Analysis of zz-menneske-no-06899619-base.sdk

Contents

Original Sudoku

level: medium

Original Sudoku

position: ...8.1..55......2...69..........6.873...8....1.....4.......96...3.4....2.596.7... initial

Autosolve

position: ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* PRF # E1: 3,7 => SOL
* DIS # E2: 3,7 => CTR => E2: 4,6
* DIS # E3: 3,7 => CTR => E3: 2,4,5
* DIS # C2: 3,7 => CTR => C2: 1,4,8
* PRF # G2: 3,7 => SOL
* DIS # D6: 3,7 => CTR => D6: 2,5
* DIS # E1: 3,4 => CTR => E1: 2,6,7
* DIS # E2: 3,4 => CTR => E2: 6,7
* DIS # E3: 3,4 => CTR => E3: 2,5,7
* DIS # F3: 3,4 => CTR => F3: 2,5
* DIS # C2: 3,4 => CTR => C2: 1,7,8
* DIS # I2: 3,4 => CTR => I2: 1,6,8,9
* DIS # C7: 1,7 => CTR => C7: 2,4,8
* PRF # C2: 1,7 => SOL
* PRF # D7: 1,5 => SOL
* DIS # D7: 2,3 => CTR => D7: 1,5
* DIS # E7: 1,5 => CTR => E7: 2,3
* DIS # E4: 1,5 => CTR => E4: 2,3,4,9
* DIS # H8: 5,7 => CTR => H8: 9
* CNT  19 HDP CHAINS /  38 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 # E1: 3,7 => SOL
* STA E1: 3,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

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

Details

Positions

...8.1..55......2...69..........6.873...8....1.....4.......96...3.4....2.596.7... initial
...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7... autosolve
243871965591364728786952143925146387364785219178293456812539674637418592459627831 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
D2: 3,7
F2: 3,4
C8: 1,7
E8: 1,5
H7: 5,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
C8,E8: 1.. / C8 = 1  =>  0 pairs (X) / E8 = 1  =>  0 pairs (_)
G4,G5: 2.. / G4 = 2  =>  0 pairs (X) / G5 = 2  =>  6 pairs (_)
A9,E9: 2.. / A9 = 2  =>  8 pairs (_) / E9 = 2  =>  0 pairs (*)
C1,C2: 3.. / C1 = 3  =>  6 pairs (_) / C2 = 3  =>  0 pairs (X)
E4,F5: 4.. / E4 = 4  =>  0 pairs (*) / F5 = 4  =>  0 pairs (X)
E3,F3: 5.. / E3 = 5  =>  0 pairs (*) / F3 = 5  =>  0 pairs (X)
E1,E2: 6.. / E1 = 6  =>  0 pairs (X) / E2 = 6  =>  5 pairs (_)
H1,I2: 6.. / H1 = 6  =>  5 pairs (_) / I2 = 6  =>  0 pairs (X)
B5,B6: 6.. / B5 = 6  =>  7 pairs (_) / B6 = 6  =>  8 pairs (_)
E1,H1: 6.. / E1 = 6  =>  0 pairs (X) / H1 = 6  =>  5 pairs (_)
E2,I2: 6.. / E2 = 6  =>  5 pairs (_) / I2 = 6  =>  0 pairs (X)
B6,C6: 8.. / B6 = 8  =>  0 pairs (X) / C6 = 8  =>  5 pairs (_)
E4,E6: 9.. / E4 = 9  =>  0 pairs (X) / E6 = 9  =>  0 pairs (_)
G8,H8: 9.. / G8 = 9  =>  0 pairs (X) / H8 = 9  =>  6 pairs (_)
A1,A4: 9.. / A1 = 9  =>  7 pairs (_) / A4 = 9  =>  0 pairs (*)
* DURATION: 0:00:21.102467  START: 06:32:27.618982  END: 06:32:48.721449 2017-05-01
* CP COUNT: (15)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D2,E8,F2,H7)
* ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7...
* PAIR D2: 3,7 BLK 2
E1: 3,7,2,4,6                            # reduction candidate for 3,7
E1: 3,7 => SOLVED
* 243871965591364728786952143925146387364785219178293456812539674637418592459627831
E1: 2,4,6                                #  5 pairs
E2: 3,7,4,6                              # reduction candidate for 3,7
E2: 3,7 => CTR
* ..3861..55....4.26..69.........46.873...8....1...934.......96..63.4.8..2.596.7...
E2: 4,6                                  #  6 pairs
E3: 3,7,2,4,5                            # reduction candidate for 3,7
E3: 3,7 => CTR
* ...821.655...64.2...69.5.......46.873...82...1...9345......96..63.4.8..2.596.7...
E3: 2,4,5                                #  5 pairs
* PAIR D2: 3,7 ROW 2
C2: 3,7,1,4,8                            # reduction candidate for 3,7
C2: 3,7 => CTR
* ...8.1.655.7364.2...69.........463873...8.2..1...934567....96..63.4.8..2.596.7...
C2: 1,4,8                                #  6 pairs
G2: 3,7,1,8,9                            # reduction candidate for 3,7
G2: 3,7 => SOLVED
* 243871965591364728786952143925146387364785219178293456812539674637418592459627831
G2: 1,8,9                                #  5 pairs
* PAIR D2: 3,7 COL D
D6: 3,7,2,5                              # reduction candidate for 3,7
D6: 3,7 => CTR
* ...8.1..55......2...69........1.638737.5842..1.....4.......967.637418592.596.7...
D6: 2,5                                  #  6 pairs
* PAIR F2: 3,4 BLK 2
E1: 3,4,2,6,7                            # reduction candidate for 3,4
E1: 3,4 => CTR
* 9238417655..763.2...69.....245.96.873.7.842..1.8.7.4....2..96..631458972.59627...
E1: 2,6,7                                #  5 pairs
E2: 3,4,6,7                              # reduction candidate for 3,4
E2: 3,4 => CTR
* 9238617455..7439264769.....245.96.873.7.842..1.8.7.4..7.4..96..63.4.8592.596.7..4
E2: 6,7                                  #  6 pairs
E3: 3,4,2,5,7                            # reduction candidate for 3,4
E3: 3,4 => CTR
* ...821.655..76..2..269.5.......96.873...84...1...724.....2.96..63.4.8..22596.7...
E3: 2,5,7                                #  5 pairs
F3: 3,4,2,5                              # reduction candidate for 3,4
F3: 3,4 => CTR
* ...821.655...6..2...695........46.873...8....1.....4.....5.967.637418..2.596.7...
F3: 2,5                                  #  6 pairs
* PAIR F2: 3,4 ROW 2
C2: 3,4,1,7,8                            # reduction candidate for 3,4
C2: 3,4 => CTR
* 9238417655.4763.2...69.....245.96.873.7.842..1.8.7.4....2..96..631458972.59627...
C2: 1,7,8                                #  6 pairs
I2: 3,4,1,6,8,9                          # reduction candidate for 3,4
I2: 3,4 => CTR
* ..38.1965598763124.169.5.7.9....6.87367.84.1.1...7.4.......96..631458792.596.7...
I2: 1,6,8,9                              #  5 pairs
* PAIR C8: 1,7 BLK 7
B7: 1,7,2,4,8                            # reduction candidate for 1,7
B7: 1,7                                  #  6 pairs
C7: 1,7,2,4,8                            # reduction candidate for 1,7
C7: 1,7 => CTR
* ...8.1..55..3.4.2...69..........6.873...8....1.8.9.4.......96..63.4.8..2.596.7...
C7: 2,4,8                                #  5 pairs
* PAIR C8: 1,7 COL C
C2: 1,7,3,4,8                            # reduction candidate for 1,7
C2: 1,7 => SOLVED
* 243871965591364728786952143925146387364785219178293456812539674637418592459627831
C2: 3,4,8                                #  5 pairs
* PAIR E8: 1,5 BLK 8
D7: 1,5,2,3                              # reduction candidate for 1,5
D7: 1,5 => SOLVED
* 243871965591364728786952143925146387364785219178293456812539674637418592459627831
D7: 2,3 => CTR
* ..38.1..55......2...69.5........6.873...8....1.....4.....2.96..63.4.8..22596.7...
E7: 1,5,2,3                              # reduction candidate for 1,5
E7: 1,5 => CTR
* ..38.1..55......2...69.5........6.873...8....1.....4.....2.96.363.4.8..2259637...
E7: 2,3                                  #  6 pairs
* PAIR E8: 1,5 COL E
E4: 1,5,2,3,4,9                          # reduction candidate for 1,5
E4: 1,5 => CTR
* ..38.1..55..7.3.2...69..........6.873...84...1...9.4.......96..63.4.8..2.596.7...
E4: 2,3,4,9                              #  5 pairs
* PAIR H7: 5,7 BLK 9
G8: 5,7,9                                # reduction candidate for 5,7
G8: 5,7                                  #  6 pairs
H8: 5,7,9                                # reduction candidate for 5,7
H8: 5,7 => CTR
* ..38.17.55..7.3.2...69..........6.873...84...1...9.4.......96..63.4.89.2.596.7...
H8: 9                                    #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-menneske-no-06899619-base-pr-000.dot
* REASONING
* PRF # E1: 3,7 => SOL
* DIS # E2: 3,7 => CTR => E2: 4,6
* DIS # E3: 3,7 => CTR => E3: 2,4,5
* DIS # C2: 3,7 => CTR => C2: 1,4,8
* PRF # G2: 3,7 => SOL
* DIS # D6: 3,7 => CTR => D6: 2,5
* DIS # E1: 3,4 => CTR => E1: 2,6,7
* DIS # E2: 3,4 => CTR => E2: 6,7
* DIS # E3: 3,4 => CTR => E3: 2,5,7
* DIS # F3: 3,4 => CTR => F3: 2,5
* DIS # C2: 3,4 => CTR => C2: 1,7,8
* DIS # I2: 3,4 => CTR => I2: 1,6,8,9
* DIS # C7: 1,7 => CTR => C7: 2,4,8
* PRF # C2: 1,7 => SOL
* PRF # D7: 1,5 => SOL
* DIS # D7: 2,3 => CTR => D7: 1,5
* DIS # E7: 1,5 => CTR => E7: 2,3
* DIS # E4: 1,5 => CTR => E4: 2,3,4,9
* DIS # H8: 5,7 => CTR => H8: 9
* CNT  19 HDP CHAINS /  38 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C8,D2,E8,F2,H7)
* ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7...
* PAIR D2: 3,7 BLK 2
E1: 3,7,2,4,6                            # reduction candidate for 3,7
E1: 3,7 => SOLVED
* 243871965591364728786952143925146387364785219178293456812539674637418592459627831
* DURATION: 0:00:02.586193  START: 06:33:14.620912  END: 06:33:17.207105 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-menneske-no-06899619-base-pr-001.dot
* REASONING
* PRF # E1: 3,7 => SOL
* STA E1: 3,7
* CNT   1 HDP CHAINS /   1 HYP OPENED

Header Info

http://www.menneske.no/sudoku/utskrift.html?number=6899619
umulig

* PAIR REDUCTION ..
* ROUND 1: ...8.1..55......2...69..........6.873...8....1.....4.......96..63.4.8..2.596.7...
D2: 3,7
E1: 2,3,4,6,7                            # reduction candidate for 3,7
E1: 3,7 => SOLVED
* 243871965591364728786952143925146387364785219178293456812539674637418592459627831
* SOLVED!

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

C2 = 1,7 => SOL

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

Solution

position: 243871965591364728786952143925146387364785219178293456812539674637418592459627831 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:

* PRF # E1: 3,7 => SOL
* INC # E1: 2,4,6 => UNS
* DIS # E2: 3,7 => CTR => E2: 4,6
* INC # E2: 4,6 => UNS
* DIS # E3: 3,7 => CTR => E3: 2,4,5
* INC # E3: 2,4,5 => UNS
* DIS # C2: 3,7 => CTR => C2: 1,4,8
* INC # C2: 1,4,8 => UNS
* PRF # G2: 3,7 => SOL
* INC # G2: 1,8,9 => UNS
* DIS # D6: 3,7 => CTR => D6: 2,5
* INC # D6: 2,5 => UNS
* DIS # E1: 3,4 => CTR => E1: 2,6,7
* INC # E1: 2,6,7 => UNS
* DIS # E2: 3,4 => CTR => E2: 6,7
* INC # E2: 6,7 => UNS
* DIS # E3: 3,4 => CTR => E3: 2,5,7
* INC # E3: 2,5,7 => UNS
* DIS # F3: 3,4 => CTR => F3: 2,5
* INC # F3: 2,5 => UNS
* DIS # C2: 3,4 => CTR => C2: 1,7,8
* INC # C2: 1,7,8 => UNS
* DIS # I2: 3,4 => CTR => I2: 1,6,8,9
* INC # I2: 1,6,8,9 => UNS
* INC # B7: 1,7 => UNS
* DIS # C7: 1,7 => CTR => C7: 2,4,8
* INC # C7: 2,4,8 => UNS
* PRF # C2: 1,7 => SOL
* INC # C2: 3,4,8 => UNS
* PRF # D7: 1,5 => SOL
* DIS # D7: 2,3 => CTR => D7: 1,5
* DIS # E7: 1,5 => CTR => E7: 2,3
* INC # E7: 2,3 => UNS
* DIS # E4: 1,5 => CTR => E4: 2,3,4,9
* INC # E4: 2,3,4,9 => UNS
* INC # G8: 5,7 => UNS
* DIS # H8: 5,7 => CTR => H8: 9
* INC # H8: 9 => UNS
* CNT  38 HDP CHAINS /  38 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* PRF # E1: 3,7 => SOL
* STA E1: 3,7
* CNT   1 HDP CHAINS /   1 HYP OPENED