Analysis of zz-sudoku-de-639650-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .8.3.9.2...15.87..5.......6..3.7.5..4.......8..6.2.4..1.......4..97.42...4.6.1.8. initial

Autosolve

position: 687349125..156874.5.42178.68.34765.24..19...8..682.4..1.89.2..43.97842.1.4.6.198. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # B2: 2,9 => SOL
* DIS # B2: 3 => CTR => B2: 2,9
* DIS # B2: 3,9 => CTR => B2: 2
* PRF # B2: 2 => SOL
* DIS # B2: 3,9 => CTR => B2: 2
* PRF # B2: 2 => SOL
* PRF # I6: 3,9 => SOL
* DIS # I6: 7 => CTR => I6: 3,9
* PRF # H6: 3,9 => SOL
* PRF # B6: 1,9 => SOL
* DIS # B6: 5,7 => CTR => B6: 1,9
* PRF # B5: 2,5 => SOL
* DIS # B5: 7 => CTR => B5: 2,5
* DIS # B6: 7,9 => CTR => B6: 1,5
* DIS # H6: 7,9 => CTR => H6: 1,3
* DIS # H6: 1,9 => CTR => H6: 3,7
* PRF # H6: 3,7 => SOL
* DIS # H5: 3,6 => CTR => H5: 7
* PRF # H5: 7 => SOL
* DIS # B7: 5,6 => CTR => B7: 7
* PRF # B7: 7 => SOL
* DIS # H7: 3,5 => CTR => H7: 6,7
* PRF # H7: 3,6 => SOL
* PRF # H7: 5,6 => SOL
* DIS # H7: 3,7 => CTR => H7: 5,6
* DIS # H7: 3,7 => CTR => H7: 5,6
* PRF # H7: 5,6 => SOL
* DIS # I6: 3,7 => CTR => I6: 9
* PRF # I6: 9 => SOL
* CNT  29 HDP CHAINS /  35 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 # B2: 2,9 => SOL
* STA B2: 2,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

.8.3.9.2...15.87..5.......6..3.7.5..4.......8..6.2.4..1.......4..97.42...4.6.1.8. initial
687349125..156874.5.42178.68.34765.24..19...8..682.4..1.89.2..43.97842.1.4.6.198. autosolve
687349125921568743534217896893476512452193678716825439178952364369784251245631987 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (19)
A2: 2,9
B3: 3,9
I2: 3,9
H3: 3,9
B4: 1,9
C5: 2,5
A6: 7,9
F5: 3,5
F6: 3,5
H4: 1,9
G5: 3,6
B8: 5,6
A9: 2,7
C9: 2,5
E7: 3,5
E9: 3,5
G7: 3,6
H8: 5,6
I9: 3,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,B6: 1.. / B4 = 1  =>  0 pairs (X) / B6 = 1  =>  0 pairs (_)
H4,H6: 1.. / H4 = 1  =>  0 pairs (*) / H6 = 1  =>  0 pairs (X)
B4,H4: 1.. / B4 = 1  =>  0 pairs (X) / H4 = 1  =>  0 pairs (_)
B6,H6: 1.. / B6 = 1  =>  0 pairs (*) / H6 = 1  =>  0 pairs (X)
A2,B2: 2.. / A2 = 2  =>  0 pairs (X) / B2 = 2  =>  0 pairs (_)
B5,C5: 2.. / B5 = 2  =>  0 pairs (X) / C5 = 2  =>  0 pairs (_)
A9,C9: 2.. / A9 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
A2,A9: 2.. / A2 = 2  =>  0 pairs (X) / A9 = 2  =>  0 pairs (_)
B2,B5: 2.. / B2 = 2  =>  0 pairs (*) / B5 = 2  =>  0 pairs (X)
C5,C9: 2.. / C5 = 2  =>  0 pairs (*) / C9 = 2  =>  0 pairs (X)
B2,B3: 3.. / B2 = 3  =>  0 pairs (X) / B3 = 3  =>  0 pairs (_)
I2,H3: 3.. / I2 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
F5,F6: 3.. / F5 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
E7,E9: 3.. / E7 = 3  =>  0 pairs (X) / E9 = 3  =>  0 pairs (_)
B2,I2: 3.. / B2 = 3  =>  0 pairs (X) / I2 = 3  =>  0 pairs (_)
B3,H3: 3.. / B3 = 3  =>  0 pairs (*) / H3 = 3  =>  0 pairs (X)
E9,I9: 3.. / E9 = 3  =>  0 pairs (*) / I9 = 3  =>  0 pairs (X)
G5,G7: 3.. / G5 = 3  =>  0 pairs (X) / G7 = 3  =>  0 pairs (_)
F5,F6: 5.. / F5 = 5  =>  0 pairs (X) / F6 = 5  =>  0 pairs (_)
E7,E9: 5.. / E7 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
H7,H8: 5.. / H7 = 5  =>  0 pairs (X) / H8 = 5  => 18 pairs (_)
B6,F6: 5.. / B6 = 5  =>  0 pairs (X) / F6 = 5  =>  0 pairs (_)
B8,H8: 5.. / B8 = 5  =>  0 pairs (X) / H8 = 5  => 18 pairs (_)
C9,E9: 5.. / C9 = 5  =>  0 pairs (*) / E9 = 5  =>  0 pairs (X)
C5,C9: 5.. / C5 = 5  =>  0 pairs (X) / C9 = 5  =>  0 pairs (_)
G5,H5: 6.. / G5 = 6  =>  0 pairs (*) / H5 = 6  =>  0 pairs (X)
B7,B8: 6.. / B7 = 6  =>  0 pairs (X) / B8 = 6  => 18 pairs (_)
B8,H8: 6.. / B8 = 6  => 18 pairs (_) / H8 = 6  =>  0 pairs (X)
G5,G7: 6.. / G5 = 6  =>  0 pairs (*) / G7 = 6  =>  0 pairs (X)
B7,A9: 7.. / B7 = 7  =>  0 pairs (*) / A9 = 7  =>  0 pairs (X)
H7,I9: 7.. / H7 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
B5,H5: 7.. / B5 = 7  =>  0 pairs (X) / H5 = 7  =>  0 pairs (_)
B7,H7: 7.. / B7 = 7  =>  0 pairs (*) / H7 = 7  =>  0 pairs (X)
A9,I9: 7.. / A9 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
A6,A9: 7.. / A6 = 7  =>  0 pairs (*) / A9 = 7  =>  0 pairs (X)
I6,I9: 7.. / I6 = 7  =>  0 pairs (X) / I9 = 7  =>  0 pairs (_)
I2,H3: 9.. / I2 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
B3,H3: 9.. / B3 = 9  =>  0 pairs (X) / H3 = 9  =>  0 pairs (_)
B4,H4: 9.. / B4 = 9  =>  0 pairs (*) / H4 = 9  =>  0 pairs (X)
A2,A6: 9.. / A2 = 9  =>  0 pairs (*) / A6 = 9  =>  0 pairs (X)
I2,I6: 9.. / I2 = 9  =>  0 pairs (X) / I6 = 9  =>  0 pairs (_)
* DURATION: 0:01:07.791832  START: 07:31:33.040009  END: 07:32:40.831841 2017-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A9,B3,B4,B8,C5,C9,E7,E9,F5,F6,G5,G7,H3,H4,H8,I2,I9)
* 687349125..156874.5.42178.68.34765.24..19...8..682.4..1.89.2..43.97842.1.4.6.198.
* PAIR A2: 2,9 BLK 1
B2: 2,9,3                                # reduction candidate for 2,9
B2: 2,9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
B2: 3 => CTR
* 6873491252315687495942178368134765924251936789768254131.89.23.43.97842.174.6.198.
* PAIR B3: 3,9 BLK 1
B2: 3,9,2                                # reduction candidate for 3,9
B2: 3,9 => CTR
* 6873491252.156874.5.42178.68.34765.24251936789768254131.89.23.43.97842.174.6.198.
B2: 2 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* PAIR I2: 3,9 ROW 2
B2: 3,9,2                                # reduction candidate for 3,9
B2: 3,9 => CTR
* 6873491252.156874.5.42178.68.34765.24251936789768254131.89.23.43.97842.174.6.198.
B2: 2 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* PAIR I2: 3,9 COL I
I6: 3,9,7                                # reduction candidate for 3,9
I6: 3,9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
I6: 7 => CTR
* 687349125..15687495942178368134765924..19.3689.68234171.8932674369784251742651983
* PAIR H3: 3,9 COL H
H6: 3,9,1,7                              # reduction candidate for 3,9
H6: 3,9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
H6: 1,7                                  # 20 pairs
* PAIR B4: 1,9 BLK 4
B6: 1,9,5,7                              # reduction candidate for 1,9
B6: 1,9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
B6: 5,7 => CTR
* 687349125231568749594217836813476592425193..89.682.41.1.89.2..43.97842.1742651983
* PAIR C5: 2,5 BLK 4
B5: 2,5,7                                # reduction candidate for 2,5
B5: 2,5 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
B5: 7 => CTR
* 687349125.2156874353421789689347651247.19...8..682.4..1.89.2..43.97842.1.4.6.198.
* PAIR A6: 7,9 BLK 4
B6: 7,9,1,5                              # reduction candidate for 7,9
B6: 7,9 => CTR
* 687349125.3156874959421783681347659242.19...8..68254131.89.23.43.97842.1.4.631987
B6: 1,5                                  # 20 pairs
* PAIR A6: 7,9 ROW 6
H6: 7,9,1,3                              # reduction candidate for 7,9
H6: 7,9 => CTR
* 687349125.315687495942178.68.34765124..19...8.168254.31.89.23.43.97842.1.4.631987
H6: 1,3                                  # 21 pairs
I6: 7,9,3                                # reduction candidate for 7,9
I6: 7,9                                  # 23 pairs
* PAIR H4: 1,9 BLK 6
H6: 1,9,3,7                              # reduction candidate for 1,9
H6: 1,9 => CTR
* 687349125.315687495942178368134765924251936789768254131.89.23.43.97842.174.6.198.
H6: 3,7 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* PAIR G5: 3,6 BLK 6
H5: 3,6,7                                # reduction candidate for 3,6
H5: 3,6 => CTR
* 687349125..156874.5.42178.68.34765.2472195..89.682.4..1.89.2..43.97842.1.4.6.198.
H5: 7 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* PAIR B8: 5,6 BLK 7
B7: 5,6,7                                # reduction candidate for 5,6
B7: 5,6 => CTR
* 687349125..156874.5.42178.68.34765.24..19...8..682.4..1.89.2.743.9784251742651983
B7: 7 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* PAIR E7: 3,5 ROW 7
H7: 3,5,6,7                              # reduction candidate for 3,5
H7: 3,5 => CTR
* 687349125..156874.5.42178.68.34765.24..19...8..682.4..1789.26.4369784251.4.6.198.
H7: 6,7                                  # 19 pairs
* PAIR G7: 3,6 BLK 9
H7: 3,6,5,7                              # reduction candidate for 3,6
H7: 3,6 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
H7: 5,7                                  # 20 pairs
* PAIR H8: 5,6 BLK 9
H7: 5,6,3,7                              # reduction candidate for 5,6
H7: 5,6 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
H7: 3,7 => CTR
* 687349125..156874.5.42178.68.34765.24721953689.682.4..1.89.26.4369784251.4.6.198.
* PAIR I9: 3,7 BLK 9
H7: 3,7,5,6                              # reduction candidate for 3,7
H7: 3,7 => CTR
* 687349125..156874.5.42178.68.34765.24721953689.682.4..1.89.26.4369784251.4.6.198.
H7: 5,6 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* PAIR I9: 3,7 COL I
I6: 3,7,9                                # reduction candidate for 3,7
I6: 3,7 => CTR
* 687349125231568749594217836813476592425193..89.682.41.1.89.2..43.97842.1742651983
I6: 9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-639650-base-pr-000.dot
* REASONING
* PRF # B2: 2,9 => SOL
* DIS # B2: 3 => CTR => B2: 2,9
* DIS # B2: 3,9 => CTR => B2: 2
* PRF # B2: 2 => SOL
* DIS # B2: 3,9 => CTR => B2: 2
* PRF # B2: 2 => SOL
* PRF # I6: 3,9 => SOL
* DIS # I6: 7 => CTR => I6: 3,9
* PRF # H6: 3,9 => SOL
* PRF # B6: 1,9 => SOL
* DIS # B6: 5,7 => CTR => B6: 1,9
* PRF # B5: 2,5 => SOL
* DIS # B5: 7 => CTR => B5: 2,5
* DIS # B6: 7,9 => CTR => B6: 1,5
* DIS # H6: 7,9 => CTR => H6: 1,3
* DIS # H6: 1,9 => CTR => H6: 3,7
* PRF # H6: 3,7 => SOL
* DIS # H5: 3,6 => CTR => H5: 7
* PRF # H5: 7 => SOL
* DIS # B7: 5,6 => CTR => B7: 7
* PRF # B7: 7 => SOL
* DIS # H7: 3,5 => CTR => H7: 6,7
* PRF # H7: 3,6 => SOL
* PRF # H7: 5,6 => SOL
* DIS # H7: 3,7 => CTR => H7: 5,6
* DIS # H7: 3,7 => CTR => H7: 5,6
* PRF # H7: 5,6 => SOL
* DIS # I6: 3,7 => CTR => I6: 9
* PRF # I6: 9 => SOL
* CNT  29 HDP CHAINS /  35 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A6,A9,B3,B4,B8,C5,C9,E7,E9,F5,F6,G5,G7,H3,H4,H8,I2,I9)
* 687349125..156874.5.42178.68.34765.24..19...8..682.4..1.89.2..43.97842.1.4.6.198.
* PAIR A2: 2,9 BLK 1
B2: 2,9,3                                # reduction candidate for 2,9
B2: 2,9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* DURATION: 0:00:01.930938  START: 07:33:18.239941  END: 07:33:20.170879 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-639650-base-pr-001.dot
* REASONING
* PRF # B2: 2,9 => SOL
* STA B2: 2,9
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/639650.html
sehr schwierig

--------------------------------------------------
level: medium

* PAIR REDUCTION ..
* ROUND 1: 687349125..156874.5.42178.68.34765.24..19...8..682.4..1.89.2..43.97842.1.4.6.198.
A2: 2,9
B2: 2,3,9                                # reduction candidate for 2,9
B2: 2,9 => SOLVED
* 687349125921568743534217896893476512452193678716825439178952364369784251245631987
* SOLVED!

--------------------------------------------------
* AUTO ..
* UNSOLVED!

|:step:| 00
--------------------------------------------------

G5,G7,H5,H7: 3,6.. => H5 = 7 or H7 = 7,5 # pair quad

H5 != 7 => CTR
=> H5 = 7
* SOLVED!

|:step:| 01
--------------------------------------------------

Solution

position: 687349125921568743534217896893476512452193678716825439178952364369784251245631987 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 # B2: 2,9 => SOL
* DIS # B2: 3 => CTR => B2: 2,9
* DIS # B2: 3,9 => CTR => B2: 2
* PRF # B2: 2 => SOL
* DIS # B2: 3,9 => CTR => B2: 2
* PRF # B2: 2 => SOL
* PRF # I6: 3,9 => SOL
* DIS # I6: 7 => CTR => I6: 3,9
* PRF # H6: 3,9 => SOL
* INC # H6: 1,7 => UNS
* PRF # B6: 1,9 => SOL
* DIS # B6: 5,7 => CTR => B6: 1,9
* PRF # B5: 2,5 => SOL
* DIS # B5: 7 => CTR => B5: 2,5
* DIS # B6: 7,9 => CTR => B6: 1,5
* INC # B6: 1,5 => UNS
* DIS # H6: 7,9 => CTR => H6: 1,3
* INC # H6: 1,3 => UNS
* INC # I6: 7,9 => UNS
* DIS # H6: 1,9 => CTR => H6: 3,7
* PRF # H6: 3,7 => SOL
* DIS # H5: 3,6 => CTR => H5: 7
* PRF # H5: 7 => SOL
* DIS # B7: 5,6 => CTR => B7: 7
* PRF # B7: 7 => SOL
* DIS # H7: 3,5 => CTR => H7: 6,7
* INC # H7: 6,7 => UNS
* PRF # H7: 3,6 => SOL
* INC # H7: 5,7 => UNS
* PRF # H7: 5,6 => SOL
* DIS # H7: 3,7 => CTR => H7: 5,6
* DIS # H7: 3,7 => CTR => H7: 5,6
* PRF # H7: 5,6 => SOL
* DIS # I6: 3,7 => CTR => I6: 9
* PRF # I6: 9 => SOL
* CNT  35 HDP CHAINS /  35 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # B2: 2,9 => SOL
* STA B2: 2,9
* CNT   1 HDP CHAINS /   1 HYP OPENED