Analysis of zz-sudoku-de-720321-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 6..1.3..8.2.7.9.3...3...2....73.69..5.......7..94.85....1...8...7.8.1.2.8..5.7..9 initial

Autosolve

position: 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G5: 4,6 => CTR => G5: 3
* PRF # G5: 3 => SOL
* PRF # I6: 6 => SOL
* PRF # B5: 3,6 => SOL
* DIS # B5: 4 => CTR => B5: 3,6
* PRF # I6: 3,6 => SOL
* DIS # I6: 2 => CTR => I6: 3,6
* DIS # G5: 4,6 => CTR => G5: 3
* PRF # G5: 3 => SOL
* PRF # B5: 4,6 => SOL
* DIS # B5: 3 => CTR => B5: 4,6
* PRF # A8: 3,9 => SOL
* DIS # A8: 4 => CTR => A8: 3,9
* DIS # E7: 3,9 => CTR => E7: 6
* PRF # E7: 6 => SOL
* DIS # A8: 9 => CTR => A8: 3,4
* PRF # B5: 6 => SOL
* DIS # E7: 3,9 => CTR => E7: 6
* PRF # E7: 6 => SOL
* PRF # A8: 3,9 => SOL
* DIS # A8: 4 => CTR => A8: 3,9
* DIS # E7: 9 => CTR => E7: 3,6
* DIS # E7: 9 => CTR => E7: 3,6
* PRF # I6: 3,6 => SOL
* DIS # I6: 2 => CTR => I6: 3,6
* DIS # A8: 9 => CTR => A8: 3,4
* PRF # G5: 3,4 => SOL
* DIS # G5: 6 => CTR => G5: 3,4
* CNT  28 HDP CHAINS /  34 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 # G5: 4,6 => CTR => G5: 3
* PRF G5: 3 => SOL
* STA G5: 3
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

6..1.3..8.2.7.9.3...3...2....73.69..5.......7..94.85....1...8...7.8.1.2.8..5.7..9 initial
694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9 autosolve
694123758125789634783645291417356982568912347239478516951264873376891425842537169 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
G2: 4,6
I2: 4,6
A4: 2,4
A6: 2,3
B6: 3,6
I4: 2,4
H5: 4,6
A7: 3,9
B9: 3,4
E8: 3,9
E9: 3,6
I7: 3,6
G8: 3,4
H9: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,A6: 2.. / A4 = 2  =>  0 pairs (X) / A6 = 2  =>  0 pairs (_)
I4,I6: 2.. / I4 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
A4,I4: 2.. / A4 = 2  =>  0 pairs (X) / I4 = 2  =>  0 pairs (_)
A6,I6: 2.. / A6 = 2  =>  0 pairs (*) / I6 = 2  =>  0 pairs (X)
G5,I6: 3.. / G5 = 3  =>  0 pairs (*) / I6 = 3  =>  0 pairs (X)
I7,G8: 3.. / I7 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
B5,G5: 3.. / B5 = 3  =>  0 pairs (X) / G5 = 3  =>  0 pairs (_)
B9,E9: 3.. / B9 = 3  =>  0 pairs (X) / E9 = 3  =>  0 pairs (_)
G5,G8: 3.. / G5 = 3  =>  0 pairs (*) / G8 = 3  =>  0 pairs (X)
I6,I7: 3.. / I6 = 3  =>  0 pairs (X) / I7 = 3  =>  0 pairs (_)
G2,I2: 4.. / G2 = 4  =>  0 pairs (X) / I2 = 4  =>  0 pairs (_)
A4,B5: 4.. / A4 = 4  =>  0 pairs (*) / B5 = 4  =>  0 pairs (X)
A8,B9: 4.. / A8 = 4  =>  0 pairs (X) / B9 = 4  =>  0 pairs (_)
G8,H9: 4.. / G8 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
A4,I4: 4.. / A4 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
A8,G8: 4.. / A8 = 4  =>  0 pairs (X) / G8 = 4  =>  0 pairs (_)
B9,H9: 4.. / B9 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
A4,A8: 4.. / A4 = 4  =>  0 pairs (*) / A8 = 4  =>  0 pairs (X)
B5,B9: 4.. / B5 = 4  =>  0 pairs (X) / B9 = 4  =>  0 pairs (_)
H5,H9: 4.. / H5 = 4  =>  0 pairs (*) / H9 = 4  =>  0 pairs (X)
I2,I4: 4.. / I2 = 4  =>  0 pairs (*) / I4 = 4  =>  0 pairs (X)
G2,I2: 6.. / G2 = 6  =>  0 pairs (*) / I2 = 6  =>  0 pairs (X)
B5,B6: 6.. / B5 = 6  =>  0 pairs (*) / B6 = 6  =>  0 pairs (X)
E7,E9: 6.. / E7 = 6  =>  0 pairs (*) / E9 = 6  =>  0 pairs (X)
I7,H9: 6.. / I7 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
B6,I6: 6.. / B6 = 6  => 15 pairs (_) / I6 = 6  =>  0 pairs (*)
E7,I7: 6.. / E7 = 6  =>  0 pairs (*) / I7 = 6  =>  0 pairs (X)
E9,H9: 6.. / E9 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
G2,G5: 6.. / G2 = 6  =>  0 pairs (*) / G5 = 6  =>  0 pairs (X)
H5,H9: 6.. / H5 = 6  =>  0 pairs (X) / H9 = 6  =>  0 pairs (_)
A7,A8: 9.. / A7 = 9  => 14 pairs (_) / A8 = 9  =>  0 pairs (X)
E7,E8: 9.. / E7 = 9  =>  0 pairs (X) / E8 = 9  => 14 pairs (_)
A7,E7: 9.. / A7 = 9  => 14 pairs (_) / E7 = 9  =>  0 pairs (X)
A8,E8: 9.. / A8 = 9  =>  0 pairs (X) / E8 = 9  => 14 pairs (_)
* DURATION: 0:00:57.515536  START: 08:17:24.645805  END: 08:18:22.161341 2017-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B6,B9,E8,E9,G2,G8,H5,H9,I2,I4,I7)
* 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9
* PAIR G2: 4,6 COL G
G5: 4,6,3                                # reduction candidate for 4,6
G5: 4,6 => CTR
* 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9
G5: 3 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
* PAIR A6: 2,3 ROW 6
I6: 2,3,6                                # reduction candidate for 2,3
I6: 6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
I6: 2,3                                  # 15 pairs
* PAIR B6: 3,6 BLK 4
B5: 3,6,4                                # reduction candidate for 3,6
B5: 3,6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
B5: 4 => CTR
* 694123758125789.3.783645291.1735698.548912367.69478512.512.487..768.1.258.25.71.9
* PAIR B6: 3,6 ROW 6
I6: 3,6,2                                # reduction candidate for 3,6
I6: 3,6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
I6: 2 => CTR
* 694123758125789.3.783645291.1735698.5.8912367.69478512.512.487..768.1.258.25.71.9
* PAIR H5: 4,6 BLK 6
G5: 4,6,3                                # reduction candidate for 4,6
G5: 4,6 => CTR
* 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9
G5: 3 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
* PAIR H5: 4,6 ROW 5
B5: 4,6,3                                # reduction candidate for 4,6
B5: 4,6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
B5: 3 => CTR
* 694123758125789.3.783645291417356982538912..7269478513.512.4876.768.1.258.25.71.9
* PAIR A7: 3,9 BLK 7
A8: 3,9,4                                # reduction candidate for 3,9
A8: 3,9 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
A8: 4 => CTR
* 694123758125789.3.783645291.1735698.5.8912..7..947851.9512.487.4768913258325.71.9
* PAIR A7: 3,9 ROW 7
E7: 3,9,6                                # reduction candidate for 3,9
E7: 3,9 => CTR
* 694123758125789.3.783645291.1735698.5.8912..7..947851..512.4876.768.13258.2567149
E7: 6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
* PAIR B9: 3,4 BLK 7
A8: 3,4,9                                # reduction candidate for 3,4
A8: 9 => CTR
* 694123758125789.3.7836452914173569825.8912..72.947851.351294876.768.1.258.25.71.9
A8: 3,4                                  # 14 pairs
* PAIR B9: 3,4 COL B
B5: 3,4,6                                # reduction candidate for 3,4
B5: 6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
B5: 3,4                                  # 15 pairs
* PAIR E8: 3,9 BLK 8
E7: 3,9,6                                # reduction candidate for 3,9
E7: 3,9 => CTR
* 694123758125789.3.783645291.1735698.5.8912..7..947851..512.4876.768.13258.2567149
E7: 6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
* PAIR E8: 3,9 ROW 8
A8: 3,9,4                                # reduction candidate for 3,9
A8: 3,9 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
A8: 4 => CTR
* 694123758125789.3.783645291.1735698.5.8912..7..947851.9512.487.4768913258325.71.9
* PAIR E9: 3,6 BLK 8
E7: 3,6,9                                # reduction candidate for 3,6
E7: 9 => CTR
* 694123758125789.3.783645291.1735698.5.8912..7..947851..51294876976831.258.25.71.9
E7: 3,6                                  # 14 pairs
* PAIR I7: 3,6 ROW 7
E7: 3,6,9                                # reduction candidate for 3,6
E7: 9 => CTR
* 694123758125789.3.783645291.1735698.5.8912..7..947851..51294876976831.258.25.71.9
E7: 3,6                                  # 14 pairs
* PAIR I7: 3,6 COL I
I6: 3,6,2                                # reduction candidate for 3,6
I6: 3,6 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
I6: 2 => CTR
* 694123758125789.3.783645291.1735698.5.8912367.69478512.512.487..768.1.258.25.71.9
* PAIR G8: 3,4 ROW 8
A8: 3,4,9                                # reduction candidate for 3,4
A8: 9 => CTR
* 694123758125789.3.7836452914173569825.8912..72.947851.351294876.768.1.258.25.71.9
A8: 3,4                                  # 14 pairs
* PAIR G8: 3,4 COL G
G5: 3,4,6                                # reduction candidate for 3,4
G5: 3,4 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
G5: 6 => CTR
* 694123758125789.3.783645291.1735698.538912647269478513.512.487..768.1.258.25.71.9
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-720321-base-pr-000.dot
* REASONING
* DIS # G5: 4,6 => CTR => G5: 3
* PRF # G5: 3 => SOL
* PRF # I6: 6 => SOL
* PRF # B5: 3,6 => SOL
* DIS # B5: 4 => CTR => B5: 3,6
* PRF # I6: 3,6 => SOL
* DIS # I6: 2 => CTR => I6: 3,6
* DIS # G5: 4,6 => CTR => G5: 3
* PRF # G5: 3 => SOL
* PRF # B5: 4,6 => SOL
* DIS # B5: 3 => CTR => B5: 4,6
* PRF # A8: 3,9 => SOL
* DIS # A8: 4 => CTR => A8: 3,9
* DIS # E7: 3,9 => CTR => E7: 6
* PRF # E7: 6 => SOL
* DIS # A8: 9 => CTR => A8: 3,4
* PRF # B5: 6 => SOL
* DIS # E7: 3,9 => CTR => E7: 6
* PRF # E7: 6 => SOL
* PRF # A8: 3,9 => SOL
* DIS # A8: 4 => CTR => A8: 3,9
* DIS # E7: 9 => CTR => E7: 3,6
* DIS # E7: 9 => CTR => E7: 3,6
* PRF # I6: 3,6 => SOL
* DIS # I6: 2 => CTR => I6: 3,6
* DIS # A8: 9 => CTR => A8: 3,4
* PRF # G5: 3,4 => SOL
* DIS # G5: 6 => CTR => G5: 3,4
* CNT  28 HDP CHAINS /  34 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,A7,B6,B9,E8,E9,G2,G8,H5,H9,I2,I4,I7)
* 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9
* PAIR G2: 4,6 COL G
G5: 4,6,3                                # reduction candidate for 4,6
G5: 4,6 => CTR
* 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9
G5: 3 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
* DURATION: 0:00:02.843322  START: 08:19:00.082094  END: 08:19:02.925416 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-720321-base-pr-001.dot
* REASONING
* DIS # G5: 4,6 => CTR => G5: 3
* PRF G5: 3 => SOL
* STA G5: 3
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.sudokus.de/720321.html
sehr schwierig

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

* PAIR REDUCTION ..
* ROUND 1: 694123758125789.3.783645291.1735698.5.8912..7..947851..512.487..768.1.258.25.71.9
G2: 4,6
G5: 3,4,6                                # reduction candidate for 4,6
G5: 4,6 => CTR
* 694123758125789.3.783645291.1735698.538912..7269478513.512.4876.768.13258425.71.9
G5: 3 => SOLVED
* 694123758125789634783645291417356982568912347239478516951264873376891425842537169
* SOLVED!
--------------------------------------------------

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

pair quad |:guess:| highlight 3,9
A7,E8,A8,E7: 3,9.. => A8 = 4 or E7 = 6 # pair quad

E7 != 6 => CTR

* DISABLE VALUE:: E7 != 6
* AUTO ..
E9: 6..               # hidden single
I7: 6..               # hidden single
E9: 6                 # naked single
E7,E8: 3,9.. => E9 != 3,9 # naked pair
I7: 6                 # naked single
A7,E7: 3,9.. => I7 != 3,9 # naked pair
G8: 3..               # hidden single
B9: 3..               # hidden single
I6: 3..               # hidden single
I6 = 3                # set value
A6: 2                 # naked single
B6: 6                 # naked single
I7 = 6                # set value
H9: 4                 # naked single
I2: 4                 # naked single
G8 = 3                # set value
E8: 9                 # naked single
B9 = 3                # set value
A7: 9                 # naked single
E9 = 6                # set value
H9 = 4                # set value
H5: 6                 # naked single
G2: 6..               # hidden single
I4: 2..               # hidden single
A8: 4..               # hidden single
E7: 3..               # hidden single
B5: 4..               # hidden single
A4..C6 != 3 => CTR

=> A8 != 4
* DISABLE VALUE:: A8 != 4

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

* AUTO ..
B9: 4..               # hidden single
G8: 4..               # hidden single
A4: 4..               # hidden single
B9: 4                 # naked single
A7,A8: 3,9.. => B9 != 3,9 # naked pair
G8: 4                 # naked single
A8,E8: 3,9.. => G8 != 3,9 # naked pair
A6: 2                 # naked single
A7,A8: 3,9.. => A6 != 3,9 # naked pair
I7: 3..               # hidden single
E9: 3..               # hidden single
G5: 3..               # hidden single
A4 = 4                # set value
I4: 2                 # naked single
I4 = 2                # set value
G5 = 3                # set value
I6: 6                 # naked single
B5: 6                 # naked single
A6 = 2                # set value
I6 = 6                # set value
H5: 4                 # naked single
I2: 4                 # naked single
I7: 3                 # naked single
B6: 3                 # naked single
I7 = 3                # set value
A7: 9                 # naked single
G8 = 4                # set value
H9: 6                 # naked single
G2: 6                 # naked single
B9 = 4                # set value
E9 = 3                # set value
E8: 9                 # naked single
H9 = 6                # set value
A8: 3..               # hidden single
E7: 6..               # hidden single
G2 = 6                # set value
I2 = 4                # set value
B5 = 6                # set value
H5 = 4                # set value
B6 = 3                # set value
A7 = 9                # set value
A8: 3                 # naked single
E7: 6                 # naked single
E7 = 6                # set value
A8 = 3                # set value
E8 = 9                # set value
* SOLVED!

Solution

position: 694123758125789634783645291417356982568912347239478516951264873376891425842537169 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:

* DIS # G5: 4,6 => CTR => G5: 3
* PRF # G5: 3 => SOL
* INC # I6: 2,3 => UNS
* PRF # I6: 6 => SOL
* PRF # B5: 3,6 => SOL
* DIS # B5: 4 => CTR => B5: 3,6
* PRF # I6: 3,6 => SOL
* DIS # I6: 2 => CTR => I6: 3,6
* DIS # G5: 4,6 => CTR => G5: 3
* PRF # G5: 3 => SOL
* PRF # B5: 4,6 => SOL
* DIS # B5: 3 => CTR => B5: 4,6
* PRF # A8: 3,9 => SOL
* DIS # A8: 4 => CTR => A8: 3,9
* DIS # E7: 3,9 => CTR => E7: 6
* PRF # E7: 6 => SOL
* INC # A8: 3,4 => UNS
* DIS # A8: 9 => CTR => A8: 3,4
* INC # B5: 3,4 => UNS
* PRF # B5: 6 => SOL
* DIS # E7: 3,9 => CTR => E7: 6
* PRF # E7: 6 => SOL
* PRF # A8: 3,9 => SOL
* DIS # A8: 4 => CTR => A8: 3,9
* INC # E7: 3,6 => UNS
* DIS # E7: 9 => CTR => E7: 3,6
* INC # E7: 3,6 => UNS
* DIS # E7: 9 => CTR => E7: 3,6
* PRF # I6: 3,6 => SOL
* DIS # I6: 2 => CTR => I6: 3,6
* INC # A8: 3,4 => UNS
* DIS # A8: 9 => CTR => A8: 3,4
* PRF # G5: 3,4 => SOL
* DIS # G5: 6 => CTR => G5: 3,4
* CNT  34 HDP CHAINS /  34 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # G5: 4,6 => CTR => G5: 3
* PRF G5: 3 => SOL
* STA G5: 3
* CNT   2 HDP CHAINS /   1 HYP OPENED