Analysis of zz-menneske-no-06913596-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ....8.......1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2..............4. initial

Autosolve

position: 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # D5: 8 => SOL
* PRF # F6: 2,7 => SOL
* DIS # F6: 2,3 => CTR => F6: 7,8,9
* PRF # D9: 2,3 => SOL
* DIS # I8: 5,9 => CTR => I8: 3,6,7
* DIS # I2: 5,9 => CTR => I2: 7,8
* CNT   6 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:

* PRF # D5: 8 => SOL
* STA D5: 8
* CNT   1 HDP CHAINS /   6 HYP OPENED

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

Details

Positions

....8.......1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2..............4. initial
2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4. autosolve
271683495369154728854972361645239817937841652182567934413726589526498173798315246 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A3: 4,8
D1: 3,6
F1: 3,5
E2: 5,6
E3: 2,7
F3: 2,7
I3: 1,8
D4: 2,3
I7: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H4,I4: 1.. / H4 = 1  =>  9 pairs (_) / I4 = 1  => 23 pairs (_)
C3,I3: 1.. / C3 = 1  => 22 pairs (_) / I3 = 1  =>  9 pairs (_)
H1,H4: 1.. / H1 = 1  => 23 pairs (_) / H4 = 1  =>  9 pairs (_)
E3,F3: 2.. / E3 = 2  =>  7 pairs (_) / F3 = 2  =>  7 pairs (_)
C4,C6: 2.. / C4 = 2  =>  0 pairs (X) / C6 = 2  =>  9 pairs (_)
G7,G9: 2.. / G7 = 2  =>  9 pairs (_) / G9 = 2  =>  8 pairs (_)
E7,G7: 2.. / E7 = 2  =>  8 pairs (_) / G7 = 2  =>  9 pairs (_)
D4,D9: 2.. / D4 = 2  =>  9 pairs (_) / D9 = 2  =>  0 pairs (X)
D1,F1: 3.. / D1 = 3  =>  9 pairs (_) / F1 = 3  => 14 pairs (_)
A3,C3: 4.. / A3 = 4  => 23 pairs (_) / C3 = 4  =>  9 pairs (_)
B4,C4: 4.. / B4 = 4  =>  9 pairs (_) / C4 = 4  => 23 pairs (_)
A7,B7: 4.. / A7 = 4  =>  9 pairs (_) / B7 = 4  => 23 pairs (_)
A3,A7: 4.. / A3 = 4  => 23 pairs (_) / A7 = 4  =>  9 pairs (_)
B4,B7: 4.. / B4 = 4  =>  9 pairs (_) / B7 = 4  => 23 pairs (_)
C3,C4: 4.. / C3 = 4  =>  9 pairs (_) / C4 = 4  => 23 pairs (_)
F1,E2: 5.. / F1 = 5  =>  9 pairs (_) / E2 = 5  => 14 pairs (_)
C4,C5: 5.. / C4 = 5  => 10 pairs (_) / C5 = 5  => 16 pairs (_)
D1,E2: 6.. / D1 = 6  => 14 pairs (_) / E2 = 6  =>  9 pairs (_)
D5,E6: 6.. / D5 = 6  =>  9 pairs (_) / E6 = 6  => 14 pairs (_)
G5,G6: 6.. / G5 = 6  => 14 pairs (_) / G6 = 6  =>  9 pairs (_)
I8,I9: 6.. / I8 = 6  =>  9 pairs (_) / I9 = 6  =>  9 pairs (_)
D5,G5: 6.. / D5 = 6  =>  9 pairs (_) / G5 = 6  => 14 pairs (_)
E6,G6: 6.. / E6 = 6  => 14 pairs (_) / G6 = 6  =>  9 pairs (_)
C8,I8: 6.. / C8 = 6  =>  9 pairs (_) / I8 = 6  =>  9 pairs (_)
D1,D5: 6.. / D1 = 6  => 14 pairs (_) / D5 = 6  =>  9 pairs (_)
E2,E6: 6.. / E2 = 6  =>  9 pairs (_) / E6 = 6  => 14 pairs (_)
E3,F3: 7.. / E3 = 7  =>  7 pairs (_) / F3 = 7  =>  7 pairs (_)
A8,A9: 7.. / A8 = 7  => 10 pairs (_) / A9 = 7  => 10 pairs (_)
I2,I3: 8.. / I2 = 8  =>  9 pairs (_) / I3 = 8  => 22 pairs (_)
D5,F6: 8.. / D5 = 8  =>  0 pairs (*) / F6 = 8  =>  0 pairs (X)
H7,H8: 8.. / H7 = 8  => 10 pairs (_) / H8 = 8  => 27 pairs (_)
D5,D9: 8.. / D5 = 8  =>  0 pairs (*) / D9 = 8  =>  0 pairs (X)
* DURATION: 0:00:49.872658  START: 07:09:35.487460  END: 07:10:25.360118 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D1,D4,E2,E3,F1,F3,I3,I7)
* 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4.
* PAIR A3: 4,8 BLK 1
C3: 4,8,1                                # reduction candidate for 4,8
C3: 1                                    # 22 pairs
C3: 4,8                                  #  9 pairs
* PAIR A3: 4,8 COL A
A7: 4,8,5                                # reduction candidate for 4,8
A7: 5                                    # 24 pairs
A7: 4,8                                  # 12 pairs
* PAIR D1: 3,6 COL D
D5: 3,6,8                                # reduction candidate for 3,6
D5: 8 => SOLVED
* 271683495369154728854972361645239817937841652182567934413726589526498173798315246
D5: 3,6                                  # 11 pairs
* PAIR F1: 3,5 COL F
F8: 3,5,8,9                              # reduction candidate for 3,5
F8: 3,5                                  # 11 pairs
F9: 3,5,2,8,9                            # reduction candidate for 3,5
F9: 3,5                                  # 11 pairs
* PAIR E3: 2,7 COL E
E4: 2,7,3,9                              # reduction candidate for 2,7
E4: 2,7                                  # 10 pairs
E6: 2,7,3,6,9                            # reduction candidate for 2,7
E6: 2,7                                  # 14 pairs
* PAIR F3: 2,7 COL F
F4: 2,7,3,9                              # reduction candidate for 2,7
F4: 2,7                                  # 10 pairs
F6: 2,7,3,8,9                            # reduction candidate for 2,7
F6: 2,7 => SOLVED
* 271683495369154728854972361645239817937841652182567934413726589526498173798315246
F6: 3,8,9                                #  9 pairs
* PAIR I3: 1,8 ROW 3
C3: 1,8,4                                # reduction candidate for 1,8
C3: 1,8                                  # 23 pairs
C3: 4                                    #  9 pairs
* PAIR D4: 2,3 BLK 5
E4: 2,3,7,9                              # reduction candidate for 2,3
E4: 2,3                                  # 15 pairs
F4: 2,3,7,9                              # reduction candidate for 2,3
F4: 2,3                                  # 16 pairs
E6: 2,3,6,7,9                            # reduction candidate for 2,3
E6: 2,3                                  # 17 pairs
F6: 2,3,7,8,9                            # reduction candidate for 2,3
F6: 2,3 => CTR
* 2..6834..3..154.2..549273616423798159.58416.21..562..44.37.6259.2.4...8....2.8.4.
F6: 7,8,9                                #  9 pairs
* PAIR D4: 2,3 COL D
D9: 2,3,8                                # reduction candidate for 2,3
D9: 2,3 => SOLVED
* 271683495369154728854972361645239817937841652182567934413726589526498173798315246
D9: 8                                    # 11 pairs
* PAIR I7: 5,9 BLK 9
G7: 5,9,1,2                              # reduction candidate for 5,9
G7: 5,9                                  # 11 pairs
H7: 5,9,8                                # reduction candidate for 5,9
H7: 5,9                                  # 27 pairs
G8: 5,9,1,7                              # reduction candidate for 5,9
G8: 5,9                                  # 14 pairs
H8: 5,9,3,7,8                            # reduction candidate for 5,9
H8: 5,9                                  # 18 pairs
I8: 5,9,3,6,7                            # reduction candidate for 5,9
I8: 5,9 => CTR
* 2..6834.7367154.288549..3616452..8139...41..21.25....44.37.6.8..264.8.3....3...46
I8: 3,6,7                                #  9 pairs
G9: 5,9,1,2,7                            # reduction candidate for 5,9
G9: 5,9                                  # 12 pairs
I9: 5,9,3,6,7                            # reduction candidate for 5,9
I9: 5,9                                  # 24 pairs
* PAIR I7: 5,9 ROW 7
E7: 5,9,1,2                              # reduction candidate for 5,9
E7: 5,9                                  # 10 pairs
E7: 1,2                                  # 10 pairs
* PAIR I7: 5,9 COL I
I1: 5,9,1,7                              # reduction candidate for 5,9
I1: 5,9                                  # 11 pairs
I2: 5,9,7,8                              # reduction candidate for 5,9
I2: 5,9 => CTR
* 2.76834..3681547294519..3686.4...8..9.5.416.21.256.9.4.437.6..5.2.4..1...1....24.
I2: 7,8                                  # 10 pairs
I4: 5,9,1,3,7                            # reduction candidate for 5,9
I4: 5,9                                  # 16 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06913596-base-pr-000.dot
* REASONING
* PRF # D5: 8 => SOL
* PRF # F6: 2,7 => SOL
* DIS # F6: 2,3 => CTR => F6: 7,8,9
* PRF # D9: 2,3 => SOL
* DIS # I8: 5,9 => CTR => I8: 3,6,7
* DIS # I2: 5,9 => CTR => I2: 7,8
* CNT   6 HDP CHAINS /  36 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,D1,D4,E2,E3,F1,F3,I3,I7)
* 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4.
* PAIR A3: 4,8 BLK 1
C3: 4,8,1                                # reduction candidate for 4,8
C3: 1                                    # 22 pairs
C3: 4,8                                  #  9 pairs
* PAIR A3: 4,8 COL A
A7: 4,8,5                                # reduction candidate for 4,8
A7: 5                                    # 24 pairs
A7: 4,8                                  # 12 pairs
* PAIR D1: 3,6 COL D
D5: 3,6,8                                # reduction candidate for 3,6
D5: 8 => SOLVED
* 271683495369154728854972361645239817937841652182567934413726589526498173798315246
* DURATION: 0:00:06.990407  START: 07:10:58.701821  END: 07:11:05.692228 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06913596-base-pr-001.dot
* REASONING
* PRF # D5: 8 => SOL
* STA D5: 8
* CNT   1 HDP CHAINS /   6 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6913596
umulig

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

* PAIR REDUCTION ..
* ROUND 1
* 2...8.4..3..1.4.2..5.9..36.6.....8..9...41..21..5....4..37.6....2.4............4.
A3: 4,8                                  # * reduce to pair
C3: 4,8,1                                # reduction candidate for 4,8
C3: 1                                    # 22 pairs
C3: 4,8                                  #  9 pairs
A7: 4,8,5                                # reduction candidate for 4,8
A7: 5                                    # 24 pairs
A7: 4,8                                  # 12 pairs
D1: 3,6                                  # * reduce to pair
D5: 3,6,8                                # reduction candidate for 3,6
D5: 8 => SOLVED
* 271683495369154728854972361645239817937841652182567934413726589526498173798315246
* SOLVED!

Solution

position: 271683495369154728854972361645239817937841652182567934413726589526498173798315246 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 # C3: 4,8 => UNS
* INC # C3: 1 => UNS
* INC # A7: 4,8 => UNS
* INC # A7: 5 => UNS
* INC # D5: 3,6 => UNS
* PRF # D5: 8 => SOL
* INC # F8: 3,5 => UNS
* INC # F9: 3,5 => UNS
* INC # E4: 2,7 => UNS
* INC # E6: 2,7 => UNS
* INC # F4: 2,7 => UNS
* PRF # F6: 2,7 => SOL
* INC # F6: 3,8,9 => UNS
* INC # C3: 1,8 => UNS
* INC # C3: 4 => UNS
* INC # E4: 2,3 => UNS
* INC # F4: 2,3 => UNS
* INC # E6: 2,3 => UNS
* DIS # F6: 2,3 => CTR => F6: 7,8,9
* INC # F6: 7,8,9 => UNS
* PRF # D9: 2,3 => SOL
* INC # D9: 8 => UNS
* INC # G7: 5,9 => UNS
* INC # H7: 5,9 => UNS
* INC # G8: 5,9 => UNS
* INC # H8: 5,9 => UNS
* DIS # I8: 5,9 => CTR => I8: 3,6,7
* INC # I8: 3,6,7 => UNS
* INC # G9: 5,9 => UNS
* INC # I9: 5,9 => UNS
* INC # E7: 5,9 => UNS
* INC # E7: 1,2 => UNS
* INC # I1: 5,9 => UNS
* DIS # I2: 5,9 => CTR => I2: 7,8
* INC # I2: 7,8 => UNS
* INC # I4: 5,9 => UNS
* CNT  36 HDP CHAINS /  36 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C3: 4,8 => UNS
* INC # C3: 1 => UNS
* INC # A7: 4,8 => UNS
* INC # A7: 5 => UNS
* INC # D5: 3,6 => UNS
* PRF # D5: 8 => SOL
* STA D5: 8
* CNT   6 HDP CHAINS /   6 HYP OPENED