Analysis of zz-sudoku-de-652632-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .4...197...8....15....7.3.4...51...8.9.....3.8...63...6.3.2....52....4...793...2. initial

Autosolve

position: .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS # D2: 2,9 => CTR => D2: 4,6
* PRF # D1: 2,6 => SOL
* DIS # D1: 8 => CTR => D1: 2,6
* DIS # D2: 2,6 => CTR => D2: 4,9
* PRF # D1: 2,6 => SOL
* DIS # D1: 8 => CTR => D1: 2,6
* PRF # I5: 7 => SOL
* DIS # D2: 2,6 => CTR => D2: 4,9
* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS # D6: 2,4 => CTR => D6: 7,9
* DIS # F8: 7,9 => CTR => F8: 8
* PRF # I5: 7 => SOL
* DIS # D6: 2,7 => CTR => D6: 4,9
* PRF # I5: 2,7 => SOL
* DIS # I5: 6 => CTR => I5: 2,7
* DIS # D6: 2,7 => CTR => D6: 4,9
* DIS # D8: 8,9 => CTR => D8: 7
* CNT  18 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:

* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS C5: 2,6 # D2: 2,9 => CTR => D2: 4,6
* PRF C5: 2,6 + D2: 4,6 # D1: 2,6 => SOL
* STA C5: 2,6 + D2: 4,6 + D1: 2,6
* CNT   3 HDP CHAINS /   4 HYP OPENED

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

Details

Positions

.4...197...8....15....7.3.4...51...8.9.....3.8...63...6.3.2....52....4...793...2. initial
.45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821 autosolve
345281976768439215912675384234517698196842537857963142683124759521798463479356821 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (18)
A1: 2,3
B2: 3,6
C3: 2,6
E1: 3,8
F2: 2,9
D3: 2,6
I1: 2,6
G2: 2,6
A4: 2,3
B4: 3,6
C4: 4,7
F4: 7,9
E5: 4,8
G4: 2,6
H4: 4,9
H6: 4,9
I6: 2,7
E8: 8,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C3: 2.. / A1 = 2  =>  0 pairs (X) / C3 = 2  =>  0 pairs (_)
I1,G2: 2.. / I1 = 2  =>  0 pairs (X) / G2 = 2  =>  0 pairs (_)
C3,D3: 2.. / C3 = 2  =>  0 pairs (*) / D3 = 2  =>  0 pairs (X)
A4,G4: 2.. / A4 = 2  =>  0 pairs (*) / G4 = 2  =>  0 pairs (X)
A1,A4: 2.. / A1 = 2  =>  0 pairs (X) / A4 = 2  =>  0 pairs (_)
F2,F5: 2.. / F2 = 2  =>  0 pairs (X) / F5 = 2  => 17 pairs (_)
G2,G4: 2.. / G2 = 2  =>  0 pairs (*) / G4 = 2  =>  0 pairs (X)
A1,B2: 3.. / A1 = 3  =>  0 pairs (*) / B2 = 3  =>  0 pairs (X)
E1,E2: 3.. / E1 = 3  =>  0 pairs (X) / E2 = 3  =>  0 pairs (_)
A4,B4: 3.. / A4 = 3  =>  0 pairs (X) / B4 = 3  =>  0 pairs (_)
A1,E1: 3.. / A1 = 3  =>  0 pairs (*) / E1 = 3  =>  0 pairs (X)
B2,E2: 3.. / B2 = 3  =>  0 pairs (X) / E2 = 3  =>  0 pairs (_)
A1,A4: 3.. / A1 = 3  =>  0 pairs (*) / A4 = 3  =>  0 pairs (X)
B2,B4: 3.. / B2 = 3  =>  0 pairs (X) / B4 = 3  =>  0 pairs (_)
D2,E2: 4.. / D2 = 4  => 18 pairs (_) / E2 = 4  =>  0 pairs (X)
H4,H6: 4.. / H4 = 4  =>  0 pairs (X) / H6 = 4  => 19 pairs (_)
C4,H4: 4.. / C4 = 4  => 19 pairs (_) / H4 = 4  =>  0 pairs (X)
E2,E5: 4.. / E2 = 4  =>  0 pairs (X) / E5 = 4  => 18 pairs (_)
B2,C3: 6.. / B2 = 6  =>  0 pairs (*) / C3 = 6  =>  0 pairs (X)
I1,G2: 6.. / I1 = 6  =>  0 pairs (*) / G2 = 6  =>  0 pairs (X)
B4,C5: 6.. / B4 = 6  =>  0 pairs (X) / C5 = 6  =>  0 pairs (_)
G4,I5: 6.. / G4 = 6  =>  0 pairs (*) / I5 = 6  =>  0 pairs (X)
D1,I1: 6.. / D1 = 6  =>  0 pairs (X) / I1 = 6  =>  0 pairs (_)
C3,D3: 6.. / C3 = 6  =>  0 pairs (X) / D3 = 6  =>  0 pairs (_)
B4,G4: 6.. / B4 = 6  =>  0 pairs (X) / G4 = 6  =>  0 pairs (_)
C5,I5: 6.. / C5 = 6  =>  0 pairs (*) / I5 = 6  =>  0 pairs (X)
B2,B4: 6.. / B2 = 6  =>  0 pairs (*) / B4 = 6  =>  0 pairs (X)
C3,C5: 6.. / C3 = 6  =>  0 pairs (X) / C5 = 6  =>  0 pairs (_)
G2,G4: 6.. / G2 = 6  =>  0 pairs (X) / G4 = 6  =>  0 pairs (_)
I1,I5: 6.. / I1 = 6  =>  0 pairs (*) / I5 = 6  =>  0 pairs (X)
I5,I6: 7.. / I5 = 7  =>  0 pairs (*) / I6 = 7  =>  0 pairs (X)
D8,F8: 7.. / D8 = 7  => 19 pairs (_) / F8 = 7  =>  0 pairs (X)
C4,F4: 7.. / C4 = 7  =>  0 pairs (X) / F4 = 7  => 19 pairs (_)
D1,E1: 8.. / D1 = 8  =>  0 pairs (X) / E1 = 8  =>  0 pairs (_)
F5,F8: 8.. / F5 = 8  =>  0 pairs (X) / F8 = 8  => 19 pairs (_)
F4,D6: 9.. / F4 = 9  =>  0 pairs (X) / D6 = 9  => 19 pairs (_)
H4,H6: 9.. / H4 = 9  => 19 pairs (_) / H6 = 9  =>  0 pairs (X)
F4,H4: 9.. / F4 = 9  =>  0 pairs (X) / H4 = 9  => 19 pairs (_)
D6,H6: 9.. / D6 = 9  => 19 pairs (_) / H6 = 9  =>  0 pairs (X)
E2,E8: 9.. / E2 = 9  =>  0 pairs (X) / E8 = 9  => 20 pairs (_)
* DURATION: 0:01:06.709378  START: 07:38:08.700769  END: 07:39:15.410147 2017-05-01
* CP COUNT: (40)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B2,B4,C3,C4,D3,E1,E5,E8,F2,F4,G2,G4,H4,H6,I1,I6)
* .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821
* PAIR C3: 2,6 COL C
C5: 2,6,4,7                              # reduction candidate for 2,6
C5: 4,7 => CTR
* .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821
C5: 2,6                                  # 20 pairs
* PAIR F2: 2,9 BLK 2
D2: 2,9,4,6                              # reduction candidate for 2,9
D2: 2,9 => CTR
* .458319767.8.4..1591..75384...51...819..8.53.85..631..683124759521.98463479356821
D2: 4,6                                  # 19 pairs
* PAIR D3: 2,6 BLK 2
D1: 2,6,8                                # reduction candidate for 2,6
D1: 2,6 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
D1: 8 => CTR
* .45831976738649215916275384...51...819....53.85..631..683124759521...463479356821
D2: 2,6,4,9                              # reduction candidate for 2,6
D2: 2,6 => CTR
* .45831976738649215916275384...517.9819..8253.85.96314.683124759521798463479356821
D2: 4,9                                  # 19 pairs
* PAIR I1: 2,6 ROW 1
D1: 2,6,8                                # reduction candidate for 2,6
D1: 2,6 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
D1: 8 => CTR
* .45831976738649215916275384...51...819....53.85..631..683124759521...463479356821
* PAIR I1: 2,6 COL I
I5: 2,6,7                                # reduction candidate for 2,6
I5: 7 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
I5: 2,6                                  # 19 pairs
* PAIR G2: 2,6 ROW 2
D2: 2,6,4,9                              # reduction candidate for 2,6
D2: 2,6 => CTR
* .45831976738649215916275384...517.9819..8253.85.96314.683124759521798463479356821
D2: 4,9                                  # 19 pairs
* PAIR C4: 4,7 BLK 4
C5: 4,7,2,6                              # reduction candidate for 4,7
C5: 4,7 => CTR
* .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821
C5: 2,6                                  # 20 pairs
C6: 4,7,2                                # reduction candidate for 4,7
C6: 4,7                                  # 20 pairs
* PAIR F4: 7,9 BLK 5
D6: 7,9,2,4                              # reduction candidate for 7,9
D6: 2,4 => CTR
* .45..197.7.8..261591..75384...519.4819....53.85..6319.683124759521...463479356821
D6: 7,9                                  # 22 pairs
* PAIR F4: 7,9 COL F
F8: 7,9,8                                # reduction candidate for 7,9
F8: 7,9 => CTR
* .45..197.7.8..261591..75384...51...819...853.85..631..683124759521...463479356821
F8: 8                                    # 19 pairs
* PAIR E5: 4,8 BLK 5
D5: 4,8,2,7                              # reduction candidate for 4,8
D5: 4,8                                  # 21 pairs
D5: 2,7                                  # 19 pairs
* PAIR G4: 2,6 BLK 6
I5: 2,6,7                                # reduction candidate for 2,6
I5: 7 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
I5: 2,6                                  # 19 pairs
* PAIR H6: 4,9 ROW 6
D6: 4,9,2,7                              # reduction candidate for 4,9
D6: 2,7 => CTR
* .45..197.7.8..261591..75384...519.4819....53.854.6319.683124759521...463479356821
D6: 4,9                                  # 21 pairs
* PAIR I6: 2,7 BLK 6
I5: 2,7,6                                # reduction candidate for 2,7
I5: 2,7 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
I5: 6 => CTR
* .456819727.8.3.61591..75384...51...819....53685..631.7683124759521...463479356821
* PAIR I6: 2,7 ROW 6
C6: 2,7,4                                # reduction candidate for 2,7
C6: 2,7                                  # 21 pairs
D6: 2,7,4,9                              # reduction candidate for 2,7
D6: 2,7 => CTR
* .45..197.7.8..261591..75384...519.4819....53.854.6319.683124759521...463479356821
D6: 4,9                                  # 21 pairs
* PAIR E8: 8,9 BLK 8
D8: 8,9,7                                # reduction candidate for 8,9
D8: 8,9 => CTR
* .45..197.7.8..261591..75384..7519.4819...853.85..6319.683124759521..7463479356821
D8: 7                                    # 19 pairs
F8: 8,9,7                                # reduction candidate for 8,9
F8: 8,9                                  # 19 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-652632-base-pr-000.dot
* REASONING
* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS # D2: 2,9 => CTR => D2: 4,6
* PRF # D1: 2,6 => SOL
* DIS # D1: 8 => CTR => D1: 2,6
* DIS # D2: 2,6 => CTR => D2: 4,9
* PRF # D1: 2,6 => SOL
* DIS # D1: 8 => CTR => D1: 2,6
* PRF # I5: 7 => SOL
* DIS # D2: 2,6 => CTR => D2: 4,9
* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS # D6: 2,4 => CTR => D6: 7,9
* DIS # F8: 7,9 => CTR => F8: 8
* PRF # I5: 7 => SOL
* DIS # D6: 2,7 => CTR => D6: 4,9
* PRF # I5: 2,7 => SOL
* DIS # I5: 6 => CTR => I5: 2,7
* DIS # D6: 2,7 => CTR => D6: 4,9
* DIS # D8: 8,9 => CTR => D8: 7
* CNT  18 HDP CHAINS /  35 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A1,A4,B2,B4,C3,C4,D3,E1,E5,E8,F2,F4,G2,G4,H4,H6,I1,I6)
* .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821
* PAIR C3: 2,6 COL C
C5: 2,6,4,7                              # reduction candidate for 2,6
C5: 4,7 => CTR
* .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821
* PAIR RESTART
* PAIR F2: 2,9 BLK 2
D2: 2,9,4,6                              # reduction candidate for 2,9
D2: 2,9 => CTR
* .458319767.8.4..1591..75384...51...819.48.53.85..631..683124759521.98463479356821
* PAIR D3: 2,6 BLK 2
D1: 2,6,8                                # reduction candidate for 2,6
D1: 2,6 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
* DURATION: 0:00:06.012108  START: 07:39:49.674298  END: 07:39:55.686406 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-652632-base-pr-001.dot
* REASONING
* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS C5: 2,6 # D2: 2,9 => CTR => D2: 4,6
* PRF C5: 2,6 + D2: 4,6 # D1: 2,6 => SOL
* STA C5: 2,6 + D2: 4,6 + D1: 2,6
* CNT   3 HDP CHAINS /   4 HYP OPENED

Header Info

http://www.sudokus.de/652632.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: .45..197.7.8....1591..75384...51...819....53.85..631..683124759521...463479356821
A1: 2,3
B2: 3,6
C3: 2,6
C5: 2,4,6,7                              # reduction candidate for 2,6
C5: 4,7 => CTR
* .45..197.7.8....15916275384.6.51.2.819....53.85..631..683124759521...463479356821
E1: 3,8
F2: 2,9
D2: 2,4,6,9                              # reduction candidate for 2,9
D2: 2,9 => CTR
* .458319767.8.4..1591..75384...51...819.48.53.85..631..683124759521.98463479356821
D3: 2,6
D1: 2,6,8                                # reduction candidate for 2,6
D1: 2,6 => SOLVED
* 345281976768439215912675384234517698196842537857963142683124759521798463479356821
* SOLVED!

--------------------------------------------------
* AUTO ..
A2 = 7                # set value
H3 = 8                # set value
B7 = 8                # set value
C8 = 1                # set value
A9: 4                 # naked single
I8 = 3                # set value
A9 = 4                # set value
A3: 9..               # hidden single
D7: 1..               # hidden single
G9: 8..               # hidden single
A3 = 9                # set value
D7 = 1                # set value
G9 = 8                # set value
E9: 5                 # naked single
B3: 1..               # hidden single
F7: 4..               # hidden single
I9: 1..               # hidden single
A5: 1..               # hidden single
B3 = 1                # set value
B6: 5                 # naked single
A5 = 1                # set value
B6 = 5                # set value
F7 = 4                # set value
E9 = 5                # set value
F9: 6                 # naked single
F9 = 6                # set value
I9: 1                 # naked single
I9 = 1                # set value
F3: 5..               # hidden single
G6: 1..               # hidden single
G5: 5..               # hidden single
H8: 6..               # hidden single
C1: 5..               # hidden single
H7: 5..               # hidden single
C1 = 5                # set value
F3 = 5                # set value
G5 = 5                # set value
G7: 7                 # naked single
G6 = 1                # set value
G7 = 7                # set value
I7: 9                 # naked single
H7 = 5                # set value
I7 = 9                # set value
H8: 6                 # naked single
H8 = 6                # set value
C4,F4,H4: 4,7,9.. => C4,F4 != 2,6 # hidden triple
* UNSOLVED!

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

highlight 6
xwing
B2: 3,6
G2: 2,6
B4: 3,6
G4: 2,6
* DISABLE VALUE:: D2 != 6

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

highlight 3
A1: 2,3
E2: 3,4,9
B4: 3,6
E1: 3,8
B2: 3,6
A4: 2,3

A1,E2,B4 = 3 => E1,B2,A4 != 3 # forced chain

E1 = 3 => E2 = 4,9 & ...
=> A1 = 2 => D1,I1 != 2 => I1 = 6 => D1 = 8 & G2 = 2
=> D2,F2 != 2 => F2 = 9 => D2,E2 != 9
=> D2,E2 = 4 => CTR
* CTR!

=> E1 != 3 & ...
* AUTO ..
* SOLVED!

|:step:| 02
--------------------------------------------------

Solution

position: 345281976768439215912675384234517698196842537857963142683124759521798463479356821 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:

* INC # C5: 2,6 => UNS
* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS # D2: 2,9 => CTR => D2: 4,6
* INC # D2: 4,6 => UNS
* PRF # D1: 2,6 => SOL
* DIS # D1: 8 => CTR => D1: 2,6
* DIS # D2: 2,6 => CTR => D2: 4,9
* INC # D2: 4,9 => UNS
* PRF # D1: 2,6 => SOL
* DIS # D1: 8 => CTR => D1: 2,6
* INC # I5: 2,6 => UNS
* PRF # I5: 7 => SOL
* DIS # D2: 2,6 => CTR => D2: 4,9
* INC # D2: 4,9 => UNS
* DIS # C5: 4,7 => CTR => C5: 2,6
* INC # C5: 2,6 => UNS
* INC # C6: 4,7 => UNS
* INC # D6: 7,9 => UNS
* DIS # D6: 2,4 => CTR => D6: 7,9
* DIS # F8: 7,9 => CTR => F8: 8
* INC # F8: 8 => UNS
* INC # D5: 4,8 => UNS
* INC # D5: 2,7 => UNS
* INC # I5: 2,6 => UNS
* PRF # I5: 7 => SOL
* INC # D6: 4,9 => UNS
* DIS # D6: 2,7 => CTR => D6: 4,9
* PRF # I5: 2,7 => SOL
* DIS # I5: 6 => CTR => I5: 2,7
* INC # C6: 2,7 => UNS
* DIS # D6: 2,7 => CTR => D6: 4,9
* INC # D6: 4,9 => UNS
* DIS # D8: 8,9 => CTR => D8: 7
* INC # D8: 7 => UNS
* INC # F8: 8,9 => UNS
* CNT  35 HDP CHAINS /  35 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C5: 2,6 => UNS
* DIS # C5: 4,7 => CTR => C5: 2,6
* DIS C5: 2,6 # D2: 2,9 => CTR => D2: 4,6
* PRF C5: 2,6 + D2: 4,6 # D1: 2,6 => SOL
* STA C5: 2,6 + D2: 4,6 + D1: 2,6
* CNT   4 HDP CHAINS /   4 HYP OPENED