Analysis of zz-menneske-no-06909146-base.sdk
Contents
Original Sudoku
level: medium
position: ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158.........6.8..4..5..... initial
Autosolve
position: ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 5,7 => SOL * DIS # B1: 5,7 => CTR => B1: 3,8 * DIS # F2: 5,7 => CTR => F2: 4,6,8 * PRF # D2: 4,7 => SOL * DIS # F2: 4,7 => CTR => F2: 5,6,8 * DIS # D8: 4,7 => CTR => D8: 1,3 * PRF # D2: 4,9 => SOL * DIS # F2: 4,8 => CTR => F2: 5,6,7 * DIS # F3: 4,8 => CTR => F3: 5 * DIS # F5: 1,3 => CTR => F5: 4,8 * DIS # D4: 1,3 => CTR => D4: 2,6 * DIS # A7: 2,9 => CTR => A7: 3,6,7 * DIS # G7: 2,9 => CTR => G7: 3,6,7 * DIS # F8: 3,7 => CTR => F8: 1,4 * PRF # A7: 3,7 => SOL * DIS # G7: 3,7 => CTR => G7: 2,6,9 * DIS # C9: 2,9 => CTR => C9: 3,7,8 * PRF # G9: 2,9 => SOL * DIS # G9: 1,3 => CTR => G9: 2,6,7,9 * CNT 19 HDP CHAINS / 56 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 5,7 => SOL * STA A1: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158.........6.8..4..5..... | initial |
| ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... | autosolve |
| 584712396179436528236985174842659713793148265651273489315897642927364851468521937 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (10) B2: 5,7 D1: 4,7 D3: 4,9 E3: 4,8 E5: 4,8 H4: 1,3 E7: 2,9 F7: 3,7 E9: 2,9 H9: 1,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A2,A3: 1.. / A2 = 1 => 11 pairs (_) / A3 = 1 => 11 pairs (_) H4,H9: 1.. / H4 = 1 => 9 pairs (_) / H9 = 1 => 12 pairs (_) A3,B3: 2.. / A3 = 2 => 12 pairs (_) / B3 = 2 => 11 pairs (_) E7,E9: 2.. / E7 = 2 => 8 pairs (_) / E9 = 2 => 8 pairs (_) H4,H9: 3.. / H4 = 3 => 12 pairs (_) / H9 = 3 => 9 pairs (_) C1,C2: 4.. / C1 = 4 => 11 pairs (_) / C2 = 4 => 15 pairs (_) D8,F8: 4.. / D8 = 4 => 0 pairs (X) / F8 = 4 => 12 pairs (_) E3,E5: 4.. / E3 = 4 => 0 pairs (X) / E5 = 4 => 12 pairs (_) F2,F3: 5.. / F2 = 5 => 0 pairs (X) / F3 = 5 => 11 pairs (_) D2,F2: 6.. / D2 = 6 => 0 pairs (X) / F2 = 6 => 0 pairs (_) A7,B9: 6.. / A7 = 6 => 0 pairs (X) / B9 = 6 => 0 pairs (_) G7,G9: 6.. / G7 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) A4,D4: 6.. / A4 = 6 => 0 pairs (X) / D4 = 6 => 0 pairs (_) A7,G7: 6.. / A7 = 6 => 0 pairs (X) / G7 = 6 => 0 pairs (_) B9,G9: 6.. / B9 = 6 => 0 pairs (*) / G9 = 6 => 0 pairs (X) B6,B9: 6.. / B6 = 6 => 0 pairs (X) / B9 = 6 => 0 pairs (_) F2,F6: 6.. / F2 = 6 => 0 pairs (*) / F6 = 6 => 0 pairs (X) I2,I3: 8.. / I2 = 8 => 10 pairs (_) / I3 = 8 => 0 pairs (X) A4,C4: 8.. / A4 = 8 => 0 pairs (*) / C4 = 8 => 0 pairs (X) E5,F5: 8.. / E5 = 8 => 0 pairs (X) / F5 = 8 => 12 pairs (_) B9,C9: 8.. / B9 = 8 => 0 pairs (X) / C9 = 8 => 0 pairs (_) F2,I2: 8.. / F2 = 8 => 0 pairs (X) / I2 = 8 => 10 pairs (_) A1,A4: 8.. / A1 = 8 => 0 pairs (X) / A4 = 8 => 0 pairs (_) B1,B9: 8.. / B1 = 8 => 0 pairs (*) / B9 = 8 => 0 pairs (X) E3,E5: 8.. / E3 = 8 => 12 pairs (_) / E5 = 8 => 0 pairs (X) D2,D3: 9.. / D2 = 9 => 0 pairs (X) / D3 = 9 => 9 pairs (_) G6,I6: 9.. / G6 = 9 => 10 pairs (_) / I6 = 9 => 17 pairs (_) E7,E9: 9.. / E7 = 9 => 8 pairs (_) / E9 = 9 => 8 pairs (_) A3,D3: 9.. / A3 = 9 => 0 pairs (X) / D3 = 9 => 9 pairs (_) * DURATION: 0:00:41.190268 START: 06:47:05.862949 END: 06:47:47.053217 2017-05-01 * CP COUNT: (29) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D1,D3,E3,E5,E7,E9,F7,H4,H9) * ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... * PAIR B2: 5,7 BLK 1 A1: 5,7,3,8 # reduction candidate for 5,7 A1: 5,7 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 A1: 3,8 # 11 pairs B1: 5,7,3,8 # reduction candidate for 5,7 B1: 5,7 => CTR * ....12.96....36.28..6.85.7..4.659....9.148.6..61273.8.6158.7.4....3648514835..6.. B1: 3,8 # 11 pairs A2: 5,7,1,9 # reduction candidate for 5,7 A2: 5,7 # 15 pairs * PAIR B2: 5,7 ROW 2 F2: 5,7,4,6,8 # reduction candidate for 5,7 F2: 5,7 => CTR * ....12.96...63..28..69...7.648.59....9.....6...1.76.8..158..64.....6.85.4..5..... F2: 4,6,8 # 11 pairs * PAIR D1: 4,7 BLK 2 D2: 4,7,6,9 # reduction candidate for 4,7 D2: 4,7 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 D2: 6,9 # 11 pairs F2: 4,7,5,6,8 # reduction candidate for 4,7 F2: 4,7 => CTR * ....12.96...63..28..69.5.7.648.59....9...8.6...1.76.8..158..64.....6.85.4..5..... F2: 5,6,8 # 10 pairs * PAIR D1: 4,7 ROW 1 C1: 4,7,3,8 # reduction candidate for 4,7 C1: 3,8 # 16 pairs C1: 4,7 # 12 pairs * PAIR D1: 4,7 COL D D8: 4,7,1,3 # reduction candidate for 4,7 D8: 4,7 => CTR * ....12.96...63..2...69...7.648.59....9.....6...1.76.8..158..64.....6.85.4..5..... D8: 1,3 # 13 pairs * PAIR D3: 4,9 BLK 2 D2: 4,9,6,7 # reduction candidate for 4,9 D2: 4,9 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 D2: 6,7 # 10 pairs * PAIR E3: 4,8 BLK 2 F2: 4,8,5,6,7 # reduction candidate for 4,8 F2: 4,8 => CTR * ....12.96...63..2...69.5.7.648.59....9.....6...1.76.8..158..64.....6.85.4..5..... F2: 5,6,7 # 10 pairs F3: 4,8,5 # reduction candidate for 4,8 F3: 4,8 => CTR * ....12.96....35.28..6....7..4..59....9.....6...1.76.8..158...4.....6.85.4685..... F3: 5 # 11 pairs * PAIR E3: 4,8 ROW 3 I3: 4,8,1,3,5 # reduction candidate for 4,8 I3: 4,8 # 12 pairs I3: 1,3,5 # 10 pairs * PAIR E5: 4,8 BLK 5 F5: 4,8,1,3 # reduction candidate for 4,8 F5: 1,3 => CTR * ...712.96...63..2...694..7.648.59....9..8..6...1.76.8..158..64.....6485.4..5..... F5: 4,8 # 14 pairs * PAIR H4: 1,3 BLK 6 G4: 1,3,2,7 # reduction candidate for 1,3 G4: 1,3 # 17 pairs I4: 1,3,2,7 # reduction candidate for 1,3 I4: 1,3 # 13 pairs G5: 1,3,2,4,5,7 # reduction candidate for 1,3 G5: 1,3 # 17 pairs I5: 1,3,2,4,5,7 # reduction candidate for 1,3 I5: 1,3 # 17 pairs * PAIR H4: 1,3 ROW 4 D4: 1,3,2,6 # reduction candidate for 1,3 D4: 1,3 => CTR * ....12.96....3..2...6....7.648.59....9.....6...1.7..8..158..64.....6.85.4..5..... D4: 2,6 # 11 pairs * PAIR E7: 2,9 ROW 7 A7: 2,9,3,6,7 # reduction candidate for 2,9 A7: 2,9 => CTR * .8..12.96....36.28..6.85.7.84.659....9.148.6.6.1273.8..158.7643...3648514685..... A7: 3,6,7 # 10 pairs G7: 2,9,3,6,7 # reduction candidate for 2,9 G7: 2,9 => CTR * ....12.96....36.28..6.85.7..4.659....9.148.6..61273.8.6158.7.43...3648514..5..6.. G7: 3,6,7 # 10 pairs I7: 2,9,3,7 # reduction candidate for 2,9 I7: 2,9 # 11 pairs * PAIR F7: 3,7 BLK 8 D8: 3,7,1,4 # reduction candidate for 3,7 D8: 3,7 # 13 pairs F8: 3,7,1,4 # reduction candidate for 3,7 F8: 3,7 => CTR * ...712.96...63..2...69...7.648.59.1..9.1...6...1.76.8..158..64....46.8514..5.1.3. F8: 1,4 # 11 pairs F9: 3,7,1 # reduction candidate for 3,7 F9: 3,7 # 14 pairs * PAIR F7: 3,7 ROW 7 A7: 3,7,2,6,9 # reduction candidate for 3,7 A7: 3,7 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 A7: 2,6,9 # 10 pairs G7: 3,7,2,6,9 # reduction candidate for 3,7 G7: 3,7 => CTR * ....12.96....36.28..6.85.7..4.659....9.148.6..612739846158.734....3648514..5..6.. G7: 2,6,9 # 10 pairs I7: 3,7,2,9 # reduction candidate for 3,7 I7: 3,7 # 11 pairs * PAIR E9: 2,9 ROW 9 C9: 2,9,3,7,8 # reduction candidate for 2,9 C9: 2,9 => CTR * ....12.96....36.28..6.85.7..4.659....9.148.6..61273.8.6158.7.4....36485148.5.1637 C9: 3,7,8 # 10 pairs G9: 2,9,1,3,6,7 # reduction candidate for 2,9 G9: 2,9 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 G9: 1,3,6,7 # 10 pairs I9: 2,9,1,3,7 # reduction candidate for 2,9 I9: 2,9 # 11 pairs * PAIR H9: 1,3 BLK 9 I8: 1,3,2,7,9 # reduction candidate for 1,3 I8: 1,3 # 11 pairs G9: 1,3,2,6,7,9 # reduction candidate for 1,3 G9: 1,3 => CTR * .8..12.96....36.28..6.85.7.84.659....9.148.6.6.1273984.158.764....3648514685.13.. G9: 2,6,7,9 # 10 pairs I9: 1,3,2,7,9 # reduction candidate for 1,3 I9: 1,3 # 13 pairs * PAIR H9: 1,3 ROW 9 F9: 1,3,7 # reduction candidate for 1,3 F9: 7 # 12 pairs F9: 1,3 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06909146-base-pr-000.dot * REASONING * PRF # A1: 5,7 => SOL * DIS # B1: 5,7 => CTR => B1: 3,8 * DIS # F2: 5,7 => CTR => F2: 4,6,8 * PRF # D2: 4,7 => SOL * DIS # F2: 4,7 => CTR => F2: 5,6,8 * DIS # D8: 4,7 => CTR => D8: 1,3 * PRF # D2: 4,9 => SOL * DIS # F2: 4,8 => CTR => F2: 5,6,7 * DIS # F3: 4,8 => CTR => F3: 5 * DIS # F5: 1,3 => CTR => F5: 4,8 * DIS # D4: 1,3 => CTR => D4: 2,6 * DIS # A7: 2,9 => CTR => A7: 3,6,7 * DIS # G7: 2,9 => CTR => G7: 3,6,7 * DIS # F8: 3,7 => CTR => F8: 1,4 * PRF # A7: 3,7 => SOL * DIS # G7: 3,7 => CTR => G7: 2,6,9 * DIS # C9: 2,9 => CTR => C9: 3,7,8 * PRF # G9: 2,9 => SOL * DIS # G9: 1,3 => CTR => G9: 2,6,7,9 * CNT 19 HDP CHAINS / 56 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,D1,D3,E3,E5,E7,E9,F7,H4,H9) * ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... * PAIR B2: 5,7 BLK 1 A1: 5,7,3,8 # reduction candidate for 5,7 A1: 5,7 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 * DURATION: 0:00:02.661182 START: 06:48:26.813437 END: 06:48:29.474619 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06909146-base-pr-001.dot * REASONING * PRF # A1: 5,7 => SOL * STA A1: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6909146 umulig * PAIR REDUCTION .. * ROUND 1: ....12.96....3..2...6....7..4..59....9.....6...1.7..8..158...4.....6.85.4..5..... B2: 5,7 A1: 3,5,7,8 # reduction candidate for 5,7 A1: 5,7 => SOLVED * 584712396179436528236985174842659713793148265651273489315897642927364851468521937 * SOLVED! |:step:| 00 -------------------------------------------------- D2 != 6,9 / D2 = 4,7 => SOL |:step:| 01 --------------------------------------------------
Solution
position: 584712396179436528236985174842659713793148265651273489315897642927364851468521937 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:
* PRF # A1: 5,7 => SOL * INC # A1: 3,8 => UNS * DIS # B1: 5,7 => CTR => B1: 3,8 * INC # B1: 3,8 => UNS * INC # A2: 5,7 => UNS * DIS # F2: 5,7 => CTR => F2: 4,6,8 * INC # F2: 4,6,8 => UNS * PRF # D2: 4,7 => SOL * INC # D2: 6,9 => UNS * DIS # F2: 4,7 => CTR => F2: 5,6,8 * INC # F2: 5,6,8 => UNS * INC # C1: 4,7 => UNS * INC # C1: 3,8 => UNS * DIS # D8: 4,7 => CTR => D8: 1,3 * INC # D8: 1,3 => UNS * PRF # D2: 4,9 => SOL * INC # D2: 6,7 => UNS * DIS # F2: 4,8 => CTR => F2: 5,6,7 * INC # F2: 5,6,7 => UNS * DIS # F3: 4,8 => CTR => F3: 5 * INC # F3: 5 => UNS * INC # I3: 4,8 => UNS * INC # I3: 1,3,5 => UNS * INC # F5: 4,8 => UNS * DIS # F5: 1,3 => CTR => F5: 4,8 * INC # G4: 1,3 => UNS * INC # I4: 1,3 => UNS * INC # G5: 1,3 => UNS * INC # I5: 1,3 => UNS * DIS # D4: 1,3 => CTR => D4: 2,6 * INC # D4: 2,6 => UNS * DIS # A7: 2,9 => CTR => A7: 3,6,7 * INC # A7: 3,6,7 => UNS * DIS # G7: 2,9 => CTR => G7: 3,6,7 * INC # G7: 3,6,7 => UNS * INC # I7: 2,9 => UNS * INC # D8: 3,7 => UNS * DIS # F8: 3,7 => CTR => F8: 1,4 * INC # F8: 1,4 => UNS * INC # F9: 3,7 => UNS * PRF # A7: 3,7 => SOL * INC # A7: 2,6,9 => UNS * DIS # G7: 3,7 => CTR => G7: 2,6,9 * INC # G7: 2,6,9 => UNS * INC # I7: 3,7 => UNS * DIS # C9: 2,9 => CTR => C9: 3,7,8 * INC # C9: 3,7,8 => UNS * PRF # G9: 2,9 => SOL * INC # G9: 1,3,6,7 => UNS * INC # I9: 2,9 => UNS * INC # I8: 1,3 => UNS * DIS # G9: 1,3 => CTR => G9: 2,6,7,9 * INC # G9: 2,6,7,9 => UNS * INC # I9: 1,3 => UNS * INC # F9: 1,3 => UNS * INC # F9: 7 => UNS * CNT 56 HDP CHAINS / 56 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 5,7 => SOL * STA A1: 5,7 * CNT 1 HDP CHAINS / 1 HYP OPENED