Analysis of zz-menneske-no-06912222-base.sdk
Contents
Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6912222
level: medium
position: .9..8......4...2.....4.2..7..81...69.........91...73..7..5.....13........2..9..1. initial
Autosolve
position: 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # C1: 1,3 => CTR => C1: 7 * DIS # C1: 1 => CTR => C1: 3,7 * PRF # D9: 6,8 => SOL * DIS # H7: 4,8 => CTR => H7: 2,3,9 * DIS # G9: 4,8 => CTR => G9: 5,6,7 * DIS # G9: 5,6 => CTR => G9: 4,7,8 * CNT 6 HDP CHAINS / 26 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # C1: 1,3 => CTR => C1: 7 * PRF C1: 7 # D9: 6,8 => SOL * STA C1: 7 + D9: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .9..8......4...2.....4.2..7..81...69.........91...73..7..5.....13........2..9..1. | initial |
| 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1. | autosolve |
| 297385641864719235351462897578123469643958172912647358786531924139274586425896713 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (7) C3: 1,3 C5: 3,7 D6: 6,8 B7: 4,8 C7: 6,9 A9: 4,8 C9: 5,6 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 1.. / C1 = 1 => 0 pairs (X) / C3 = 1 => 7 pairs (_) G5,I5: 1.. / G5 = 1 => 7 pairs (_) / I5 = 1 => 0 pairs (X) E7,F7: 1.. / E7 = 1 => 7 pairs (_) / F7 = 1 => 7 pairs (_) H5,I5: 2.. / H5 = 2 => 0 pairs (X) / I5 = 2 => 7 pairs (_) H7,I7: 2.. / H7 = 2 => 7 pairs (_) / I7 = 2 => 0 pairs (X) H5,H7: 2.. / H5 = 2 => 0 pairs (X) / H7 = 2 => 7 pairs (_) I5,I7: 2.. / I5 = 2 => 7 pairs (_) / I7 = 2 => 0 pairs (X) A4,F4: 3.. / A4 = 3 => 0 pairs (X) / F4 = 3 => 10 pairs (_) B7,A9: 4.. / B7 = 4 => 6 pairs (_) / A9 = 4 => 7 pairs (_) C8,C9: 5.. / C8 = 5 => 5 pairs (_) / C9 = 5 => 7 pairs (_) A5,B5: 6.. / A5 = 6 => 7 pairs (_) / B5 = 6 => 8 pairs (_) D6,E6: 6.. / D6 = 6 => 10 pairs (_) / E6 = 6 => 0 pairs (X) C1,B2: 7.. / C1 = 7 => 9 pairs (_) / B2 = 7 => 0 pairs (X) E8,D9: 7.. / E8 = 7 => 0 pairs (*) / D9 = 7 => 0 pairs (X) C1,D1: 7.. / C1 = 7 => 9 pairs (_) / D1 = 7 => 0 pairs (X) B4,G4: 7.. / B4 = 7 => 0 pairs (*) / G4 = 7 => 0 pairs (X) D9,G9: 7.. / D9 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) C1,C5: 7.. / C1 = 7 => 9 pairs (_) / C5 = 7 => 0 pairs (X) E2,E8: 7.. / E2 = 7 => 0 pairs (X) / E8 = 7 => 0 pairs (_) H5,H8: 7.. / H5 = 7 => 0 pairs (*) / H8 = 7 => 0 pairs (X) B7,A9: 8.. / B7 = 8 => 7 pairs (_) / A9 = 8 => 6 pairs (_) D2,F2: 9.. / D2 = 9 => 8 pairs (_) / F2 = 9 => 7 pairs (_) G3,H3: 9.. / G3 = 9 => 10 pairs (_) / H3 = 9 => 7 pairs (_) D5,F5: 9.. / D5 = 9 => 7 pairs (_) / F5 = 9 => 8 pairs (_) C7,C8: 9.. / C7 = 9 => 7 pairs (_) / C8 = 9 => 5 pairs (_) D2,D5: 9.. / D2 = 9 => 8 pairs (_) / D5 = 9 => 7 pairs (_) F2,F5: 9.. / F2 = 9 => 7 pairs (_) / F5 = 9 => 8 pairs (_) * DURATION: 0:00:36.579537 START: 06:55:42.729737 END: 06:56:19.309274 2017-05-01 * CP COUNT: (27) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,C3,C5,C7,C9,D6) * 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1. * PAIR C3: 1,3 BLK 1 C1: 1,3,7 # reduction candidate for 1,3 C1: 1,3 => CTR * 29.78.....74...2.....4.2..7..812.769..7......912..73..7..5.....13.27.....2..9..1. C1: 7 # 9 pairs * PAIR C3: 1,3 ROW 3 E3: 1,3,5,6 # reduction candidate for 1,3 E3: 5,6 # 8 pairs E3: 1,3 # 8 pairs * PAIR C5: 3,7 COL C C1: 3,7,1 # reduction candidate for 3,7 C1: 1 => CTR * 29178.....74...2....34.2..7..812.769..7......912..73..7..5.....13.27.....2..9..1. C1: 3,7 # 7 pairs * PAIR D6: 6,8 COL D D9: 6,8,3,7 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 297385641864719235351462897578123469643958172912647358786531924139274586425896713 D9: 3,7 # 8 pairs * PAIR B7: 4,8 ROW 7 F7: 4,8,1,3,6 # reduction candidate for 4,8 F7: 4,8 # 11 pairs G7: 4,8,6,9 # reduction candidate for 4,8 G7: 4,8 # 8 pairs H7: 4,8,2,3,9 # reduction candidate for 4,8 H7: 4,8 => CTR * 297.8......4.7.2....14.2.97..812..69..3....2.912..73..7..513..213.2...7..2.79..13 H7: 2,3,9 # 7 pairs I7: 4,8,2,3,6 # reduction candidate for 4,8 I7: 4,8 # 11 pairs * PAIR C7: 6,9 BLK 7 C8: 6,9,5 # reduction candidate for 6,9 C8: 6,9 # 7 pairs C8: 5 # 5 pairs * PAIR C7: 6,9 ROW 7 G7: 6,9,4,8 # reduction candidate for 6,9 G7: 6,9 # 8 pairs G7: 4,8 # 8 pairs * PAIR A9: 4,8 ROW 9 F9: 4,8,3,6 # reduction candidate for 4,8 F9: 4,8 # 8 pairs G9: 4,8,5,6,7 # reduction candidate for 4,8 G9: 4,8 => CTR * 297.8......4.7.2....1432..7..8123.69..3......912..73..7..51....13.2......2.79..13 G9: 5,6,7 # 7 pairs I9: 4,8,3,5,6 # reduction candidate for 4,8 I9: 4,8 # 11 pairs * PAIR C9: 5,6 BLK 7 C8: 5,6,9 # reduction candidate for 5,6 C8: 5,6 # 7 pairs C8: 9 # 5 pairs * PAIR C9: 5,6 ROW 9 G9: 5,6,4,7,8 # reduction candidate for 5,6 G9: 5,6 => CTR * 297.8......4.7.2....1432..7..8123.69..3......912..73..7..51....13.2......2.79..13 G9: 4,7,8 # 7 pairs I9: 5,6,3,4,8 # reduction candidate for 5,6 I9: 5,6 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06912222-base-pr-000.dot * REASONING * DIS # C1: 1,3 => CTR => C1: 7 * DIS # C1: 1 => CTR => C1: 3,7 * PRF # D9: 6,8 => SOL * DIS # H7: 4,8 => CTR => H7: 2,3,9 * DIS # G9: 4,8 => CTR => G9: 5,6,7 * DIS # G9: 5,6 => CTR => G9: 4,7,8 * CNT 6 HDP CHAINS / 26 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A9,B7,C3,C5,C7,C9,D6) * 29..8......4...2.....4.2..7..812..69.........912..73..7..5.....13.2......2..9..1. * PAIR C3: 1,3 BLK 1 C1: 1,3,7 # reduction candidate for 1,3 C1: 1,3 => CTR * 29.78.....74...2.....4.2..7..812.769..7......912..73..7..5.....13.27.....2..9..1. * PAIR D6: 6,8 COL D D9: 6,8,3,7 # reduction candidate for 6,8 D9: 6,8 => SOLVED * 297385641864719235351462897578123469643958172912647358786531924139274586425896713 * DURATION: 0:00:04.153713 START: 06:56:37.946978 END: 06:56:42.100691 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06912222-base-pr-001.dot * REASONING * DIS # C1: 1,3 => CTR => C1: 7 * PRF C1: 7 # D9: 6,8 => SOL * STA C1: 7 + D9: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6912222 umulig
Solution
position: 297385641864719235351462897578123469643958172912647358786531924139274586425896713 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 # C1: 1,3 => CTR => C1: 7 * INC # C1: 7 => UNS * INC # E3: 1,3 => UNS * INC # E3: 5,6 => UNS * INC # C1: 3,7 => UNS * DIS # C1: 1 => CTR => C1: 3,7 * PRF # D9: 6,8 => SOL * INC # D9: 3,7 => UNS * INC # F7: 4,8 => UNS * INC # G7: 4,8 => UNS * DIS # H7: 4,8 => CTR => H7: 2,3,9 * INC # H7: 2,3,9 => UNS * INC # I7: 4,8 => UNS * INC # C8: 6,9 => UNS * INC # C8: 5 => UNS * INC # G7: 6,9 => UNS * INC # G7: 4,8 => UNS * INC # F9: 4,8 => UNS * DIS # G9: 4,8 => CTR => G9: 5,6,7 * INC # G9: 5,6,7 => UNS * INC # I9: 4,8 => UNS * INC # C8: 5,6 => UNS * INC # C8: 9 => UNS * DIS # G9: 5,6 => CTR => G9: 4,7,8 * INC # G9: 4,7,8 => UNS * INC # I9: 5,6 => UNS * CNT 26 HDP CHAINS / 26 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # C1: 1,3 => CTR => C1: 7 * PRF C1: 7 # D9: 6,8 => SOL * STA C1: 7 + D9: 6,8 * CNT 2 HDP CHAINS / 2 HYP OPENED