Analysis of zz-sudoku-de-781180-base.sdk
Contents
Original Sudoku
level: medium
position: ...3.1....4.....5.175...836..21.93..4.......2..94.51..826...917.9.....8....9.7... initial
Autosolve
position: 268351..9943768251175294836.821793..4..836.92.394251.8826543917.9.612.8....98762. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # I8: 4,5 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 7 => CTR => A8: 3,5 * PRF # I9: 3,5 => SOL * DIS # I9: 4 => CTR => I9: 3,5 * PRF # I8: 4,5 => SOL * CNT 6 HDP CHAINS / 10 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # I8: 4,5 => SOL * STA I8: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ...3.1....4.....5.175...836..21.93..4.......2..94.51..826...917.9.....8....9.7... | initial |
| 268351..9943768251175294836.821793..4..836.92.394251.8826543917.9.612.8....98762. | autosolve |
| 268351479943768251175294836682179345451836792739425168826543917397612584514987623 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (15) G1: 4,7 H1: 4,7 A4: 5,6 B5: 1,5 C5: 1,7 A6: 6,7 H4: 4,6 I4: 4,5 G5: 5,7 H6: 6,7 C8: 4,7 A9: 3,5 B9: 1,5 C9: 1,4 G8: 4,5 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,C5: 1.. / B5 = 1 => 0 pairs (X) / C5 = 1 => 0 pairs (_) B9,C9: 1.. / B9 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) B5,B9: 1.. / B5 = 1 => 0 pairs (X) / B9 = 1 => 0 pairs (_) C5,C9: 1.. / C5 = 1 => 0 pairs (*) / C9 = 1 => 0 pairs (X) A8,A9: 3.. / A8 = 3 => 0 pairs (*) / A9 = 3 => 0 pairs (X) I8,I9: 3.. / I8 = 3 => 16 pairs (_) / I9 = 3 => 0 pairs (*) A8,I8: 3.. / A8 = 3 => 0 pairs (*) / I8 = 3 => 0 pairs (X) A9,I9: 3.. / A9 = 3 => 16 pairs (_) / I9 = 3 => 0 pairs (*) G1,H1: 4.. / G1 = 4 => 0 pairs (*) / H1 = 4 => 0 pairs (X) H4,I4: 4.. / H4 = 4 => 0 pairs (*) / I4 = 4 => 0 pairs (X) C8,C9: 4.. / C8 = 4 => 0 pairs (X) / C9 = 4 => 0 pairs (_) C9,I9: 4.. / C9 = 4 => 0 pairs (*) / I9 = 4 => 0 pairs (X) G1,G8: 4.. / G1 = 4 => 0 pairs (*) / G8 = 4 => 0 pairs (X) H1,H4: 4.. / H1 = 4 => 0 pairs (X) / H4 = 4 => 0 pairs (_) A4,B5: 5.. / A4 = 5 => 0 pairs (X) / B5 = 5 => 0 pairs (_) I4,G5: 5.. / I4 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) A4,I4: 5.. / A4 = 5 => 0 pairs (X) / I4 = 5 => 0 pairs (_) B5,G5: 5.. / B5 = 5 => 0 pairs (*) / G5 = 5 => 0 pairs (X) B5,B9: 5.. / B5 = 5 => 0 pairs (*) / B9 = 5 => 0 pairs (X) G5,G8: 5.. / G5 = 5 => 0 pairs (X) / G8 = 5 => 0 pairs (_) A4,A6: 6.. / A4 = 6 => 0 pairs (*) / A6 = 6 => 0 pairs (X) H4,H6: 6.. / H4 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) A4,H4: 6.. / A4 = 6 => 0 pairs (*) / H4 = 6 => 0 pairs (X) A6,H6: 6.. / A6 = 6 => 0 pairs (X) / H6 = 6 => 0 pairs (_) G1,H1: 7.. / G1 = 7 => 0 pairs (X) / H1 = 7 => 0 pairs (_) C5,A6: 7.. / C5 = 7 => 0 pairs (X) / A6 = 7 => 0 pairs (_) G5,H6: 7.. / G5 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) A8,C8: 7.. / A8 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) C5,G5: 7.. / C5 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) A6,H6: 7.. / A6 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) A6,A8: 7.. / A6 = 7 => 0 pairs (*) / A8 = 7 => 0 pairs (X) C5,C8: 7.. / C5 = 7 => 0 pairs (X) / C8 = 7 => 0 pairs (_) G1,G5: 7.. / G1 = 7 => 0 pairs (X) / G5 = 7 => 0 pairs (_) H1,H6: 7.. / H1 = 7 => 0 pairs (*) / H6 = 7 => 0 pairs (X) * DURATION: 0:00:54.930230 START: 08:48:20.336832 END: 08:49:15.267062 2017-05-01 * CP COUNT: (34) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A9,B5,B9,C5,C8,C9,G1,G5,G8,H1,H4,H6,I4) * 268351..9943768251175294836.821793..4..836.92.394251.8826543917.9.612.8....98762. * PAIR I4: 4,5 COL I I8: 4,5,3 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 268351479943768251175294836682179345451836792739425168826543917397612584514987623 I8: 3 # 16 pairs I9: 4,5,3 # reduction candidate for 4,5 I9: 4,5 # 16 pairs * PAIR A9: 3,5 BLK 7 A8: 3,5,7 # reduction candidate for 3,5 A8: 3,5 => SOLVED * 268351479943768251175294836682179345451836792739425168826543917397612584514987623 A8: 7 => CTR * 268351..9943768251175294836.821793..4..836.92.394251.8826543917794612583351987624 * PAIR A9: 3,5 ROW 9 I9: 3,5,4 # reduction candidate for 3,5 I9: 3,5 => SOLVED * 268351479943768251175294836682179345451836792739425168826543917397612584514987623 I9: 4 => CTR * 2683514799437682511752948365821793..4..836.92.394251.8826543917.9.612.83351987624 * PAIR G8: 4,5 BLK 9 I8: 4,5,3 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 268351479943768251175294836682179345451836792739425168826543917397612584514987623 I8: 3 # 16 pairs I9: 4,5,3 # reduction candidate for 4,5 I9: 4,5 # 16 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-sudoku-de-781180-base-pr-000.dot * REASONING * PRF # I8: 4,5 => SOL * PRF # A8: 3,5 => SOL * DIS # A8: 7 => CTR => A8: 3,5 * PRF # I9: 3,5 => SOL * DIS # I9: 4 => CTR => I9: 3,5 * PRF # I8: 4,5 => SOL * CNT 6 HDP CHAINS / 10 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A9,B5,B9,C5,C8,C9,G1,G5,G8,H1,H4,H6,I4) * 268351..9943768251175294836.821793..4..836.92.394251.8826543917.9.612.8....98762. * PAIR I4: 4,5 COL I I8: 4,5,3 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 268351479943768251175294836682179345451836792739425168826543917397612584514987623 * DURATION: 0:00:02.099103 START: 08:49:27.204054 END: 08:49:29.303157 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-sudoku-de-781180-base-pr-001.dot * REASONING * PRF # I8: 4,5 => SOL * STA I8: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokus.de/781180.html sehr schwierig * STABLE PAIRS (16p + 65s = 81c) # zz-sudoku-de-781180-base.sdk position: I25vdGU6IFBhaXIgUmVkdWN0aW9uIEFuYWx5c2lzICogU1RBQkxFIFBBSVJTICgxNnAgKyA2NXMgPSA4MWMpCgojZGlhZ29uYWxzOiAwCgojZGlzYWJsZWQ6IEkvOC80CiNkaXNhYmxlZDogSS84LzUKMjY4MzUxLi45OTQzNzY4MjUxMTc1Mjk0ODM2LjgyMTc5My4uNC4uODM2LjkyLjM5NDI1MS44ODI2NTQzOTE3LjkuNjEyLjgzMy4uOTg3NjIu * STABLE PAIRS (16p + 65s = 81c) # zz-sudoku-de-781180-base.sdk position: I25vdGU6IFBhaXIgUmVkdWN0aW9uIEFuYWx5c2lzICogU1RBQkxFIFBBSVJTICgxNnAgKyA2NXMgPSA4MWMpCgojZGlhZ29uYWxzOiAwCgojZGlzYWJsZWQ6IEkvOS8zCjI2ODM1MS4uOTk0Mzc2ODI1MTE3NTI5NDgzNi44MjE3OTMuLjQuLjgzNi45Mi4zOTQyNTEuODgyNjU0MzkxNy45LjYxMi44MzMuLjk4NzYyLg== * STABLE PAIRS (16p + 65s = 81c) # zz-sudoku-de-781180-base.sdk position: I25vdGU6IFBhaXIgUmVkdWN0aW9uIEFuYWx5c2lzICogU1RBQkxFIFBBSVJTICgxNnAgKyA2NXMgPSA4MWMpCgojZGlhZ29uYWxzOiAwCgojZGlzYWJsZWQ6IEkvOC80CiNkaXNhYmxlZDogSS84LzUKMjY4MzUxLi45OTQzNzY4MjUxMTc1Mjk0ODM2LjgyMTc5My4uNC4uODM2LjkyLjM5NDI1MS44ODI2NTQzOTE3LjkuNjEyLjgzMy4uOTg3NjIu * STABLE PAIRS (16p + 65s = 81c) # zz-sudoku-de-781180-base.sdk position: I25vdGU6IFBhaXIgUmVkdWN0aW9uIEFuYWx5c2lzICogU1RBQkxFIFBBSVJTICgxNnAgKyA2NXMgPSA4MWMpCgojZGlhZ29uYWxzOiAwCgojZGlzYWJsZWQ6IEkvOS8zCjI2ODM1MS4uOTk0Mzc2ODI1MTE3NTI5NDgzNi44MjE3OTMuLjQuLjgzNi45Mi4zOTQyNTEuODgyNjU0MzkxNy45LjYxMi44MzMuLjk4NzYyLg== -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 268351..9943768251175294836.821793..4..836.92.394251.8826543917.9.612.8....98762. G1: 4,7 H1: 4,7 A4: 5,6 B5: 1,5 C5: 1,7 A6: 6,7 H4: 4,6 I4: 4,5 I8: 3,4,5 # reduction candidate for 4,5 I8: 4,5 => SOLVED * 268351479943768251175294836682179345451836792739425168826543917397612584514987623 * SOLVED! -------------------------------------------------- |:step:| 00 -------------------------------------------------- highlight 3 I8 = 3 # set value A9: 3.. # hidden single => AMBIGUOUS * DISABLE VALUE:: I8 != 3 I9: 3.. # hidden single A8: 3.. # hidden single * SOLVED! |:step:| 01 --------------------------------------------------
Solution
position: 268351479943768251175294836682179345451836792739425168826543917397612584514987623 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 # I8: 4,5 => SOL * INC # I8: 3 => UNS * INC # I9: 4,5 => UNS * PRF # A8: 3,5 => SOL * DIS # A8: 7 => CTR => A8: 3,5 * PRF # I9: 3,5 => SOL * DIS # I9: 4 => CTR => I9: 3,5 * PRF # I8: 4,5 => SOL * INC # I8: 3 => UNS * INC # I9: 4,5 => UNS * CNT 10 HDP CHAINS / 10 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # I8: 4,5 => SOL * STA I8: 4,5 * CNT 1 HDP CHAINS / 1 HYP OPENED