Analysis of zz-menneske-no-06913681-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: .95.........16.....3.8....1.41.....5..29..4.....3...7.2..5...4.....86.........89. initial

Autosolve

position: 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H8: 3,5 => CTR => H8: 1,2
* DIS # H8: 2,5 => CTR => H8: 1,3
* PRF # F4: 8 => SOL
* DIS # E3: 2,7 => CTR => E3: 4,5,9
* PRF # B7: 1,7 => SOL
* DIS # B9: 1,7 => CTR => B9: 5,6
* DIS # G8: 1,7 => CTR => G8: 2,3,5
* CNT   7 HDP CHAINS /  24 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 # H8: 3,5 => CTR => H8: 1,2
* DIS H8: 1,2 # F2: 4,7,9 => CTR => F2: 3,5
* DIS H8: 1,2 + F2: 3,5 # E3: 2,5 => CTR => E3: 4,7,9
* DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 # F3: 2,5 => CTR => F3: 4,7,9
* DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 # F4: 2,7 => CTR => F4: 8
* PRF H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 => SOL
* STA H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8
* CNT   6 HDP CHAINS /  10 HYP OPENED

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

Details

Positions

.95.........16.....3.8....1.41.....5..29..4.....3...7.2..5...4.....86.........89. initial
195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89. autosolve
195732684824165739637849251341678925782951463569324178218597346973486512456213897 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
H2: 3,5
H3: 2,5
E4: 2,7
B8: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H5,G6: 1.. / H5 = 1  =>  0 pairs (X) / G6 = 1  =>  0 pairs (_)
H5,H8: 1.. / H5 = 1  =>  0 pairs (X) / H8 = 1  =>  0 pairs (_)
A4,A5: 3.. / A4 = 3  =>  0 pairs (*) / A5 = 3  =>  0 pairs (X)
I1,I2: 4.. / I1 = 4  =>  0 pairs (*) / I2 = 4  =>  0 pairs (X)
E6,F6: 4.. / E6 = 4  =>  4 pairs (_) / F6 = 4  =>  4 pairs (_)
A9,B9: 5.. / A9 = 5  =>  4 pairs (_) / B9 = 5  =>  5 pairs (_)
G8,H8: 5.. / G8 = 5  =>  4 pairs (_) / H8 = 5  =>  0 pairs (X)
A3,C3: 6.. / A3 = 6  =>  5 pairs (_) / C3 = 6  =>  6 pairs (_)
H1,H5: 6.. / H1 = 6  =>  0 pairs (X) / H5 = 6  =>  0 pairs (_)
A2,C2: 8.. / A2 = 8  =>  5 pairs (_) / C2 = 8  =>  7 pairs (_)
H1,I1: 8.. / H1 = 8  =>  0 pairs (*) / I1 = 8  =>  0 pairs (X)
B7,C7: 8.. / B7 = 8  =>  5 pairs (_) / C7 = 8  =>  6 pairs (_)
A8,C8: 9.. / A8 = 9  =>  0 pairs (*) / C8 = 9  =>  0 pairs (X)
E7,F7: 9.. / E7 = 9  =>  4 pairs (_) / F7 = 9  =>  4 pairs (_)
A4,G4: 9.. / A4 = 9  =>  0 pairs (X) / G4 = 9  =>  0 pairs (_)
C6,C8: 9.. / C6 = 9  =>  0 pairs (*) / C8 = 9  =>  0 pairs (X)
E3,E7: 9.. / E3 = 9  =>  4 pairs (_) / E7 = 9  =>  4 pairs (_)
I2,I6: 9.. / I2 = 9  =>  0 pairs (*) / I6 = 9  =>  0 pairs (X)
* DURATION: 0:00:25.044800  START: 07:11:21.238432  END: 07:11:46.283232 2017-05-01
* CP COUNT: (18)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E4,H2,H3)
* 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89.
* PAIR H2: 3,5 BLK 3
G2: 3,5,7,9                              # reduction candidate for 3,5
G2: 3,5                                  #  8 pairs
G2: 7,9                                  #  5 pairs
* PAIR H2: 3,5 ROW 2
F2: 3,5,4,7,9                            # reduction candidate for 3,5
F2: 4,7,9                                #  7 pairs
F2: 3,5                                  #  6 pairs
* PAIR H2: 3,5 COL H
H8: 3,5,1,2                              # reduction candidate for 3,5
H8: 3,5 => CTR
* 195....68.2.16...4.3.8...219416..385372958416...3..2792..5..64..19.86.........89.
H8: 1,2                                  #  5 pairs
* PAIR H3: 2,5 BLK 3
G3: 2,5,7,9                              # reduction candidate for 2,5
G3: 2,5                                  # 12 pairs
G3: 7,9                                  #  5 pairs
* PAIR H3: 2,5 ROW 3
E3: 2,5,4,7,9                            # reduction candidate for 2,5
E3: 2,5                                  #  6 pairs
F3: 2,5,4,7,9                            # reduction candidate for 2,5
F3: 2,5                                  #  6 pairs
* PAIR H3: 2,5 COL H
H8: 2,5,1,3                              # reduction candidate for 2,5
H8: 2,5 => CTR
* 195....68.2.16..34.3.8....19416..385372958416...3..2792..5..64..19.86..3......892
H8: 1,3                                  #  6 pairs
* PAIR E4: 2,7 BLK 5
F4: 2,7,8                                # reduction candidate for 2,7
F4: 8 => SOLVED
* 195732684824165739637849251341678925782951463569324178218597346973486512456213897
F4: 2,7                                  #  8 pairs
* PAIR E4: 2,7 COL E
E1: 2,7,3,4                              # reduction candidate for 2,7
E1: 2,7                                  #  6 pairs
E3: 2,7,4,5,9                            # reduction candidate for 2,7
E3: 2,7 => CTR
* 195.......2.16...4.3.8....19416....537295.416...3..2792..59..4..19.86.........89.
E3: 4,5,9                                #  4 pairs
E9: 2,7,1,3,4                            # reduction candidate for 2,7
E9: 2,7                                  #  9 pairs
* PAIR B8: 1,7 BLK 7
B7: 1,7,6,8                              # reduction candidate for 1,7
B7: 1,7 => SOLVED
* 195732684824165739637849251341678925782951463569324178218597346973486512456213897
B7: 6,8                                  #  5 pairs
B9: 1,7,5,6                              # reduction candidate for 1,7
B9: 1,7 => CTR
* 195...68482.165739.378..251341678925782951463.593..178268519347973486512514...89.
B9: 5,6                                  #  5 pairs
* PAIR B8: 1,7 ROW 8
G8: 1,7,2,3,5                            # reduction candidate for 1,7
G8: 1,7 => CTR
* 195...768.2.16..34.3.8...219416..385372958416...3..2792..5..647.19.86.53......892
G8: 2,3,5                                #  4 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06913681-base-pr-000.dot
* REASONING
* DIS # H8: 3,5 => CTR => H8: 1,2
* DIS # H8: 2,5 => CTR => H8: 1,3
* PRF # F4: 8 => SOL
* DIS # E3: 2,7 => CTR => E3: 4,5,9
* PRF # B7: 1,7 => SOL
* DIS # B9: 1,7 => CTR => B9: 5,6
* DIS # G8: 1,7 => CTR => G8: 2,3,5
* CNT   7 HDP CHAINS /  24 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B8,E4,H2,H3)
* 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89.
* PAIR H2: 3,5 BLK 3
G2: 3,5,7,9                              # reduction candidate for 3,5
G2: 3,5                                  #  8 pairs
G2: 7,9                                  #  5 pairs
* PAIR H2: 3,5 ROW 2
F2: 3,5,4,7,9                            # reduction candidate for 3,5
F2: 4,7,9                                #  7 pairs
F2: 3,5                                  #  6 pairs
* PAIR H2: 3,5 COL H
H8: 3,5,1,2                              # reduction candidate for 3,5
H8: 3,5 => CTR
* 195....68.2.16...4.3.8...219416..385372958416...3..2792..5..64..19.86.........89.
* PAIR RESTART
* PAIR H2: 3,5 ROW 2
F2: 3,5,4,7,9                            # reduction candidate for 3,5
F2: 4,7,9 => CTR
* 195.......2.16.35..3.8..921941678235..29..4.....3..1792..5...4..79.86513......892
* PAIR RESTART
* PAIR H3: 2,5 ROW 3
E3: 2,5,4,7,9                            # reduction candidate for 2,5
E3: 2,5 => CTR
* 195.....2.2.16.9.4.3.82975194167...53729..41....3...792..59..4..19.86523......89.
F3: 2,5,4,7,9                            # reduction candidate for 2,5
F3: 2,5 => CTR
* 195.....2.2.16.9.4.3.8927519416....537295.41....3...792..5.9.4..19.86523......89.
* PAIR RESTART
* PAIR E4: 2,7 BLK 5
F4: 2,7,8                                # reduction candidate for 2,7
F4: 2,7 => CTR
* 195....68.2.165.3..3.8..251.416...85..29..4.....3...722..5...4.....8652.......89.
F4: 8 => SOLVED
* 195732684824165739637849251341678925782951463569324178218597346973486512456213897
* DURATION: 0:00:10.912017  START: 07:12:04.661430  END: 07:12:15.573447 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06913681-base-pr-001.dot
* REASONING
* DIS # H8: 3,5 => CTR => H8: 1,2
* DIS H8: 1,2 # F2: 4,7,9 => CTR => F2: 3,5
* DIS H8: 1,2 + F2: 3,5 # E3: 2,5 => CTR => E3: 4,7,9
* DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 # F3: 2,5 => CTR => F3: 4,7,9
* DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 # F4: 2,7 => CTR => F4: 8
* PRF H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 => SOL
* STA H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8
* CNT   6 HDP CHAINS /  10 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6913681
umulig

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

* PAIR REDUCTION ..
* ROUND 1: 195.......2.16.....3.8....1.416....5..29..4.....3...7.2..5...4.....86.........89.
H2: 3,5
G2: 3,5,7,9                              # reduction candidate for 3,5
F2: 3,4,5,7,9                            # reduction candidate for 3,5
H8: 1,2,3,5                              # reduction candidate for 3,5
H8: 3,5 => CTR
* 195....68.2.16...4.3.8...219416..385372958416...3..2792..5..64..19.86.........89.
H3: 2,5
E3: 2,4,5,7,9                            # reduction candidate for 2,5
F3: 2,4,5,7,9                            # reduction candidate for 2,5
E4: 2,7
F4: 2,7,8                                # reduction candidate for 2,7
F4: 8 => SOLVED
* 195732684824165739637849251341678925782951463569324178218597346973486512456213897
* SOLVED!

Solution

position: 195732684824165739637849251341678925782951463569324178218597346973486512456213897 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 # G2: 3,5 => UNS
* INC # G2: 7,9 => UNS
* INC # F2: 3,5 => UNS
* INC # F2: 4,7,9 => UNS
* DIS # H8: 3,5 => CTR => H8: 1,2
* INC # H8: 1,2 => UNS
* INC # G3: 2,5 => UNS
* INC # G3: 7,9 => UNS
* INC # E3: 2,5 => UNS
* INC # F3: 2,5 => UNS
* DIS # H8: 2,5 => CTR => H8: 1,3
* INC # H8: 1,3 => UNS
* INC # F4: 2,7 => UNS
* PRF # F4: 8 => SOL
* INC # E1: 2,7 => UNS
* DIS # E3: 2,7 => CTR => E3: 4,5,9
* INC # E3: 4,5,9 => UNS
* INC # E9: 2,7 => UNS
* PRF # B7: 1,7 => SOL
* INC # B7: 6,8 => UNS
* DIS # B9: 1,7 => CTR => B9: 5,6
* INC # B9: 5,6 => UNS
* DIS # G8: 1,7 => CTR => G8: 2,3,5
* INC # G8: 2,3,5 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G2: 3,5 => UNS
* INC # G2: 7,9 => UNS
* INC # F2: 3,5 => UNS
* INC # F2: 4,7,9 => UNS
* DIS # H8: 3,5 => CTR => H8: 1,2
* INC H8: 1,2 # F2: 3,5 => UNS
* DIS H8: 1,2 # F2: 4,7,9 => CTR => F2: 3,5
* DIS H8: 1,2 + F2: 3,5 # E3: 2,5 => CTR => E3: 4,7,9
* DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 # F3: 2,5 => CTR => F3: 4,7,9
* DIS H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 # F4: 2,7 => CTR => F4: 8
* PRF H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8 => SOL
* STA H8: 1,2 + F2: 3,5 + E3: 4,7,9 + F3: 4,7,9 + F4: 8
* CNT  11 HDP CHAINS /  10 HYP OPENED