Analysis of zz-www.sudokuwiki.org-0008-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=8

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=8

position: .1...9.4...3...5..9....38..5..1...3....652....6...8..7..8.....3..6...4...2.4...6. initial

Autosolve

position: .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I2: 2,6 => CTR => I2: 1,9
* DIS # I3: 2,6 => CTR => I3: 1
* PRF # E1: 2,6 => SOL
* DIS # H5: 1,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* DIS # I5: 1,9 => CTR => I5: 4,8
* PRF # G6: 1,9 => SOL
* DIS # G6: 2 => CTR => G6: 1,9
* DIS # C5: 1,9 => CTR => C5: 4,7
* DIS # G7: 1,9 => CTR => G7: 2,7
* DIS # G9: 1,9 => CTR => G9: 7
* CNT  11 HDP CHAINS /  27 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 # I2: 2,6 => CTR => I2: 1,9
* DIS I2: 1,9 # I3: 2,6 => CTR => I3: 1
* DIS I2: 1,9 + I3: 1 # H5: 1,9 => CTR => H5: 8
* PRF I2: 1,9 + I3: 1 + H5: 8 => SOL
* STA I2: 1,9 + I3: 1 + H5: 8
* CNT   4 HDP CHAINS /   9 HYP OPENED

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

Details

Positions

.1...9.4...3...5..9....38..5..1...3....652....6...8..7..8.....3..6...4...2.4...6. initial
.1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6. autosolve
815729346673814529942563871584197632397652184261348957458976213736281495129435768 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
I1: 2,6
F4: 4,7
D6: 3,9
G5: 1,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,G6: 2.. / I4 = 2  =>  0 pairs (*) / G6 = 2  =>  0 pairs (X)
C4,I4: 2.. / C4 = 2  =>  0 pairs (X) / I4 = 2  =>  0 pairs (_)
G6,G7: 2.. / G6 = 2  =>  0 pairs (X) / G7 = 2  =>  0 pairs (_)
A5,B5: 3.. / A5 = 3  =>  0 pairs (*) / B5 = 3  =>  0 pairs (X)
D6,E6: 3.. / D6 = 3  =>  4 pairs (_) / E6 = 3  =>  9 pairs (_)
A9,E9: 3.. / A9 = 3  =>  5 pairs (_) / E9 = 3  =>  0 pairs (*)
B5,B8: 3.. / B5 = 3  =>  4 pairs (_) / B8 = 3  =>  0 pairs (*)
D6,D8: 3.. / D6 = 3  =>  4 pairs (_) / D8 = 3  =>  9 pairs (_)
I4,I5: 4.. / I4 = 4  =>  0 pairs (X) / I5 = 4  =>  4 pairs (_)
A7,B7: 4.. / A7 = 4  =>  5 pairs (_) / B7 = 4  =>  0 pairs (X)
F2,F4: 4.. / F2 = 4  => 10 pairs (_) / F4 = 4  =>  7 pairs (_)
D1,D3: 5.. / D1 = 5  =>  6 pairs (_) / D3 = 5  =>  5 pairs (_)
I8,I9: 5.. / I8 = 5  =>  5 pairs (_) / I9 = 5  =>  7 pairs (_)
C1,D1: 5.. / C1 = 5  =>  5 pairs (_) / D1 = 5  =>  6 pairs (_)
B7,F7: 5.. / B7 = 5  =>  6 pairs (_) / F7 = 5  =>  0 pairs (X)
A1,A2: 6.. / A1 = 6  =>  0 pairs (X) / A2 = 6  =>  6 pairs (_)
E7,F7: 6.. / E7 = 6  =>  0 pairs (X) / F7 = 6  =>  6 pairs (_)
E3,I3: 6.. / E3 = 6  => 10 pairs (_) / I3 = 6  =>  0 pairs (X)
F2,F7: 6.. / F2 = 6  =>  0 pairs (X) / F7 = 6  =>  6 pairs (_)
H2,H3: 7.. / H2 = 7  =>  7 pairs (_) / H3 = 7  =>  9 pairs (_)
E4,F4: 7.. / E4 = 7  =>  7 pairs (_) / F4 = 7  => 10 pairs (_)
G7,G9: 7.. / G7 = 7  =>  0 pairs (X) / G9 = 7  =>  6 pairs (_)
B4,I4: 8.. / B4 = 8  =>  0 pairs (*) / I4 = 8  =>  0 pairs (X)
E9,I9: 8.. / E9 = 8  =>  5 pairs (_) / I9 = 8  =>  0 pairs (*)
H5,H8: 8.. / H5 = 8  =>  0 pairs (*) / H8 = 8  =>  0 pairs (X)
H2,I2: 9.. / H2 = 9  =>  0 pairs (X) / I2 = 9  =>  4 pairs (_)
* DURATION: 0:00:37.664623  START: 03:29:36.992560  END: 03:30:14.657183 2017-05-01
* CP COUNT: (26)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,F4,G5,I1)
* .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6.
* PAIR I1: 2,6 BLK 3
I2: 2,6,1,9                              # reduction candidate for 2,6
I2: 2,6 => CTR
* .1758934..83...59.9452638715.21..63....652...16...8257458..6..3.96...4...214...6.
I2: 1,9                                  #  5 pairs
I3: 2,6,1                                # reduction candidate for 2,6
I3: 2,6 => CTR
* 2158793466832.45799745638125.21.7638837652194.6..38257..8..6923..6.2.48.32.48.76.
I3: 1                                    # 10 pairs
* PAIR I1: 2,6 ROW 1
A1: 2,6,7,8                              # reduction candidate for 2,6
A1: 2,6                                  #  9 pairs
E1: 2,6,7,8                              # reduction candidate for 2,6
E1: 2,6 => SOLVED
* 815729346673814529942563871584197632397652184261348957458976213736281495129435768
E1: 7,8                                  #  6 pairs
* PAIR F4: 4,7 BLK 5
E4: 4,7,9                                # reduction candidate for 4,7
E4: 9                                    # 21 pairs
E4: 4,7                                  #  9 pairs
* PAIR F4: 4,7 COL F
F2: 4,7,1,6                              # reduction candidate for 4,7
F2: 4,7                                  # 10 pairs
F2: 1,6                                  #  9 pairs
* PAIR D6: 3,9 BLK 5
E6: 3,9,4                                # reduction candidate for 3,9
E6: 4                                    # 21 pairs
E6: 3,9                                  #  9 pairs
* PAIR D6: 3,9 COL D
D8: 3,9,2,7,8                            # reduction candidate for 3,9
D8: 3,9                                  #  6 pairs
D8: 2,7,8                                #  5 pairs
* PAIR G5: 1,9 BLK 6
H5: 1,9,8                                # reduction candidate for 1,9
H5: 1,9 => CTR
* 2158793466832145799745638..592147638837652..4461..8257..8..6..3..6...48.32948.76.
H5: 8 => SOLVED
* 815729346673814529942563871584197632397652184261348957458976213736281495129435768
I5: 1,9,4,8                              # reduction candidate for 1,9
I5: 1,9 => CTR
* .15..934..73..45..94...387.582197634..7652.8.169348257.58..6..3.96..1425.214.5.68
I5: 4,8                                  #  5 pairs
G6: 1,9,2                                # reduction candidate for 1,9
G6: 1,9 => SOLVED
* 815729346673814529942563871584197632397652184261348957458976213736281495129435768
G6: 2 => CTR
* 2158793466832145799745638..592147638837652..4461..8257..8..6..3..6...48.32948.76.
* PAIR G5: 1,9 ROW 5
C5: 1,9,4,7                              # reduction candidate for 1,9
C5: 1,9 => CTR
* 81...93466.3...5.99...638.158.1..632...652.8426...8.57458..62.3.96...41.12.4..76.
C5: 4,7                                  #  5 pairs
* PAIR G5: 1,9 COL G
G7: 1,9,2,7                              # reduction candidate for 1,9
G7: 1,9 => CTR
* 2158793466832.45799745638..592147638837652..4461..8257.48.....3..6...48.32948.76.
G7: 2,7                                  #  5 pairs
G9: 1,9,7                                # reduction candidate for 1,9
G9: 1,9 => CTR
* .1587934..832..5799745.38..5.21.7638837652..4.6...8257..89..7.3.96...48..2.48..6.
G9: 7                                    #  6 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0008-base-pr-000.dot
* REASONING
* DIS # I2: 2,6 => CTR => I2: 1,9
* DIS # I3: 2,6 => CTR => I3: 1
* PRF # E1: 2,6 => SOL
* DIS # H5: 1,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* DIS # I5: 1,9 => CTR => I5: 4,8
* PRF # G6: 1,9 => SOL
* DIS # G6: 2 => CTR => G6: 1,9
* DIS # C5: 1,9 => CTR => C5: 4,7
* DIS # G7: 1,9 => CTR => G7: 2,7
* DIS # G9: 1,9 => CTR => G9: 7
* CNT  11 HDP CHAINS /  27 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D6,F4,G5,I1)
* .1...934...3...5..9....38..5..1..63....652....6...8.57..8.....3..6...4...2.4...6.
* PAIR I1: 2,6 BLK 3
I2: 2,6,1,9                              # reduction candidate for 2,6
I2: 2,6 => CTR
* .1758934..83...59.9452638715.21..63....652...16...8257458..6..3.96...4...214...6.
I3: 2,6,1                                # reduction candidate for 2,6
I3: 2,6 => CTR
* 2158793466832.45799745638125.21.7638837652194.6..38257..8..6923..6.2.48.32.48.76.
* PAIR F4: 4,7 BLK 5
E4: 4,7,9                                # reduction candidate for 4,7
E4: 9                                    # 23 pairs
E4: 4,7                                  # 18 pairs
* PAIR D6: 3,9 BLK 5
E6: 3,9,4                                # reduction candidate for 3,9
E6: 4                                    # 23 pairs
E6: 3,9                                  # 18 pairs
* PAIR D6: 3,9 COL D
D8: 3,9,2,7,8                            # reduction candidate for 3,9
D8: 2,7,8                                # 17 pairs
D8: 3,9                                  # 16 pairs
* PAIR G5: 1,9 BLK 6
H5: 1,9,8                                # reduction candidate for 1,9
H5: 1,9 => CTR
* .1...93466.3...5.99...638.15.21..63..3.652...16...8257458..6..3796315482321487965
H5: 8 => SOLVED
* 815729346673814529942563871584197632397652184261348957458976213736281495129435768
* DURATION: 0:00:09.965329  START: 03:30:37.704778  END: 03:30:47.670107 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0008-base-pr-001.dot
* REASONING
* DIS # I2: 2,6 => CTR => I2: 1,9
* DIS I2: 1,9 # I3: 2,6 => CTR => I3: 1
* DIS I2: 1,9 + I3: 1 # H5: 1,9 => CTR => H5: 8
* PRF I2: 1,9 + I3: 1 + H5: 8 => SOL
* STA I2: 1,9 + I3: 1 + H5: 8
* CNT   4 HDP CHAINS /   9 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=8

Solution

position: 815729346673814529942563871584197632397652184261348957458976213736281495129435768 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 # I2: 2,6 => CTR => I2: 1,9
* INC # I2: 1,9 => UNS
* DIS # I3: 2,6 => CTR => I3: 1
* INC # I3: 1 => UNS
* INC # A1: 2,6 => UNS
* PRF # E1: 2,6 => SOL
* INC # E1: 7,8 => UNS
* INC # E4: 4,7 => UNS
* INC # E4: 9 => UNS
* INC # F2: 4,7 => UNS
* INC # F2: 1,6 => UNS
* INC # E6: 3,9 => UNS
* INC # E6: 4 => UNS
* INC # D8: 3,9 => UNS
* INC # D8: 2,7,8 => UNS
* DIS # H5: 1,9 => CTR => H5: 8
* PRF # H5: 8 => SOL
* DIS # I5: 1,9 => CTR => I5: 4,8
* INC # I5: 4,8 => UNS
* PRF # G6: 1,9 => SOL
* DIS # G6: 2 => CTR => G6: 1,9
* DIS # C5: 1,9 => CTR => C5: 4,7
* INC # C5: 4,7 => UNS
* DIS # G7: 1,9 => CTR => G7: 2,7
* INC # G7: 2,7 => UNS
* DIS # G9: 1,9 => CTR => G9: 7
* INC # G9: 7 => UNS
* CNT  27 HDP CHAINS /  27 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # I2: 2,6 => CTR => I2: 1,9
* DIS I2: 1,9 # I3: 2,6 => CTR => I3: 1
* INC I2: 1,9 + I3: 1 # E4: 4,7 => UNS
* INC I2: 1,9 + I3: 1 # E4: 9 => UNS
* INC I2: 1,9 + I3: 1 # E6: 3,9 => UNS
* INC I2: 1,9 + I3: 1 # E6: 4 => UNS
* INC I2: 1,9 + I3: 1 # D8: 3,9 => UNS
* INC I2: 1,9 + I3: 1 # D8: 2,7,8 => UNS
* DIS I2: 1,9 + I3: 1 # H5: 1,9 => CTR => H5: 8
* PRF I2: 1,9 + I3: 1 + H5: 8 => SOL
* STA I2: 1,9 + I3: 1 + H5: 8
* CNT  10 HDP CHAINS /   9 HYP OPENED