Analysis of zz-menneske-no-06912567-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .....69....9.3....68......4....1.6.5.....8.1..28...7..4...8..562...9......53..... initial

Autosolve

position: .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D4: 4,7 => CTR => D4: 2,9
* DIS # F4: 4,7 => CTR => F4: 2,3,9
* DIS # D5: 4,7 => CTR => D5: 9
* DIS # B5: 4,7 => CTR => B5: 3,5,6
* DIS # C5: 4,7 => CTR => C5: 3,6
* PRF # E9: 4,7 => SOL
* DIS # I5: 3,9 => CTR => I5: 2
* DIS # F6: 3,9 => CTR => F6: 4,5
* CNT   8 HDP CHAINS /  25 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 # D4: 4,7 => CTR => D4: 2,9
* DIS D4: 2,9 # F4: 4,7 => CTR => F4: 2,3,9
* DIS D4: 2,9 + F4: 2,3,9 # D5: 4,7 => CTR => D5: 9
* PRF D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 3 => SOL
* STA D4: 2,9 + F4: 2,3,9 + D5: 9 + A1: 3
* CNT   4 HDP CHAINS /  12 HYP OPENED

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

Details

Positions

.....69....9.3....68......4....1.6.5.....8.1..28...7..4...8..562...9......53..... initial
.....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53..... autosolve
342856971759431268681729534974213685536978412128564793497182356213695847865347129 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
A2: 5,7
E5: 4,7
I6: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C1,C3: 2.. / C1 = 2  =>  5 pairs (_) / C3 = 2  =>  6 pairs (_)
D4,F4: 2.. / D4 = 2  =>  4 pairs (_) / F4 = 2  =>  0 pairs (X)
G5,I5: 2.. / G5 = 2  =>  0 pairs (X) / I5 = 2  =>  4 pairs (_)
F4,F6: 3.. / F4 = 3  => 10 pairs (_) / F6 = 3  =>  0 pairs (X)
C7,G7: 3.. / C7 = 3  =>  6 pairs (_) / G7 = 3  =>  0 pairs (*)
G5,H6: 4.. / G5 = 4  => 11 pairs (_) / H6 = 4  =>  0 pairs (X)
G2,G3: 5.. / G2 = 5  =>  5 pairs (_) / G3 = 5  =>  4 pairs (_)
A5,B5: 5.. / A5 = 5  =>  4 pairs (_) / B5 = 5  =>  3 pairs (_)
D8,F8: 5.. / D8 = 5  =>  0 pairs (X) / F8 = 5  =>  5 pairs (_)
B5,C5: 6.. / B5 = 6  =>  0 pairs (X) / C5 = 6  =>  3 pairs (_)
D6,E6: 6.. / D6 = 6  =>  0 pairs (X) / E6 = 6  =>  4 pairs (_)
D8,E9: 6.. / D8 = 6  =>  4 pairs (_) / E9 = 6  =>  0 pairs (X)
B9,E9: 6.. / B9 = 6  =>  4 pairs (_) / E9 = 6  =>  0 pairs (X)
C5,C8: 6.. / C5 = 6  =>  3 pairs (_) / C8 = 6  =>  0 pairs (X)
D6,D8: 6.. / D6 = 6  =>  0 pairs (X) / D8 = 6  =>  4 pairs (_)
E6,E9: 6.. / E6 = 6  =>  4 pairs (_) / E9 = 6  =>  0 pairs (X)
D1,D2: 8.. / D1 = 8  =>  3 pairs (_) / D2 = 8  =>  3 pairs (_)
G8,I8: 8.. / G8 = 8  =>  3 pairs (_) / I8 = 8  =>  4 pairs (_)
D1,I1: 8.. / D1 = 8  =>  3 pairs (_) / I1 = 8  =>  3 pairs (_)
G2,G8: 8.. / G2 = 8  =>  4 pairs (_) / G8 = 8  =>  3 pairs (_)
D3,F3: 9.. / D3 = 9  =>  0 pairs (X) / F3 = 9  =>  3 pairs (_)
A4,A5: 9.. / A4 = 9  =>  3 pairs (_) / A5 = 9  =>  0 pairs (X)
H9,I9: 9.. / H9 = 9  =>  0 pairs (X) / I9 = 9  =>  9 pairs (_)
H6,H9: 9.. / H6 = 9  =>  9 pairs (_) / H9 = 9  =>  0 pairs (X)
* DURATION: 0:00:33.356117  START: 07:00:20.583166  END: 07:00:53.939283 2017-05-01
* CP COUNT: (24)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E5,I6)
* .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53.....
* PAIR A2: 5,7 BLK 1
A1: 5,7,3                                # reduction candidate for 5,7
A1: 5,7                                  # 10 pairs
B1: 5,7,1,3,4                            # reduction candidate for 5,7
B1: 5,7                                  #  8 pairs
B2: 5,7,1,4                              # reduction candidate for 5,7
B2: 5,7                                  # 12 pairs
* PAIR A2: 5,7 ROW 2
D2: 5,7,1,2,4,8                          # reduction candidate for 5,7
D2: 5,7                                  #  6 pairs
F2: 5,7,1,2,4                            # reduction candidate for 5,7
F2: 5,7                                  #  6 pairs
* PAIR A2: 5,7 COL A
A5: 5,7,3,9                              # reduction candidate for 5,7
A5: 5,7                                  #  5 pairs
A5: 3,9                                  #  5 pairs
* PAIR E5: 4,7 BLK 5
D4: 4,7,2,9                              # reduction candidate for 4,7
D4: 4,7 => CTR
* 3..8.69....923..6.68...9..49...12685...9.8312128.63749493.8.2562..6954..8.532..9.
D4: 2,9                                  #  4 pairs
F4: 4,7,2,3,9                            # reduction candidate for 4,7
F4: 4,7 => CTR
* 3....69....9.32.6.68...9..49..21.685...9.8312128.63749493.8.2562..6954..8.532..9.
F4: 2,3,9                                #  3 pairs
D5: 4,7,9                                # reduction candidate for 4,7
D5: 4,7 => CTR
* ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197
D5: 9                                    #  4 pairs
* PAIR E5: 4,7 ROW 5
B5: 4,7,3,5,6                            # reduction candidate for 4,7
B5: 4,7 => CTR
* 3....69..7.9.3..6.68...9..49...1.6855.69.8312128.63749493.8.2562..6954..8.532..9.
B5: 3,5,6                                #  3 pairs
C5: 4,7,3,6                              # reduction candidate for 4,7
C5: 4,7 => CTR
* 3....69..7.9.3..6.68...9..49...1.68556.9.8.1.12865374949..8..562.6.9....8.536..9.
C5: 3,6                                  #  4 pairs
* PAIR E5: 4,7 COL E
E1: 4,7,2,5                              # reduction candidate for 4,7
E1: 4,7                                  #  7 pairs
E9: 4,7,2,6                              # reduction candidate for 4,7
E9: 4,7 => SOLVED
* 342856971759431268681729534974213685536978412128564793497182356213695847865347129
E9: 2,6                                  #  4 pairs
* PAIR I6: 3,9 BLK 6
I5: 3,9,2                                # reduction candidate for 3,9
I5: 3,9 => CTR
* .....69....9.3..6.68......4....1.685.....821.128...74.49..8..562...9....8.53...92
I5: 2                                    #  4 pairs
H6: 3,9,4                                # reduction candidate for 3,9
H6: 3,9                                  # 11 pairs
* PAIR I6: 3,9 ROW 6
F6: 3,9,4,5                              # reduction candidate for 3,9
F6: 3,9 => CTR
* ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197
F6: 4,5                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06912567-base-pr-000.dot
* REASONING
* DIS # D4: 4,7 => CTR => D4: 2,9
* DIS # F4: 4,7 => CTR => F4: 2,3,9
* DIS # D5: 4,7 => CTR => D5: 9
* DIS # B5: 4,7 => CTR => B5: 3,5,6
* DIS # C5: 4,7 => CTR => C5: 3,6
* PRF # E9: 4,7 => SOL
* DIS # I5: 3,9 => CTR => I5: 2
* DIS # F6: 3,9 => CTR => F6: 4,5
* CNT   8 HDP CHAINS /  25 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A2,E5,I6)
* .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53.....
* PAIR A2: 5,7 BLK 1
A1: 5,7,3                                # reduction candidate for 5,7
A1: 5,7                                  # 10 pairs
B1: 5,7,1,3,4                            # reduction candidate for 5,7
B1: 5,7                                  #  8 pairs
B2: 5,7,1,4                              # reduction candidate for 5,7
B2: 5,7                                  # 12 pairs
* PAIR A2: 5,7 ROW 2
D2: 5,7,1,2,4,8                          # reduction candidate for 5,7
D2: 5,7                                  #  6 pairs
F2: 5,7,1,2,4                            # reduction candidate for 5,7
F2: 5,7                                  #  6 pairs
* PAIR A2: 5,7 COL A
A5: 5,7,3,9                              # reduction candidate for 5,7
A5: 5,7                                  #  5 pairs
A5: 3,9                                  #  5 pairs
* PAIR E5: 4,7 BLK 5
D4: 4,7,2,9                              # reduction candidate for 4,7
D4: 4,7 => CTR
* 3..8.69....923..6.68...9..49...12685...9.8312128.63749493.8.2562..6954..8.532..9.
F4: 4,7,2,3,9                            # reduction candidate for 4,7
F4: 4,7 => CTR
* 3....69....9.32.6.68...9..49..21.685...9.8312128.63749493.8.2562..6954..8.532..9.
D5: 4,7,9                                # reduction candidate for 4,7
D5: 4,7 => CTR
* ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A2,A5,B4,C4,C5,D7,E3,F6,G9,H6,I6)
* .....69....9.3..6.68...9..49..213685...978412128...7..49..8..562...9....8.53.....
* PAIR A2: 5,7 BLK 1
A1: 5,7,3                                # reduction candidate for 5,7
A1: 3 => SOLVED
* 342856971759431268681729534974213685536978412128564793497182356213695847865347129
* DURATION: 0:00:10.818424  START: 07:01:11.750259  END: 07:01:22.568683 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06912567-base-pr-001.dot
* REASONING
* DIS # D4: 4,7 => CTR => D4: 2,9
* DIS D4: 2,9 # F4: 4,7 => CTR => F4: 2,3,9
* DIS D4: 2,9 + F4: 2,3,9 # D5: 4,7 => CTR => D5: 9
* PRF D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 3 => SOL
* STA D4: 2,9 + F4: 2,3,9 + D5: 9 + A1: 3
* CNT   4 HDP CHAINS /  12 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6912567
umulig

* PAIR REDUCTION ..
* ROUND 1: .....69....9.3..6.68......4....1.685.....8.1.128...7..49..8..562...9....8.53.....
A2: 5,7
A1: 3,5,7                                # reduction candidate for 5,7
B1: 1,3,4,5,7                            # reduction candidate for 5,7
B2: 1,4,5,7                              # reduction candidate for 5,7
B2: 1,4,5,7                              # reduction candidate for 5,7
D2: 1,2,4,5,7,8                          # reduction candidate for 5,7
F2: 1,2,4,5,7                            # reduction candidate for 5,7
A1: 3,5,7                                # reduction candidate for 5,7
A5: 3,5,7,9                              # reduction candidate for 5,7
E5: 4,7
D4: 2,4,7,9                              # reduction candidate for 4,7
D4: 4,7 => CTR
* 3..8.69....923..6.68...9..49...12685...9.8312128.63749493.8.2562..6954..8.532..9.
F4: 2,3,4,7,9                            # reduction candidate for 4,7
F4: 4,7 => CTR
* 3....69....9.32.6.68...9..49..21.685...9.8312128.63749493.8.2562..6954..8.532..9.
D5: 4,7,9                                # reduction candidate for 4,7
D5: 4,7 => CTR
* ...8.69.3..9.3.86168....5.43...1.685956..8312128563749493.8.2562..695438865324197
I6: 3,9
* ROUND 2: .....69....9.3..6.68...9..49..213685...978412128...7..49..8..562...9....8.53.....
A2: 5,7
A1: 3,5,7                                # reduction candidate for 5,7
A1: 3 => SOLVED
* 342856971759431268681729534974213685536978412128564793497182356213695847865347129
* SOLVED!

|:step:| 00
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|:step:| 01
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Solution

position: 342856971759431268681729534974213685536978412128564793497182356213695847865347129 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 # A1: 5,7 => UNS
* INC # B1: 5,7 => UNS
* INC # B2: 5,7 => UNS
* INC # D2: 5,7 => UNS
* INC # F2: 5,7 => UNS
* INC # A5: 5,7 => UNS
* INC # A5: 3,9 => UNS
* DIS # D4: 4,7 => CTR => D4: 2,9
* INC # D4: 2,9 => UNS
* DIS # F4: 4,7 => CTR => F4: 2,3,9
* INC # F4: 2,3,9 => UNS
* DIS # D5: 4,7 => CTR => D5: 9
* INC # D5: 9 => UNS
* DIS # B5: 4,7 => CTR => B5: 3,5,6
* INC # B5: 3,5,6 => UNS
* DIS # C5: 4,7 => CTR => C5: 3,6
* INC # C5: 3,6 => UNS
* INC # E1: 4,7 => UNS
* PRF # E9: 4,7 => SOL
* INC # E9: 2,6 => UNS
* DIS # I5: 3,9 => CTR => I5: 2
* INC # I5: 2 => UNS
* INC # H6: 3,9 => UNS
* DIS # F6: 3,9 => CTR => F6: 4,5
* INC # F6: 4,5 => UNS
* CNT  25 HDP CHAINS /  25 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,7 => UNS
* INC # B1: 5,7 => UNS
* INC # B2: 5,7 => UNS
* INC # D2: 5,7 => UNS
* INC # F2: 5,7 => UNS
* INC # A5: 5,7 => UNS
* INC # A5: 3,9 => UNS
* DIS # D4: 4,7 => CTR => D4: 2,9
* DIS D4: 2,9 # F4: 4,7 => CTR => F4: 2,3,9
* DIS D4: 2,9 + F4: 2,3,9 # D5: 4,7 => CTR => D5: 9
* INC D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 5,7 => UNS
* PRF D4: 2,9 + F4: 2,3,9 + D5: 9 # A1: 3 => SOL
* STA D4: 2,9 + F4: 2,3,9 + D5: 9 + A1: 3
* CNT  12 HDP CHAINS /  12 HYP OPENED