Analysis of zz-menneske-no-06902129-base.sdk

Contents

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6902129

level: medium

Sudoku from http://www.menneske.no/sudoku/utskrift.html?number=6902129

position: ..6...32....1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. initial

Autosolve

position: ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D5: 4,5 => CTR => D5: 2,6,8
* PRF # D5: 2,6,8 => SOL
* DIS # D3: 3 => CTR => D3: 2,6
* DIS # F5: 2,6 => CTR => F5: 1,5
* PRF # F5: 1,5 => SOL
* DIS # D4: 2,8 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # E4: 2,8 => SOL
* DIS # D5: 2,8 => CTR => D5: 4,5,6
* DIS # E5: 2,8 => CTR => E5: 1,4
* DIS # I6: 2,8 => CTR => I6: 5,6,9
* DIS # E8: 2,8 => CTR => E8: 1,3,7
* DIS # F7: 1,2 => CTR => F7: 7
* PRF # F7: 7 => SOL
* PRF # E8: 1,2 => SOL
* DIS # B9: 3,4,8 => CTR => B9: 1,2
* PRF # F5: 1,2 => SOL
* CNT  17 HDP CHAINS /  36 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 # D5: 4,5 => CTR => D5: 2,6,8
* PRF D5: 2,6,8 => SOL
* STA D5: 2,6,8
* CNT   2 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

..6...32....1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. initial
..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75. autosolve
986475321245138967731296548624589173397641285158723496462357819579814632813962754 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
D1: 4,5
F1: 5,7
F3: 2,6
H2: 6,7
I2: 6,7
G3: 5,8
H3: 4,8
E6: 2,8
F9: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B9,F9: 1.. / B9 = 1  =>  0 pairs (*) / F9 = 1  =>  0 pairs (X)
H3,I3: 4.. / H3 = 4  =>  9 pairs (_) / I3 = 4  =>  9 pairs (_)
D5,E5: 4.. / D5 = 4  =>  0 pairs (X) / E5 = 4  =>  0 pairs (_)
D1,D5: 4.. / D1 = 4  =>  0 pairs (*) / D5 = 4  =>  0 pairs (X)
H3,H7: 4.. / H3 = 4  =>  9 pairs (_) / H7 = 4  =>  9 pairs (_)
D1,F1: 5.. / D1 = 5  =>  0 pairs (X) / F1 = 5  =>  0 pairs (_)
G3,I3: 5.. / G3 = 5  =>  9 pairs (_) / I3 = 5  =>  7 pairs (_)
A8,B8: 5.. / A8 = 5  =>  9 pairs (_) / B8 = 5  =>  0 pairs (X)
F1,F5: 5.. / F1 = 5  =>  0 pairs (*) / F5 = 5  =>  0 pairs (X)
D3,F3: 6.. / D3 = 6  =>  0 pairs (X) / F3 = 6  =>  0 pairs (_)
H2,I2: 6.. / H2 = 6  =>  8 pairs (_) / I2 = 6  =>  7 pairs (_)
D5,F5: 6.. / D5 = 6  =>  0 pairs (*) / F5 = 6  =>  0 pairs (X)
H6,I6: 6.. / H6 = 6  =>  7 pairs (_) / I6 = 6  =>  8 pairs (_)
B7,B8: 6.. / B7 = 6  =>  9 pairs (_) / B8 = 6  =>  0 pairs (X)
G7,G8: 6.. / G7 = 6  =>  0 pairs (X) / G8 = 6  =>  9 pairs (_)
B7,G7: 6.. / B7 = 6  =>  9 pairs (_) / G7 = 6  =>  0 pairs (X)
B8,G8: 6.. / B8 = 6  =>  0 pairs (X) / G8 = 6  =>  9 pairs (_)
D3,D5: 6.. / D3 = 6  =>  0 pairs (X) / D5 = 6  =>  0 pairs (_)
F3,F5: 6.. / F3 = 6  =>  0 pairs (*) / F5 = 6  =>  0 pairs (X)
H2,H6: 6.. / H2 = 6  =>  8 pairs (_) / H6 = 6  =>  7 pairs (_)
I2,I6: 6.. / I2 = 6  =>  7 pairs (_) / I6 = 6  =>  8 pairs (_)
E1,F1: 7.. / E1 = 7  =>  0 pairs (*) / F1 = 7  =>  0 pairs (X)
H2,I2: 7.. / H2 = 7  =>  7 pairs (_) / I2 = 7  =>  8 pairs (_)
F7,E8: 7.. / F7 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
B8,E8: 7.. / B8 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
C5,C7: 7.. / C5 = 7  =>  0 pairs (*) / C7 = 7  =>  0 pairs (X)
E1,E8: 7.. / E1 = 7  =>  0 pairs (*) / E8 = 7  =>  0 pairs (X)
F1,F7: 7.. / F1 = 7  =>  0 pairs (X) / F7 = 7  =>  0 pairs (_)
A1,B1: 8.. / A1 = 8  => 12 pairs (_) / B1 = 8  => 10 pairs (_)
E1,E3: 9.. / E1 = 9  =>  0 pairs (X) / E3 = 9  => 14 pairs (_)
D7,D9: 9.. / D7 = 9  =>  9 pairs (_) / D9 = 9  =>  9 pairs (_)
B3,E3: 9.. / B3 = 9  =>  0 pairs (X) / E3 = 9  => 14 pairs (_)
D9,I9: 9.. / D9 = 9  =>  9 pairs (_) / I9 = 9  =>  9 pairs (_)
A1,A5: 9.. / A1 = 9  => 12 pairs (_) / A5 = 9  => 12 pairs (_)
* DURATION: 0:00:48.623792  START: 06:36:03.840200  END: 06:36:52.463992 2017-05-01
* CP COUNT: (34)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2)
* ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75.
* PAIR D1: 4,5 COL D
D5: 4,5,2,6,8                            # reduction candidate for 4,5
D5: 4,5 => CTR
* ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175.
D5: 2,6,8 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
* PAIR F3: 2,6 BLK 2
D3: 2,6,3                                # reduction candidate for 2,6
D3: 3 => CTR
* ..6475321...1289..721396...6.4519......642...1.27834......57....79.3461.....6175.
D3: 2,6                                  # 13 pairs
* PAIR F3: 2,6 COL F
F5: 2,6,1,5                              # reduction candidate for 2,6
F5: 2,6 => CTR
* ..6..5321...1.89..7.1......6.4..9............1..7.34......57....79..46......6175.
F5: 1,5 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
* PAIR G3: 5,8 BLK 3
I3: 5,8,4                                # reduction candidate for 5,8
I3: 5,8                                  #  9 pairs
I3: 4                                    #  9 pairs
* PAIR G3: 5,8 COL G
G4: 5,8,1,2                              # reduction candidate for 5,8
G4: 5,8                                  # 11 pairs
G5: 5,8,1,2                              # reduction candidate for 5,8
G5: 5,8                                  # 11 pairs
* PAIR H3: 4,8 BLK 3
I3: 4,8,5                                # reduction candidate for 4,8
I3: 4,8                                  #  9 pairs
I3: 5                                    #  7 pairs
* PAIR H3: 4,8 COL H
H7: 4,8,1,3,9                            # reduction candidate for 4,8
H7: 4,8                                  # 12 pairs
H7: 1,3,9                                #  9 pairs
* PAIR E6: 2,8 BLK 5
D4: 2,8,5                                # reduction candidate for 2,8
D4: 2,8 => CTR
* ..64.5321...1.89..7.1......6.4.19......546...1..7.34......57....79..461.....6175.
D4: 5 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E4: 2,8,1                                # reduction candidate for 2,8
E4: 2,8 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E4: 1                                    #  9 pairs
D5: 2,8,4,5,6                            # reduction candidate for 2,8
D5: 2,8 => CTR
* ..64.5321...1.89..7.16.2...6.45.9.......46...1..7.34......57....79..46......6175.
D5: 4,5,6                                #  9 pairs
E5: 2,8,1,4                              # reduction candidate for 2,8
E5: 2,8 => CTR
* ..65.7321...1.89..7.16.2...6.4.19......4.6...1..7.34......51.....9..4.......6.75.
E5: 1,4                                  # 10 pairs
* PAIR E6: 2,8 ROW 6
B6: 2,8,5,9                              # reduction candidate for 2,8
B6: 2,8                                  # 13 pairs
C6: 2,8,5                                # reduction candidate for 2,8
C6: 2,8                                  # 12 pairs
I6: 2,8,5,6,9                            # reduction candidate for 2,8
I6: 2,8 => CTR
* 986.47321...138976731.9....6.4..9......4.....1957.346...7.5......9.74.......6.75.
I6: 5,6,9                                #  9 pairs
* PAIR E6: 2,8 COL E
E8: 2,8,1,3,7                            # reduction candidate for 2,8
E8: 2,8 => CTR
* ..6.75321...1.89..7.1.9....6.4..9............1..7.34......57....79..461.....6175.
E8: 1,3,7                                # 10 pairs
* PAIR F9: 1,2 BLK 8
F7: 1,2,7                                # reduction candidate for 1,2
F7: 1,2 => CTR
* ..65.7321...1.89..7.1..6...6.4..9........5...1..7.34......5......9.74.......6.75.
F7: 7 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E8: 1,2,3,7,8                            # reduction candidate for 1,2
E8: 1,2 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E8: 3,7,8                                #  9 pairs
* PAIR F9: 1,2 ROW 9
B9: 1,2,3,4,8                            # reduction candidate for 1,2
B9: 3,4,8 => CTR
* ..6..7321...1.89..7.1..6...6.4..9......645...1..7.34....7.52...5.9.74.......6175.
B9: 1,2                                  # 11 pairs
* PAIR F9: 1,2 COL F
F5: 1,2,5,6                              # reduction candidate for 1,2
F5: 1,2 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
F5: 5,6                                  # 10 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06902129-base-pr-000.dot
* REASONING
* DIS # D5: 4,5 => CTR => D5: 2,6,8
* PRF # D5: 2,6,8 => SOL
* DIS # D3: 3 => CTR => D3: 2,6
* DIS # F5: 2,6 => CTR => F5: 1,5
* PRF # F5: 1,5 => SOL
* DIS # D4: 2,8 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # E4: 2,8 => SOL
* DIS # D5: 2,8 => CTR => D5: 4,5,6
* DIS # E5: 2,8 => CTR => E5: 1,4
* DIS # I6: 2,8 => CTR => I6: 5,6,9
* DIS # E8: 2,8 => CTR => E8: 1,3,7
* DIS # F7: 1,2 => CTR => F7: 7
* PRF # F7: 7 => SOL
* PRF # E8: 1,2 => SOL
* DIS # B9: 3,4,8 => CTR => B9: 1,2
* PRF # F5: 1,2 => SOL
* CNT  17 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2)
* ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75.
* PAIR D1: 4,5 COL D
D5: 4,5,2,6,8                            # reduction candidate for 4,5
D5: 4,5 => CTR
* ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175.
D5: 2,6,8 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
* DURATION: 0:00:03.318960  START: 06:37:23.349027  END: 06:37:26.667987 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06902129-base-pr-001.dot
* REASONING
* DIS # D5: 4,5 => CTR => D5: 2,6,8
* PRF D5: 2,6,8 => SOL
* STA D5: 2,6,8
* CNT   2 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6902129
umulig

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

* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2)
* ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75.
* PAIR D1: 4,5 COL D
D5: 4,5,2,6,8                            # reduction candidate for 4,5
D5: 4,5 => CTR
* ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175.
D5: 2,6,8 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
* PAIR F3: 2,6 BLK 2
D3: 2,6,3                                # reduction candidate for 2,6
D3: 3 => CTR
* ..6475321...1289..721396...6.4519......642...1.27834......57....79.3461.....6175.
D3: 2,6                                  # 13 pairs
* PAIR F3: 2,6 COL F
F5: 2,6,1,5                              # reduction candidate for 2,6
F5: 2,6 => CTR
* ..6..5321...1.89..7.1......6.4..9............1..7.34......57....79..46......6175.
F5: 1,5 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
* PAIR G3: 5,8 BLK 3
I3: 5,8,4                                # reduction candidate for 5,8
I3: 5,8                                  #  9 pairs
I3: 4                                    #  9 pairs
* PAIR G3: 5,8 COL G
G4: 5,8,1,2                              # reduction candidate for 5,8
G4: 5,8                                  # 11 pairs
G5: 5,8,1,2                              # reduction candidate for 5,8
G5: 5,8                                  # 11 pairs
* PAIR H3: 4,8 BLK 3
I3: 4,8,5                                # reduction candidate for 4,8
I3: 4,8                                  #  9 pairs
I3: 5                                    #  7 pairs
* PAIR H3: 4,8 COL H
H7: 4,8,1,3,9                            # reduction candidate for 4,8
H7: 4,8                                  # 12 pairs
H7: 1,3,9                                #  9 pairs
* PAIR E6: 2,8 BLK 5
D4: 2,8,5                                # reduction candidate for 2,8
D4: 2,8 => CTR
* ..64.5321...1.89..7.1......6.4.19......546...1..7.34......57....79..461.....6175.
D4: 5 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E4: 2,8,1                                # reduction candidate for 2,8
E4: 2,8 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E4: 1                                    #  9 pairs
D5: 2,8,4,5,6                            # reduction candidate for 2,8
D5: 2,8 => CTR
* ..64.5321...1.89..7.16.2...6.45.9.......46...1..7.34......57....79..46......6175.
D5: 4,5,6                                #  9 pairs
E5: 2,8,1,4                              # reduction candidate for 2,8
E5: 2,8 => CTR
* ..65.7321...1.89..7.16.2...6.4.19......4.6...1..7.34......51.....9..4.......6.75.
E5: 1,4                                  # 10 pairs
* PAIR E6: 2,8 ROW 6
B6: 2,8,5,9                              # reduction candidate for 2,8
B6: 2,8                                  # 13 pairs
C6: 2,8,5                                # reduction candidate for 2,8
C6: 2,8                                  # 12 pairs
I6: 2,8,5,6,9                            # reduction candidate for 2,8
I6: 2,8 => CTR
* 986.47321...138976731.9....6.4..9......4.....1957.346...7.5......9.74.......6.75.
I6: 5,6,9                                #  9 pairs
* PAIR E6: 2,8 COL E
E8: 2,8,1,3,7                            # reduction candidate for 2,8
E8: 2,8 => CTR
* ..6.75321...1.89..7.1.9....6.4..9............1..7.34......57....79..461.....6175.
E8: 1,3,7                                # 10 pairs
* PAIR F9: 1,2 BLK 8
F7: 1,2,7                                # reduction candidate for 1,2
F7: 1,2 => CTR
* ..65.7321...1.89..7.1..6...6.4..9........5...1..7.34......5......9.74.......6.75.
F7: 7 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E8: 1,2,3,7,8                            # reduction candidate for 1,2
E8: 1,2 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
E8: 3,7,8                                #  9 pairs
* PAIR F9: 1,2 ROW 9
B9: 1,2,3,4,8                            # reduction candidate for 1,2
B9: 3,4,8 => CTR
* ..6..7321...1.89..7.1..6...6.4..9......645...1..7.34....7.52...5.9.74.......6175.
B9: 1,2                                  # 11 pairs
* PAIR F9: 1,2 COL F
F5: 1,2,5,6                              # reduction candidate for 1,2
F5: 1,2 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
F5: 5,6                                  # 10 pairs
* UNSOLVED!
* SAVE PR GRAPH zz-menneske-no-06902129-base-pr-000.dot
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D1,E6,F1,F3,F9,G3,H2,H3,I2)
* ..6...321...1.89..7.1......6.4..9............1..7.34......5......9..4.......6.75.
* PAIR D1: 4,5 COL D
D5: 4,5,2,6,8                            # reduction candidate for 4,5
D5: 4,5 => CTR
* ..6..5321...1.89..7.16.2...6.4..9........6...1..7.34......57....79..461.....6175.
D5: 2,6,8 => SOLVED
* 986475321245138967731296548624589173397641285158723496462357819579814632813962754
* SOLVED!
* SAVE PR GRAPH zz-menneske-no-06902129-base-pr-001.dot

Solution

position: 986475321245138967731296548624589173397641285158723496462357819579814632813962754 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 # D5: 4,5 => CTR => D5: 2,6,8
* PRF # D5: 2,6,8 => SOL
* INC # D3: 2,6 => UNS
* DIS # D3: 3 => CTR => D3: 2,6
* DIS # F5: 2,6 => CTR => F5: 1,5
* PRF # F5: 1,5 => SOL
* INC # I3: 5,8 => UNS
* INC # I3: 4 => UNS
* INC # G4: 5,8 => UNS
* INC # G5: 5,8 => UNS
* INC # I3: 4,8 => UNS
* INC # I3: 5 => UNS
* INC # H7: 4,8 => UNS
* INC # H7: 1,3,9 => UNS
* DIS # D4: 2,8 => CTR => D4: 5
* PRF # D4: 5 => SOL
* PRF # E4: 2,8 => SOL
* INC # E4: 1 => UNS
* DIS # D5: 2,8 => CTR => D5: 4,5,6
* INC # D5: 4,5,6 => UNS
* DIS # E5: 2,8 => CTR => E5: 1,4
* INC # E5: 1,4 => UNS
* INC # B6: 2,8 => UNS
* INC # C6: 2,8 => UNS
* DIS # I6: 2,8 => CTR => I6: 5,6,9
* INC # I6: 5,6,9 => UNS
* DIS # E8: 2,8 => CTR => E8: 1,3,7
* INC # E8: 1,3,7 => UNS
* DIS # F7: 1,2 => CTR => F7: 7
* PRF # F7: 7 => SOL
* PRF # E8: 1,2 => SOL
* INC # E8: 3,7,8 => UNS
* INC # B9: 1,2 => UNS
* DIS # B9: 3,4,8 => CTR => B9: 1,2
* PRF # F5: 1,2 => SOL
* INC # F5: 5,6 => UNS
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # D5: 4,5 => CTR => D5: 2,6,8
* PRF D5: 2,6,8 => SOL
* STA D5: 2,6,8
* CNT   2 HDP CHAINS /   1 HYP OPENED