Analysis of zz-menneske-no-06912567-base.sdk
Contents
Original Sudoku
level: medium
position: .....69....9.3....68......4....1.6.5.....8.1..28...7..4...8..562...9......53..... initial
Autosolve
position: .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D4: 4,7 => CTR => D4: 2,9 * DIS # F4: 4,7 => CTR => F4: 2,3,9 * DIS # D5: 4,7 => CTR => D5: 9 * DIS # B5: 4,7 => CTR => B5: 3,5,6 * DIS # C5: 4,7 => CTR => C5: 3,6 * PRF # E9: 4,7 => SOL * DIS # I5: 3,9 => CTR => I5: 2 * DIS # F6: 3,9 => CTR => F6: 4,5 * CNT 8 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D4: 4,7 => CTR => D4: 2,9 * DIS D4: 2,9 # F4: 4,7 => CTR => F4: 2,3,9 * DIS D4: 2,9 + F4: 2,3,9 # D5: 4,7 => CTR => D5: 9 * PRF D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 3 => SOL * STA D4: 2,9 + F4: 2,3,9 + D5: 9 + A1: 3 * CNT 4 HDP CHAINS / 12 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .....69....9.3....68......4....1.6.5.....8.1..28...7..4...8..562...9......53..... | initial |
| .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... | autosolve |
| 342856971759431268681729534974213685536978412128564793497182356213695847865347129 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (3) A2: 5,7 E5: 4,7 I6: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) C1,C3: 2.. / C1 = 2 => 5 pairs (_) / C3 = 2 => 6 pairs (_) D4,F4: 2.. / D4 = 2 => 4 pairs (_) / F4 = 2 => 0 pairs (X) G5,I5: 2.. / G5 = 2 => 0 pairs (X) / I5 = 2 => 4 pairs (_) F4,F6: 3.. / F4 = 3 => 10 pairs (_) / F6 = 3 => 0 pairs (X) C7,G7: 3.. / C7 = 3 => 6 pairs (_) / G7 = 3 => 0 pairs (*) G5,H6: 4.. / G5 = 4 => 11 pairs (_) / H6 = 4 => 0 pairs (X) G2,G3: 5.. / G2 = 5 => 5 pairs (_) / G3 = 5 => 4 pairs (_) A5,B5: 5.. / A5 = 5 => 4 pairs (_) / B5 = 5 => 3 pairs (_) D8,F8: 5.. / D8 = 5 => 0 pairs (X) / F8 = 5 => 5 pairs (_) B5,C5: 6.. / B5 = 6 => 0 pairs (X) / C5 = 6 => 3 pairs (_) D6,E6: 6.. / D6 = 6 => 0 pairs (X) / E6 = 6 => 4 pairs (_) D8,E9: 6.. / D8 = 6 => 4 pairs (_) / E9 = 6 => 0 pairs (X) B9,E9: 6.. / B9 = 6 => 4 pairs (_) / E9 = 6 => 0 pairs (X) C5,C8: 6.. / C5 = 6 => 3 pairs (_) / C8 = 6 => 0 pairs (X) D6,D8: 6.. / D6 = 6 => 0 pairs (X) / D8 = 6 => 4 pairs (_) E6,E9: 6.. / E6 = 6 => 4 pairs (_) / E9 = 6 => 0 pairs (X) D1,D2: 8.. / D1 = 8 => 3 pairs (_) / D2 = 8 => 3 pairs (_) G8,I8: 8.. / G8 = 8 => 3 pairs (_) / I8 = 8 => 4 pairs (_) D1,I1: 8.. / D1 = 8 => 3 pairs (_) / I1 = 8 => 3 pairs (_) G2,G8: 8.. / G2 = 8 => 4 pairs (_) / G8 = 8 => 3 pairs (_) D3,F3: 9.. / D3 = 9 => 0 pairs (X) / F3 = 9 => 3 pairs (_) A4,A5: 9.. / A4 = 9 => 3 pairs (_) / A5 = 9 => 0 pairs (X) H9,I9: 9.. / H9 = 9 => 0 pairs (X) / I9 = 9 => 9 pairs (_) H6,H9: 9.. / H6 = 9 => 9 pairs (_) / H9 = 9 => 0 pairs (X) * DURATION: 0:00:33.356117 START: 07:00:20.583166 END: 07:00:53.939283 2017-05-01 * CP COUNT: (24) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E5,I6) * .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... * PAIR A2: 5,7 BLK 1 A1: 5,7,3 # reduction candidate for 5,7 A1: 5,7 # 10 pairs B1: 5,7,1,3,4 # reduction candidate for 5,7 B1: 5,7 # 8 pairs B2: 5,7,1,4 # reduction candidate for 5,7 B2: 5,7 # 12 pairs * PAIR A2: 5,7 ROW 2 D2: 5,7,1,2,4,8 # reduction candidate for 5,7 D2: 5,7 # 6 pairs F2: 5,7,1,2,4 # reduction candidate for 5,7 F2: 5,7 # 6 pairs * PAIR A2: 5,7 COL A A5: 5,7,3,9 # reduction candidate for 5,7 A5: 5,7 # 5 pairs A5: 3,9 # 5 pairs * PAIR E5: 4,7 BLK 5 D4: 4,7,2,9 # reduction candidate for 4,7 D4: 4,7 => CTR * 3..8.69....923..6.68...9..49...12685...9.8312128.63749493.8.2562..6954..8.532..9. D4: 2,9 # 4 pairs F4: 4,7,2,3,9 # reduction candidate for 4,7 F4: 4,7 => CTR * 3....69....9.32.6.68...9..49..21.685...9.8312128.63749493.8.2562..6954..8.532..9. F4: 2,3,9 # 3 pairs D5: 4,7,9 # reduction candidate for 4,7 D5: 4,7 => CTR * ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197 D5: 9 # 4 pairs * PAIR E5: 4,7 ROW 5 B5: 4,7,3,5,6 # reduction candidate for 4,7 B5: 4,7 => CTR * 3....69..7.9.3..6.68...9..49...1.6855.69.8312128.63749493.8.2562..6954..8.532..9. B5: 3,5,6 # 3 pairs C5: 4,7,3,6 # reduction candidate for 4,7 C5: 4,7 => CTR * 3....69..7.9.3..6.68...9..49...1.68556.9.8.1.12865374949..8..562.6.9....8.536..9. C5: 3,6 # 4 pairs * PAIR E5: 4,7 COL E E1: 4,7,2,5 # reduction candidate for 4,7 E1: 4,7 # 7 pairs E9: 4,7,2,6 # reduction candidate for 4,7 E9: 4,7 => SOLVED * 342856971759431268681729534974213685536978412128564793497182356213695847865347129 E9: 2,6 # 4 pairs * PAIR I6: 3,9 BLK 6 I5: 3,9,2 # reduction candidate for 3,9 I5: 3,9 => CTR * .....69....9.3..6.68......4....1.685.....821.128...74.49..8..562...9....8.53...92 I5: 2 # 4 pairs H6: 3,9,4 # reduction candidate for 3,9 H6: 3,9 # 11 pairs * PAIR I6: 3,9 ROW 6 F6: 3,9,4,5 # reduction candidate for 3,9 F6: 3,9 => CTR * ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197 F6: 4,5 # 11 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06912567-base-pr-000.dot * REASONING * DIS # D4: 4,7 => CTR => D4: 2,9 * DIS # F4: 4,7 => CTR => F4: 2,3,9 * DIS # D5: 4,7 => CTR => D5: 9 * DIS # B5: 4,7 => CTR => B5: 3,5,6 * DIS # C5: 4,7 => CTR => C5: 3,6 * PRF # E9: 4,7 => SOL * DIS # I5: 3,9 => CTR => I5: 2 * DIS # F6: 3,9 => CTR => F6: 4,5 * CNT 8 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E5,I6) * .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... * PAIR A2: 5,7 BLK 1 A1: 5,7,3 # reduction candidate for 5,7 A1: 5,7 # 10 pairs B1: 5,7,1,3,4 # reduction candidate for 5,7 B1: 5,7 # 8 pairs B2: 5,7,1,4 # reduction candidate for 5,7 B2: 5,7 # 12 pairs * PAIR A2: 5,7 ROW 2 D2: 5,7,1,2,4,8 # reduction candidate for 5,7 D2: 5,7 # 6 pairs F2: 5,7,1,2,4 # reduction candidate for 5,7 F2: 5,7 # 6 pairs * PAIR A2: 5,7 COL A A5: 5,7,3,9 # reduction candidate for 5,7 A5: 5,7 # 5 pairs A5: 3,9 # 5 pairs * PAIR E5: 4,7 BLK 5 D4: 4,7,2,9 # reduction candidate for 4,7 D4: 4,7 => CTR * 3..8.69....923..6.68...9..49...12685...9.8312128.63749493.8.2562..6954..8.532..9. F4: 4,7,2,3,9 # reduction candidate for 4,7 F4: 4,7 => CTR * 3....69....9.32.6.68...9..49..21.685...9.8312128.63749493.8.2562..6954..8.532..9. D5: 4,7,9 # reduction candidate for 4,7 D5: 4,7 => CTR * ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197 * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A5,B4,C4,C5,D7,E3,F6,G9,H6,I6) * .....69....9.3..6.68...9..49..213685...978412128...7..49..8..562...9....8.53..... * PAIR A2: 5,7 BLK 1 A1: 5,7,3 # reduction candidate for 5,7 A1: 3 => SOLVED * 342856971759431268681729534974213685536978412128564793497182356213695847865347129 * DURATION: 0:00:10.818424 START: 07:01:11.750259 END: 07:01:22.568683 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06912567-base-pr-001.dot * REASONING * DIS # D4: 4,7 => CTR => D4: 2,9 * DIS D4: 2,9 # F4: 4,7 => CTR => F4: 2,3,9 * DIS D4: 2,9 + F4: 2,3,9 # D5: 4,7 => CTR => D5: 9 * PRF D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 3 => SOL * STA D4: 2,9 + F4: 2,3,9 + D5: 9 + A1: 3 * CNT 4 HDP CHAINS / 12 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6912567 umulig * PAIR REDUCTION .. * ROUND 1: .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... A2: 5,7 A1: 3,5,7 # reduction candidate for 5,7 B1: 1,3,4,5,7 # reduction candidate for 5,7 B2: 1,4,5,7 # reduction candidate for 5,7 B2: 1,4,5,7 # reduction candidate for 5,7 D2: 1,2,4,5,7,8 # reduction candidate for 5,7 F2: 1,2,4,5,7 # reduction candidate for 5,7 A1: 3,5,7 # reduction candidate for 5,7 A5: 3,5,7,9 # reduction candidate for 5,7 E5: 4,7 D4: 2,4,7,9 # reduction candidate for 4,7 D4: 4,7 => CTR * 3..8.69....923..6.68...9..49...12685...9.8312128.63749493.8.2562..6954..8.532..9. F4: 2,3,4,7,9 # reduction candidate for 4,7 F4: 4,7 => CTR * 3....69....9.32.6.68...9..49..21.685...9.8312128.63749493.8.2562..6954..8.532..9. D5: 4,7,9 # reduction candidate for 4,7 D5: 4,7 => CTR * ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197 I6: 3,9 * ROUND 2: .....69....9.3..6.68...9..49..213685...978412128...7..49..8..562...9....8.53..... A2: 5,7 A1: 3,5,7 # reduction candidate for 5,7 A1: 3 => SOLVED * 342856971759431268681729534974213685536978412128564793497182356213695847865347129 * SOLVED! |:step:| 00 -------------------------------------------------- |:step:| 01 --------------------------------------------------
Solution
position: 342856971759431268681729534974213685536978412128564793497182356213695847865347129 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:
* INC # A1: 5,7 => UNS * INC # B1: 5,7 => UNS * INC # B2: 5,7 => UNS * INC # D2: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # A5: 5,7 => UNS * INC # A5: 3,9 => UNS * DIS # D4: 4,7 => CTR => D4: 2,9 * INC # D4: 2,9 => UNS * DIS # F4: 4,7 => CTR => F4: 2,3,9 * INC # F4: 2,3,9 => UNS * DIS # D5: 4,7 => CTR => D5: 9 * INC # D5: 9 => UNS * DIS # B5: 4,7 => CTR => B5: 3,5,6 * INC # B5: 3,5,6 => UNS * DIS # C5: 4,7 => CTR => C5: 3,6 * INC # C5: 3,6 => UNS * INC # E1: 4,7 => UNS * PRF # E9: 4,7 => SOL * INC # E9: 2,6 => UNS * DIS # I5: 3,9 => CTR => I5: 2 * INC # I5: 2 => UNS * INC # H6: 3,9 => UNS * DIS # F6: 3,9 => CTR => F6: 4,5 * INC # F6: 4,5 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # A1: 5,7 => UNS * INC # B1: 5,7 => UNS * INC # B2: 5,7 => UNS * INC # D2: 5,7 => UNS * INC # F2: 5,7 => UNS * INC # A5: 5,7 => UNS * INC # A5: 3,9 => UNS * DIS # D4: 4,7 => CTR => D4: 2,9 * DIS D4: 2,9 # F4: 4,7 => CTR => F4: 2,3,9 * DIS D4: 2,9 + F4: 2,3,9 # D5: 4,7 => CTR => D5: 9 * INC D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 5,7 => UNS * PRF D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 3 => SOL * STA D4: 2,9 + F4: 2,3,9 + D5: 9 + A1: 3 * CNT 12 HDP CHAINS / 12 HYP OPENED