Analysis of zz-sudoku-de-622251-base.sdk
Contents
Original Sudoku
level: medium
position: ......2...2....495...2...63...1..9.75...7...43.1..6...86...5...297....8...5...... initial
Autosolve
position: ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # F2: 1,7 => SOL * PRF # E3: 9 => SOL * DIS # E1: 4,9 => CTR => E1: 1,3,6 * DIS # A1: 1,4 => CTR => A1: 9 * PRF # E8: 4,6 => SOL * DIS # E9: 6,8 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # D2: 6,8 => SOL * DIS # D2: 7 => CTR => D2: 6,8 * DIS # F3: 4 => CTR => F3: 7,9 * PRF # E8: 1,6 => SOL * CNT 11 HDP CHAINS / 23 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # F2: 1,7 => SOL * STA F2: 1,7 * CNT 1 HDP CHAINS / 3 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ......2...2....495...2...63...1..9.75...7...43.1..6...86...5...297....8...5...... | initial |
| ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... | autosolve |
| 916534278723681495458297163642158937589372614371946852864715329297463581135829746 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (20) B1: 1,3 A2: 1,7 C3: 4,8 D6: 4,9 E6: 4,9 C7: 3,4 A9: 1,4 B9: 1,3 D7: 7,9 E7: 1,2 D8: 4,6 D9: 6,8 F9: 7,9 G7: 3,7 H7: 2,4 I7: 1,9 I8: 1,6 G9: 3,7 H9: 2,4 I9: 6,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) A9,B9: 1.. / A9 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) I7,I8: 1.. / I7 = 1 => 0 pairs (X) / I8 = 1 => 0 pairs (_) E7,I7: 1.. / E7 = 1 => 0 pairs (*) / I7 = 1 => 0 pairs (X) B1,B9: 1.. / B1 = 1 => 0 pairs (*) / B9 = 1 => 0 pairs (X) E7,E9: 2.. / E7 = 2 => 0 pairs (X) / E9 = 2 => 0 pairs (_) H7,H9: 2.. / H7 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) E7,H7: 2.. / E7 = 2 => 0 pairs (X) / H7 = 2 => 0 pairs (_) E9,H9: 2.. / E9 = 2 => 0 pairs (*) / H9 = 2 => 0 pairs (X) C7,B9: 3.. / C7 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) E8,F8: 3.. / E8 = 3 => 21 pairs (_) / F8 = 3 => 0 pairs (*) G7,G9: 3.. / G7 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) C7,G7: 3.. / C7 = 3 => 0 pairs (X) / G7 = 3 => 0 pairs (_) B9,G9: 3.. / B9 = 3 => 0 pairs (*) / G9 = 3 => 0 pairs (X) B1,B9: 3.. / B1 = 3 => 0 pairs (X) / B9 = 3 => 0 pairs (_) D6,E6: 4.. / D6 = 4 => 0 pairs (X) / E6 = 4 => 0 pairs (_) C7,A9: 4.. / C7 = 4 => 0 pairs (*) / A9 = 4 => 0 pairs (X) H7,H9: 4.. / H7 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) C7,H7: 4.. / C7 = 4 => 0 pairs (*) / H7 = 4 => 0 pairs (X) A9,H9: 4.. / A9 = 4 => 0 pairs (X) / H9 = 4 => 0 pairs (_) D6,D8: 4.. / D6 = 4 => 0 pairs (X) / D8 = 4 => 0 pairs (_) C1,C2: 6.. / C1 = 6 => 21 pairs (_) / C2 = 6 => 24 pairs (_) I8,I9: 6.. / I8 = 6 => 0 pairs (X) / I9 = 6 => 0 pairs (_) C1,E1: 6.. / C1 = 6 => 21 pairs (_) / E1 = 6 => 24 pairs (_) A2,A3: 7.. / A2 = 7 => 0 pairs (*) / A3 = 7 => 0 pairs (X) D7,F9: 7.. / D7 = 7 => 0 pairs (*) / F9 = 7 => 0 pairs (X) G7,G9: 7.. / G7 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) A3,F3: 7.. / A3 = 7 => 0 pairs (X) / F3 = 7 => 0 pairs (_) D7,G7: 7.. / D7 = 7 => 0 pairs (*) / G7 = 7 => 0 pairs (X) F9,G9: 7.. / F9 = 7 => 0 pairs (X) / G9 = 7 => 0 pairs (_) D2,D7: 7.. / D2 = 7 => 0 pairs (X) / D7 = 7 => 0 pairs (_) C2,C3: 8.. / C2 = 8 => 0 pairs (X) / C3 = 8 => 21 pairs (_) D9,E9: 8.. / D9 = 8 => 21 pairs (_) / E9 = 8 => 0 pairs (X) C3,E3: 8.. / C3 = 8 => 21 pairs (_) / E3 = 8 => 0 pairs (X) D2,D9: 8.. / D2 = 8 => 0 pairs (X) / D9 = 8 => 21 pairs (_) A1,A3: 9.. / A1 = 9 => 21 pairs (_) / A3 = 9 => 0 pairs (X) D6,E6: 9.. / D6 = 9 => 0 pairs (*) / E6 = 9 => 0 pairs (X) D7,F9: 9.. / D7 = 9 => 0 pairs (X) / F9 = 9 => 0 pairs (_) I7,I9: 9.. / I7 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) D7,I7: 9.. / D7 = 9 => 0 pairs (X) / I7 = 9 => 0 pairs (_) F9,I9: 9.. / F9 = 9 => 0 pairs (*) / I9 = 9 => 0 pairs (X) D6,D7: 9.. / D6 = 9 => 0 pairs (*) / D7 = 9 => 0 pairs (X) * DURATION: 0:01:16.590995 START: 07:23:00.583697 END: 07:24:17.174692 2017-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B1,B9,C3,C7,D6,D7,D8,D9,E6,E7,F9,G7,G9,H7,H9,I7,I8,I9) * ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... * PAIR B1: 1,3 ROW 1 E1: 1,3,4,6,9 # reduction candidate for 1,3 E1: 1,3 # 28 pairs F1: 1,3,4,9 # reduction candidate for 1,3 F1: 1,3 # 23 pairs * PAIR A2: 1,7 ROW 2 F2: 1,7,3 # reduction candidate for 1,7 F2: 1,7 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 F2: 3 # 22 pairs * PAIR C3: 4,8 ROW 3 E3: 4,8,9 # reduction candidate for 4,8 E3: 9 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 E3: 4,8 # 24 pairs * PAIR E6: 4,9 COL E E1: 4,9,1,3,6 # reduction candidate for 4,9 E1: 4,9 => CTR * .365..278.2876.495.5428.163642158937589372614371..6852863..574.297...58.4158.7329 E1: 1,3,6 # 20 pairs E3: 4,9,8 # reduction candidate for 4,9 E3: 4,9 # 21 pairs * PAIR C7: 3,4 COL C C1: 3,4,6 # reduction candidate for 3,4 C1: 3,4 # 24 pairs C1: 6 # 21 pairs * PAIR A9: 1,4 COL A A1: 1,4,9 # reduction candidate for 1,4 A1: 1,4 => CTR * .1.59.27872...149595.2.7163642158937589372614371946852864715329297463581135829746 A1: 9 # 21 pairs * PAIR D8: 4,6 BLK 8 E8: 4,6,1,3 # reduction candidate for 4,6 E8: 4,6 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 E8: 1,3 # 21 pairs * PAIR D9: 6,8 BLK 8 E9: 6,8,2 # reduction candidate for 6,8 E9: 6,8 => CTR * .3.5..278.2....495.5.2..163642158937589372614371..68528639257412974..586415...329 E9: 2 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 * PAIR D9: 6,8 COL D D2: 6,8,7 # reduction candidate for 6,8 D2: 6,8 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 D2: 7 => CTR * ...5..278.2.7..49575.2..163642158937589372614371..685286.9.57.1297...586..5...... * PAIR F9: 7,9 COL F F3: 7,9,4 # reduction candidate for 7,9 F3: 4 => CTR * ...5..278.2....49575.29416364215893758937261437194685286.7.53.92974..581.35..97.6 F3: 7,9 # 22 pairs * PAIR I8: 1,6 ROW 8 E8: 1,6,3,4 # reduction candidate for 1,6 E8: 1,6 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 E8: 3,4 # 21 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-622251-base-pr-000.dot * REASONING * PRF # F2: 1,7 => SOL * PRF # E3: 9 => SOL * DIS # E1: 4,9 => CTR => E1: 1,3,6 * DIS # A1: 1,4 => CTR => A1: 9 * PRF # E8: 4,6 => SOL * DIS # E9: 6,8 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # D2: 6,8 => SOL * DIS # D2: 7 => CTR => D2: 6,8 * DIS # F3: 4 => CTR => F3: 7,9 * PRF # E8: 1,6 => SOL * CNT 11 HDP CHAINS / 23 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B1,B9,C3,C7,D6,D7,D8,D9,E6,E7,F9,G7,G9,H7,H9,I7,I8,I9) * ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... * PAIR B1: 1,3 ROW 1 E1: 1,3,4,6,9 # reduction candidate for 1,3 E1: 1,3 # 28 pairs F1: 1,3,4,9 # reduction candidate for 1,3 F1: 1,3 # 23 pairs * PAIR A2: 1,7 ROW 2 F2: 1,7,3 # reduction candidate for 1,7 F2: 1,7 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 * DURATION: 0:00:04.204302 START: 07:24:43.193261 END: 07:24:47.397563 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-622251-base-pr-001.dot * REASONING * PRF # F2: 1,7 => SOL * STA F2: 1,7 * CNT 1 HDP CHAINS / 3 HYP OPENED
Header Info
http://www.sudokus.de/622251.html sehr schwierig level: medium * PAIR REDUCTION .. * ROUND 1: ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... B1: 1,3 E1: 1,3,4,6,9 # reduction candidate for 1,3 F1: 1,3,4,9 # reduction candidate for 1,3 A2: 1,7 F2: 1,3,7 # reduction candidate for 1,7 F2: 1,7 => SOLVED * 916534278723681495458297163642158937589372614371946852864715329297463581135829746 * SOLVED! -------------------------------------------------- * AUTO .. Q7: 1.. = A9,B9: 1.. => E9,F9,I9 != 1 Q7,Q9: 3.. => E7,E9,F9 != 3 Q7,Q9: 4.. => D7,E7,D9,E9,F9 != 4 D7,F9: 7,9.. => E7,D9,E9 != 7,9 # naked pair * UNSOLVED! |:step:| 00 -------------------------------------------------- first block pair-elimination candidate: D9: 6,8 E9: 2,6,8 * DISABLE:: E9 != 8 * DISABLE:: E9 != 6 * AUTO .. * SOLVED! |:step:| 01 -------------------------------------------------- * DISABLE VALUE:: D2 != 7 => D2,D9: 6,8 # naked pair * AUTO .. * SOLVED! |:step:| alternate --------------------------------------------------
Solution
position: 916534278723681495458297163642158937589372614371946852864715329297463581135829746 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 # E1: 1,3 => UNS * INC # F1: 1,3 => UNS * PRF # F2: 1,7 => SOL * INC # F2: 3 => UNS * INC # E3: 4,8 => UNS * PRF # E3: 9 => SOL * DIS # E1: 4,9 => CTR => E1: 1,3,6 * INC # E1: 1,3,6 => UNS * INC # E3: 4,9 => UNS * INC # C1: 3,4 => UNS * INC # C1: 6 => UNS * DIS # A1: 1,4 => CTR => A1: 9 * INC # A1: 9 => UNS * PRF # E8: 4,6 => SOL * INC # E8: 1,3 => UNS * DIS # E9: 6,8 => CTR => E9: 2 * PRF # E9: 2 => SOL * PRF # D2: 6,8 => SOL * DIS # D2: 7 => CTR => D2: 6,8 * INC # F3: 7,9 => UNS * DIS # F3: 4 => CTR => F3: 7,9 * PRF # E8: 1,6 => SOL * INC # E8: 3,4 => UNS * CNT 23 HDP CHAINS / 23 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # E1: 1,3 => UNS * INC # F1: 1,3 => UNS * PRF # F2: 1,7 => SOL * STA F2: 1,7 * CNT 3 HDP CHAINS / 3 HYP OPENED