 1,9 * INC # I2: 1,9 => UNS * DIS # I3: 2,6 => CTR => I3: 1 * INC # I3: 1 => UNS * INC # A1: 2,6 => UNS * PRF # E1: 2,6 => SOL * INC # E1: 7,8 => UNS * INC # E4: 4,7 => UNS * INC # E4: 9 => UNS * INC # F2: 4,7 => UNS * INC # F2: 1,6 => UNS * INC # E6: 3,9 => UNS * INC # E6: 4 => UNS * INC # D8: 3,9 => UNS * INC # D8: 2,7,8 => UNS * DIS # H5: 1,9 => CTR => H5: 8 * PRF # H5: 8 => SOL * DIS # I5: 1,9 => CTR => I5: 4,8 * INC # I5: 4,8 => UNS * PRF # G6: 1,9 => SOL * DIS # G6: 2 => CTR => G6: 1,9 * DIS # C5: 1,9 => CTR => C5: 4,7 * INC # C5: 4,7 => UNS * DIS # G7: 1,9 => CTR => G7: 2,7 * INC # G7: 2,7 => UNS * DIS # G9: 1,9 => CTR => G9: 7 * INC # G9: 7 => UNS * CNT 27 HDP CHAINS / 27 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # I2: 2,6 => CTR => I2: 1,9 * DIS I2: 1,9 # I3: 2,6 => CTR => I3: 1 * INC I2: 1,9 + I3: 1 # E4: 4,7 => UNS * INC I2: 1,9 + I3: 1 # E4: 9 => UNS * INC I2: 1,9 + I3: 1 # E6: 3,9 => UNS * INC I2: 1,9 + I3: 1 # E6: 4 => UNS * INC I2: 1,9 + I3: 1 # D8: 3,9 => UNS * INC I2: 1,9 + I3: 1 # D8: 2,7,8 => UNS * DIS I2: 1,9 + I3: 1 # H5: 1,9 => CTR => H5: 8 * PRF I2: 1,9 + I3: 1 + H5: 8 => SOL * STA I2: 1,9 + I3: 1 + H5: 8 * CNT 10 HDP CHAINS / 9 HYP OPENED