Analysis of zz-menneske-no-06902995-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4......8...39....5 initial

Autosolve

position: 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # B1: 4,9 => CTR => B1: 2,3
* DIS # E1: 4,9 => CTR => E1: 2,5
* DIS # H1: 4,9 => CTR => H1: 3,5
* PRF # I1: 4,9 => SOL
* DIS # I1: 3,7 => CTR => I1: 4,9
* DIS # E4: 1,6 => CTR => E4: 5,8,9
* PRF # B8: 2,9 => SOL
* DIS # B1: 2,9 => CTR => B1: 3,4
* DIS # I7: 7,9 => CTR => I7: 3,4
* DIS # C2: 7,9 => CTR => C2: 4,6,8
* DIS # C3: 7,9 => CTR => C3: 4,8
* DIS # G8: 2,7 => CTR => G8: 3,9
* DIS # A9: 2,7 => CTR => A9: 6
* PRF # A9: 6 => SOL
* PRF # E9: 2,7 => SOL
* DIS # E9: 2,4 => CTR => E9: 1,6,7,8
* DIS # F9: 2,4 => CTR => F9: 1,8
* CNT  17 HDP CHAINS /  40 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 # B1: 4,9 => CTR => B1: 2,3
* DIS B1: 2,3 # E1: 4,9 => CTR => E1: 2,5
* DIS B1: 2,3 + E1: 2,5 # H1: 4,9 => CTR => H1: 3,5
* PRF B1: 2,3 + E1: 2,5 + H1: 3,5 # I1: 4,9 => SOL
* STA B1: 2,3 + E1: 2,5 + H1: 3,5 + I1: 4,9
* CNT   4 HDP CHAINS /   7 HYP OPENED

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

Details

Positions

1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4......8...39....5 initial
1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5 autosolve
139826754768495132254713896382157469546289371971634528897542613425361987613978245 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C1: 4,9
G2: 1,8
G3: 1,8
D4: 1,6
B7: 2,9
C7: 7,9
G9: 2,7
H9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 1.. / G2 = 1  =>  7 pairs (_) / G3 = 1  =>  6 pairs (_)
C5,C6: 1.. / C5 = 1  =>  8 pairs (_) / C6 = 1  =>  9 pairs (_)
B8,B9: 1.. / B8 = 1  =>  0 pairs (X) / B9 = 1  =>  8 pairs (_)
B1,A3: 2.. / B1 = 2  =>  0 pairs (X) / A3 = 2  => 10 pairs (_)
B1,E1: 2.. / B1 = 2  =>  0 pairs (X) / E1 = 2  => 10 pairs (_)
A3,A9: 2.. / A3 = 2  => 10 pairs (_) / A9 = 2  =>  0 pairs (X)
H6,H9: 2.. / H6 = 2  =>  0 pairs (*) / H9 = 2  =>  0 pairs (X)
F7,I7: 3.. / F7 = 3  =>  9 pairs (_) / I7 = 3  =>  0 pairs (*)
I7,H9: 4.. / I7 = 4  =>  0 pairs (X) / H9 = 4  =>  0 pairs (_)
I1,I7: 4.. / I1 = 4  =>  0 pairs (*) / I7 = 4  =>  0 pairs (X)
H4,H6: 6.. / H4 = 6  =>  7 pairs (_) / H6 = 6  =>  0 pairs (X)
G1,I1: 7.. / G1 = 7  =>  0 pairs (*) / I1 = 7  =>  0 pairs (X)
C7,A9: 7.. / C7 = 7  =>  9 pairs (_) / A9 = 7  =>  0 pairs (X)
G2,G3: 8.. / G2 = 8  =>  6 pairs (_) / G3 = 8  =>  7 pairs (_)
E9,F9: 8.. / E9 = 8  =>  8 pairs (_) / F9 = 8  =>  8 pairs (_)
C3,G3: 8.. / C3 = 8  =>  6 pairs (_) / G3 = 8  =>  7 pairs (_)
* DURATION: 0:00:20.245619  START: 06:37:41.639118  END: 06:38:01.884737 2017-05-01
* CP COUNT: (16)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C1,C7,D4,G2,G3,G9,H9)
* 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5
* PAIR C1: 4,9 BLK 1
B1: 4,9,2,3                              # reduction candidate for 4,9
B1: 4,9 => CTR
* 1..826...........225......6..2..74.........7..7..3....8..5736144.5....8.7.39...25
B1: 2,3                                  #  9 pairs
B2: 4,9,3,6,8                            # reduction candidate for 4,9
B2: 4,9                                  # 11 pairs
C2: 4,9,6,7,8                            # reduction candidate for 4,9
C2: 4,9                                  # 15 pairs
C3: 4,9,7,8                              # reduction candidate for 4,9
C3: 4,9                                  # 10 pairs
* PAIR C1: 4,9 ROW 1
E1: 4,9,2,5                              # reduction candidate for 4,9
E1: 4,9 => CTR
* 12.8.6...........2.5......6..2..74.........7..7..3....8975..61.4.5....8.2.39..745
E1: 2,5                                  #  9 pairs
H1: 4,9,3,5                              # reduction candidate for 4,9
H1: 4,9 => CTR
* 13.8265.77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725
H1: 3,5                                  #  9 pairs
I1: 4,9,3,7                              # reduction candidate for 4,9
I1: 4,9 => SOLVED
* 139826754768495132254713896382157469546289371971634528897542613425361987613978245
I1: 3,7 => CTR
* 1..826..77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725
* PAIR C1: 4,9 COL C
C5: 4,9,1,6,8                            # reduction candidate for 4,9
C5: 4,9                                  # 10 pairs
C6: 4,9,1,6,8                            # reduction candidate for 4,9
C6: 4,9                                  #  9 pairs
* PAIR D4: 1,6 BLK 5
E4: 1,6,5,8,9                            # reduction candidate for 1,6
E4: 1,6 => CTR
* 1..826..77.......225......6..2..74.........7..7..3..6.8.75..6144.5....8...39..725
E4: 5,8,9                                #  8 pairs
D5: 1,6,2,4                              # reduction candidate for 1,6
D5: 1,6                                  # 10 pairs
E5: 1,6,2,4,5,8,9                        # reduction candidate for 1,6
E5: 1,6                                  # 11 pairs
D6: 1,6,2,4                              # reduction candidate for 1,6
D6: 1,6                                  # 11 pairs
* PAIR D4: 1,6 COL D
D8: 1,6,2,3,7                            # reduction candidate for 1,6
D8: 1,6                                  # 13 pairs
D8: 2,3,7                                #  8 pairs
* PAIR B7: 2,9 BLK 7
B8: 2,9,1,6                              # reduction candidate for 2,9
B8: 2,9 => SOLVED
* 139826754768495132254713896382157469546289371971634528897542613425361987613978245
B8: 1,6                                  #  9 pairs
* PAIR B7: 2,9 COL B
B1: 2,9,3,4                              # reduction candidate for 2,9
B1: 2,9 => CTR
* 1.98.6734.......52.5.....96..21.746........7..7..3..2.8975..61.4.5....8...39...45
B1: 3,4                                  # 11 pairs
* PAIR C7: 7,9 ROW 7
I7: 7,9,3,4                              # reduction candidate for 7,9
I7: 7,9 => CTR
* 1398267547..3...9225.7...36.821.74633...8..71.71634.288275436194952..387613978245
I7: 3,4                                  #  9 pairs
* PAIR C7: 7,9 COL C
C2: 7,9,4,6,8                            # reduction candidate for 7,9
C2: 7,9 => CTR
* 1.4826..7769...8.2258...1.6.82..74...4.....7..7..3....8..5.36144.5....8...39..725
C2: 4,6,8                                #  8 pairs
C3: 7,9,4,8                              # reduction candidate for 7,9
C3: 7,9 => CTR
* 1.4826..77.....1.2259...8.6..2..74...4.....7..7..3....8..5.36144.5....8...39..725
C3: 4,8                                  #  9 pairs
* PAIR G9: 2,7 BLK 9
G8: 2,7,3,9                              # reduction candidate for 2,7
G8: 2,7 => CTR
* 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5
G8: 3,9                                  # 12 pairs
* PAIR G9: 2,7 ROW 9
A9: 2,7,6                                # reduction candidate for 2,7
A9: 2,7 => CTR
* 1.98.67.4........2.5......6..21.746........7..7..3..2.8975..61.4.5....8...39...45
A9: 6 => SOLVED
* 139826754768495132254713896382157469546289371971634528897542613425361987613978245
E9: 2,7,1,4,6,8                          # reduction candidate for 2,7
E9: 2,7 => SOLVED
* 139826754768495132254713896382157469546289371971634528897542613425361987613978245
E9: 1,4,6,8                              #  8 pairs
* PAIR H9: 2,4 ROW 9
E9: 2,4,1,6,7,8                          # reduction candidate for 2,4
E9: 2,4 => CTR
* 1..826..7........225......6..2..74.........7..7..3....8.75..6144.5....8.613948725
E9: 1,6,7,8                              #  8 pairs
F9: 2,4,1,8                              # reduction candidate for 2,4
F9: 2,4 => CTR
* 1..826..7........225......6..2..74.........7..7..3....8.75..6144.5....8.613984725
F9: 1,8                                  #  9 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06902995-base-pr-000.dot
* REASONING
* DIS # B1: 4,9 => CTR => B1: 2,3
* DIS # E1: 4,9 => CTR => E1: 2,5
* DIS # H1: 4,9 => CTR => H1: 3,5
* PRF # I1: 4,9 => SOL
* DIS # I1: 3,7 => CTR => I1: 4,9
* DIS # E4: 1,6 => CTR => E4: 5,8,9
* PRF # B8: 2,9 => SOL
* DIS # B1: 2,9 => CTR => B1: 3,4
* DIS # I7: 7,9 => CTR => I7: 3,4
* DIS # C2: 7,9 => CTR => C2: 4,6,8
* DIS # C3: 7,9 => CTR => C3: 4,8
* DIS # G8: 2,7 => CTR => G8: 3,9
* DIS # A9: 2,7 => CTR => A9: 6
* PRF # A9: 6 => SOL
* PRF # E9: 2,7 => SOL
* DIS # E9: 2,4 => CTR => E9: 1,6,7,8
* DIS # F9: 2,4 => CTR => F9: 1,8
* CNT  17 HDP CHAINS /  40 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B7,C1,C7,D4,G2,G3,G9,H9)
* 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5
* PAIR C1: 4,9 BLK 1
B1: 4,9,2,3                              # reduction candidate for 4,9
B1: 4,9 => CTR
* 1..826...........225......6..2..74.........7..7..3....8..5736144.5....8.7.39...25
B2: 4,9,3,6,8                            # reduction candidate for 4,9
B2: 4,9                                  # 11 pairs
C2: 4,9,6,7,8                            # reduction candidate for 4,9
C2: 4,9                                  # 15 pairs
C3: 4,9,7,8                              # reduction candidate for 4,9
C3: 4,9                                  # 10 pairs
* PAIR C1: 4,9 ROW 1
E1: 4,9,2,5                              # reduction candidate for 4,9
E1: 4,9 => CTR
* 12.8.6...........2.5......6..2..74.........7..7..3....8975..61.4.5....8.2.39..745
H1: 4,9,3,5                              # reduction candidate for 4,9
H1: 4,9 => CTR
* 13.8265.77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725
I1: 4,9,7                                # reduction candidate for 4,9
I1: 4,9 => SOLVED
* 139826754768495132254713896382157469546289371971634528897542613425361987613978245
* DURATION: 0:00:07.293286  START: 06:38:31.359623  END: 06:38:38.652909 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06902995-base-pr-001.dot
* REASONING
* DIS # B1: 4,9 => CTR => B1: 2,3
* DIS B1: 2,3 # E1: 4,9 => CTR => E1: 2,5
* DIS B1: 2,3 + E1: 2,5 # H1: 4,9 => CTR => H1: 3,5
* PRF B1: 2,3 + E1: 2,5 + H1: 3,5 # I1: 4,9 => SOL
* STA B1: 2,3 + E1: 2,5 + H1: 3,5 + I1: 4,9
* CNT   4 HDP CHAINS /   7 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6902995
umulig

* PAIR REDUCTION ..
* ROUND 1: 1..8.6...........2.5......6..2..74.........7..7..3....8..5..61.4.5....8...39....5
C1: 4,9
B1: 2,3,4,9                              # reduction candidate for 4,9
B1: 4,9 => CTR
* 1..826...........225......6..2..74.........7..7..3....8..5736144.5....8.7.39...25
B2: 3,4,6,8,9                            # reduction candidate for 4,9
C2: 4,6,7,8,9                            # reduction candidate for 4,9
C3: 4,7,8,9                              # reduction candidate for 4,9
E1: 2,4,5,9                              # reduction candidate for 4,9
E1: 4,9 => CTR
* 12.8.6...........2.5......6..2..74.........7..7..3....8975..61.4.5....8.2.39..745
H1: 3,4,5,9                              # reduction candidate for 4,9
H1: 4,9 => CTR
* 13.8265.77.......225......6..2..74.........7..7..3....82.5.36144.5....8...39..725
I1: 4,7,9                                # reduction candidate for 4,9
I1: 4,9 => SOLVED
* 139826754768495132254713896382157469546289371971634528897542613425361987613978245
* SOLVED!

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

I8 = 7 => SOL

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

Solution

position: 139826754768495132254713896382157469546289371971634528897542613425361987613978245 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 # B1: 4,9 => CTR => B1: 2,3
* INC # B1: 2,3 => UNS
* INC # B2: 4,9 => UNS
* INC # C2: 4,9 => UNS
* INC # C3: 4,9 => UNS
* DIS # E1: 4,9 => CTR => E1: 2,5
* INC # E1: 2,5 => UNS
* DIS # H1: 4,9 => CTR => H1: 3,5
* INC # H1: 3,5 => UNS
* PRF # I1: 4,9 => SOL
* DIS # I1: 3,7 => CTR => I1: 4,9
* INC # C5: 4,9 => UNS
* INC # C6: 4,9 => UNS
* DIS # E4: 1,6 => CTR => E4: 5,8,9
* INC # E4: 5,8,9 => UNS
* INC # D5: 1,6 => UNS
* INC # E5: 1,6 => UNS
* INC # D6: 1,6 => UNS
* INC # D8: 1,6 => UNS
* INC # D8: 2,3,7 => UNS
* PRF # B8: 2,9 => SOL
* INC # B8: 1,6 => UNS
* DIS # B1: 2,9 => CTR => B1: 3,4
* INC # B1: 3,4 => UNS
* DIS # I7: 7,9 => CTR => I7: 3,4
* INC # I7: 3,4 => UNS
* DIS # C2: 7,9 => CTR => C2: 4,6,8
* INC # C2: 4,6,8 => UNS
* DIS # C3: 7,9 => CTR => C3: 4,8
* INC # C3: 4,8 => UNS
* DIS # G8: 2,7 => CTR => G8: 3,9
* INC # G8: 3,9 => UNS
* DIS # A9: 2,7 => CTR => A9: 6
* PRF # A9: 6 => SOL
* PRF # E9: 2,7 => SOL
* INC # E9: 1,4,6,8 => UNS
* DIS # E9: 2,4 => CTR => E9: 1,6,7,8
* INC # E9: 1,6,7,8 => UNS
* DIS # F9: 2,4 => CTR => F9: 1,8
* INC # F9: 1,8 => UNS
* CNT  40 HDP CHAINS /  40 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # B1: 4,9 => CTR => B1: 2,3
* INC B1: 2,3 # B2: 4,9 => UNS
* INC B1: 2,3 # C2: 4,9 => UNS
* INC B1: 2,3 # C3: 4,9 => UNS
* DIS B1: 2,3 # E1: 4,9 => CTR => E1: 2,5
* DIS B1: 2,3 + E1: 2,5 # H1: 4,9 => CTR => H1: 3,5
* PRF B1: 2,3 + E1: 2,5 + H1: 3,5 # I1: 4,9 => SOL
* STA B1: 2,3 + E1: 2,5 + H1: 3,5 + I1: 4,9
* CNT   7 HDP CHAINS /   7 HYP OPENED