Analysis of zz-sudoku-de-622251-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ......2...2....495...2...63...1..9.75...7...43.1..6...86...5...297....8...5...... initial

Autosolve

position: ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # F2: 1,7 => SOL
* PRF # E3: 9 => SOL
* DIS # E1: 4,9 => CTR => E1: 1,3,6
* DIS # A1: 1,4 => CTR => A1: 9
* PRF # E8: 4,6 => SOL
* DIS # E9: 6,8 => CTR => E9: 2
* PRF # E9: 2 => SOL
* PRF # D2: 6,8 => SOL
* DIS # D2: 7 => CTR => D2: 6,8
* DIS # F3: 4 => CTR => F3: 7,9
* PRF # E8: 1,6 => SOL
* CNT  11 HDP CHAINS /  23 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 # F2: 1,7 => SOL
* STA F2: 1,7
* CNT   1 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

......2...2....495...2...63...1..9.75...7...43.1..6...86...5...297....8...5...... initial
...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5...... autosolve
916534278723681495458297163642158937589372614371946852864715329297463581135829746 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (20)
B1: 1,3
A2: 1,7
C3: 4,8
D6: 4,9
E6: 4,9
C7: 3,4
A9: 1,4
B9: 1,3
D7: 7,9
E7: 1,2
D8: 4,6
D9: 6,8
F9: 7,9
G7: 3,7
H7: 2,4
I7: 1,9
I8: 1,6
G9: 3,7
H9: 2,4
I9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A9,B9: 1.. / A9 = 1  =>  0 pairs (*) / B9 = 1  =>  0 pairs (X)
I7,I8: 1.. / I7 = 1  =>  0 pairs (X) / I8 = 1  =>  0 pairs (_)
E7,I7: 1.. / E7 = 1  =>  0 pairs (*) / I7 = 1  =>  0 pairs (X)
B1,B9: 1.. / B1 = 1  =>  0 pairs (*) / B9 = 1  =>  0 pairs (X)
E7,E9: 2.. / E7 = 2  =>  0 pairs (X) / E9 = 2  =>  0 pairs (_)
H7,H9: 2.. / H7 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
E7,H7: 2.. / E7 = 2  =>  0 pairs (X) / H7 = 2  =>  0 pairs (_)
E9,H9: 2.. / E9 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
C7,B9: 3.. / C7 = 3  =>  0 pairs (X) / B9 = 3  =>  0 pairs (_)
E8,F8: 3.. / E8 = 3  => 21 pairs (_) / F8 = 3  =>  0 pairs (*)
G7,G9: 3.. / G7 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
C7,G7: 3.. / C7 = 3  =>  0 pairs (X) / G7 = 3  =>  0 pairs (_)
B9,G9: 3.. / B9 = 3  =>  0 pairs (*) / G9 = 3  =>  0 pairs (X)
B1,B9: 3.. / B1 = 3  =>  0 pairs (X) / B9 = 3  =>  0 pairs (_)
D6,E6: 4.. / D6 = 4  =>  0 pairs (X) / E6 = 4  =>  0 pairs (_)
C7,A9: 4.. / C7 = 4  =>  0 pairs (*) / A9 = 4  =>  0 pairs (X)
H7,H9: 4.. / H7 = 4  =>  0 pairs (X) / H9 = 4  =>  0 pairs (_)
C7,H7: 4.. / C7 = 4  =>  0 pairs (*) / H7 = 4  =>  0 pairs (X)
A9,H9: 4.. / A9 = 4  =>  0 pairs (X) / H9 = 4  =>  0 pairs (_)
D6,D8: 4.. / D6 = 4  =>  0 pairs (X) / D8 = 4  =>  0 pairs (_)
C1,C2: 6.. / C1 = 6  => 21 pairs (_) / C2 = 6  => 24 pairs (_)
I8,I9: 6.. / I8 = 6  =>  0 pairs (X) / I9 = 6  =>  0 pairs (_)
C1,E1: 6.. / C1 = 6  => 21 pairs (_) / E1 = 6  => 24 pairs (_)
A2,A3: 7.. / A2 = 7  =>  0 pairs (*) / A3 = 7  =>  0 pairs (X)
D7,F9: 7.. / D7 = 7  =>  0 pairs (*) / F9 = 7  =>  0 pairs (X)
G7,G9: 7.. / G7 = 7  =>  0 pairs (X) / G9 = 7  =>  0 pairs (_)
A3,F3: 7.. / A3 = 7  =>  0 pairs (X) / F3 = 7  =>  0 pairs (_)
D7,G7: 7.. / D7 = 7  =>  0 pairs (*) / G7 = 7  =>  0 pairs (X)
F9,G9: 7.. / F9 = 7  =>  0 pairs (X) / G9 = 7  =>  0 pairs (_)
D2,D7: 7.. / D2 = 7  =>  0 pairs (X) / D7 = 7  =>  0 pairs (_)
C2,C3: 8.. / C2 = 8  =>  0 pairs (X) / C3 = 8  => 21 pairs (_)
D9,E9: 8.. / D9 = 8  => 21 pairs (_) / E9 = 8  =>  0 pairs (X)
C3,E3: 8.. / C3 = 8  => 21 pairs (_) / E3 = 8  =>  0 pairs (X)
D2,D9: 8.. / D2 = 8  =>  0 pairs (X) / D9 = 8  => 21 pairs (_)
A1,A3: 9.. / A1 = 9  => 21 pairs (_) / A3 = 9  =>  0 pairs (X)
D6,E6: 9.. / D6 = 9  =>  0 pairs (*) / E6 = 9  =>  0 pairs (X)
D7,F9: 9.. / D7 = 9  =>  0 pairs (X) / F9 = 9  =>  0 pairs (_)
I7,I9: 9.. / I7 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
D7,I7: 9.. / D7 = 9  =>  0 pairs (X) / I7 = 9  =>  0 pairs (_)
F9,I9: 9.. / F9 = 9  =>  0 pairs (*) / I9 = 9  =>  0 pairs (X)
D6,D7: 9.. / D6 = 9  =>  0 pairs (*) / D7 = 9  =>  0 pairs (X)
* DURATION: 0:01:16.590995  START: 07:23:00.583697  END: 07:24:17.174692 2017-05-01
* CP COUNT: (41)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B1,B9,C3,C7,D6,D7,D8,D9,E6,E7,F9,G7,G9,H7,H9,I7,I8,I9)
* ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5......
* PAIR B1: 1,3 ROW 1
E1: 1,3,4,6,9                            # reduction candidate for 1,3
E1: 1,3                                  # 28 pairs
F1: 1,3,4,9                              # reduction candidate for 1,3
F1: 1,3                                  # 23 pairs
* PAIR A2: 1,7 ROW 2
F2: 1,7,3                                # reduction candidate for 1,7
F2: 1,7 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
F2: 3                                    # 22 pairs
* PAIR C3: 4,8 ROW 3
E3: 4,8,9                                # reduction candidate for 4,8
E3: 9 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
E3: 4,8                                  # 24 pairs
* PAIR E6: 4,9 COL E
E1: 4,9,1,3,6                            # reduction candidate for 4,9
E1: 4,9 => CTR
* .365..278.2876.495.5428.163642158937589372614371..6852863..574.297...58.4158.7329
E1: 1,3,6                                # 20 pairs
E3: 4,9,8                                # reduction candidate for 4,9
E3: 4,9                                  # 21 pairs
* PAIR C7: 3,4 COL C
C1: 3,4,6                                # reduction candidate for 3,4
C1: 3,4                                  # 24 pairs
C1: 6                                    # 21 pairs
* PAIR A9: 1,4 COL A
A1: 1,4,9                                # reduction candidate for 1,4
A1: 1,4 => CTR
* .1.59.27872...149595.2.7163642158937589372614371946852864715329297463581135829746
A1: 9                                    # 21 pairs
* PAIR D8: 4,6 BLK 8
E8: 4,6,1,3                              # reduction candidate for 4,6
E8: 4,6 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
E8: 1,3                                  # 21 pairs
* PAIR D9: 6,8 BLK 8
E9: 6,8,2                                # reduction candidate for 6,8
E9: 6,8 => CTR
* .3.5..278.2....495.5.2..163642158937589372614371..68528639257412974..586415...329
E9: 2 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
* PAIR D9: 6,8 COL D
D2: 6,8,7                                # reduction candidate for 6,8
D2: 6,8 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
D2: 7 => CTR
* ...5..278.2.7..49575.2..163642158937589372614371..685286.9.57.1297...586..5......
* PAIR F9: 7,9 COL F
F3: 7,9,4                                # reduction candidate for 7,9
F3: 4 => CTR
* ...5..278.2....49575.29416364215893758937261437194685286.7.53.92974..581.35..97.6
F3: 7,9                                  # 22 pairs
* PAIR I8: 1,6 ROW 8
E8: 1,6,3,4                              # reduction candidate for 1,6
E8: 1,6 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
E8: 3,4                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-sudoku-de-622251-base-pr-000.dot
* REASONING
* PRF # F2: 1,7 => SOL
* PRF # E3: 9 => SOL
* DIS # E1: 4,9 => CTR => E1: 1,3,6
* DIS # A1: 1,4 => CTR => A1: 9
* PRF # E8: 4,6 => SOL
* DIS # E9: 6,8 => CTR => E9: 2
* PRF # E9: 2 => SOL
* PRF # D2: 6,8 => SOL
* DIS # D2: 7 => CTR => D2: 6,8
* DIS # F3: 4 => CTR => F3: 7,9
* PRF # E8: 1,6 => SOL
* CNT  11 HDP CHAINS /  23 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,A9,B1,B9,C3,C7,D6,D7,D8,D9,E6,E7,F9,G7,G9,H7,H9,I7,I8,I9)
* ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5......
* PAIR B1: 1,3 ROW 1
E1: 1,3,4,6,9                            # reduction candidate for 1,3
E1: 1,3                                  # 28 pairs
F1: 1,3,4,9                              # reduction candidate for 1,3
F1: 1,3                                  # 23 pairs
* PAIR A2: 1,7 ROW 2
F2: 1,7,3                                # reduction candidate for 1,7
F2: 1,7 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
* DURATION: 0:00:04.204302  START: 07:24:43.193261  END: 07:24:47.397563 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-sudoku-de-622251-base-pr-001.dot
* REASONING
* PRF # F2: 1,7 => SOL
* STA F2: 1,7
* CNT   1 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokus.de/622251.html
sehr schwierig

level: medium

* PAIR REDUCTION ..
* ROUND 1: ...5..278.2....495.5.2..163642158937589372614371..685286...5...297...58...5......
B1: 1,3
E1: 1,3,4,6,9                            # reduction candidate for 1,3
F1: 1,3,4,9                              # reduction candidate for 1,3
A2: 1,7
F2: 1,3,7                                # reduction candidate for 1,7
F2: 1,7 => SOLVED
* 916534278723681495458297163642158937589372614371946852864715329297463581135829746
* SOLVED!

--------------------------------------------------
* AUTO ..
Q7: 1.. = A9,B9: 1.. => E9,F9,I9 != 1
Q7,Q9: 3.. => E7,E9,F9 != 3
Q7,Q9: 4.. => D7,E7,D9,E9,F9 != 4
D7,F9: 7,9.. => E7,D9,E9 != 7,9 # naked pair
* UNSOLVED!

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

first block pair-elimination candidate:
D9: 6,8
E9: 2,6,8

* DISABLE:: E9 != 8
* DISABLE:: E9 != 6
* AUTO ..
* SOLVED!

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

* DISABLE VALUE:: D2 != 7
=> D2,D9: 6,8 # naked pair
* AUTO ..
* SOLVED!

|:step:| alternate
--------------------------------------------------

Solution

position: 916534278723681495458297163642158937589372614371946852864715329297463581135829746 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 # E1: 1,3 => UNS
* INC # F1: 1,3 => UNS
* PRF # F2: 1,7 => SOL
* INC # F2: 3 => UNS
* INC # E3: 4,8 => UNS
* PRF # E3: 9 => SOL
* DIS # E1: 4,9 => CTR => E1: 1,3,6
* INC # E1: 1,3,6 => UNS
* INC # E3: 4,9 => UNS
* INC # C1: 3,4 => UNS
* INC # C1: 6 => UNS
* DIS # A1: 1,4 => CTR => A1: 9
* INC # A1: 9 => UNS
* PRF # E8: 4,6 => SOL
* INC # E8: 1,3 => UNS
* DIS # E9: 6,8 => CTR => E9: 2
* PRF # E9: 2 => SOL
* PRF # D2: 6,8 => SOL
* DIS # D2: 7 => CTR => D2: 6,8
* INC # F3: 7,9 => UNS
* DIS # F3: 4 => CTR => F3: 7,9
* PRF # E8: 1,6 => SOL
* INC # E8: 3,4 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E1: 1,3 => UNS
* INC # F1: 1,3 => UNS
* PRF # F2: 1,7 => SOL
* STA F2: 1,7
* CNT   3 HDP CHAINS /   3 HYP OPENED