Analysis of zz-sudoku-de-781180-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

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
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

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
Solution

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