Analysis of zz-www.sudokuwiki.org-0040-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=40

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=40

position: .7...6.8..9.4...7...2...1.....2..9..5...1...6..4..8.......7.5...8...9.2..6.5...9. initial

Autosolve

position: .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A1: 1,3 => CTR => A1: 4
* PRF # C2: 1,3 => SOL
* PRF # D3: 3,7 => SOL
* DIS # F4: 3,7 => CTR => F4: 4,5
* DIS # B6: 2 => CTR => B6: 1,3
* DIS # G5: 2,3 => CTR => G5: 4,7,8
* PRF # G5: 3,4 => SOL
* PRF # F5: 7 => SOL
* CNT   8 HDP CHAINS /  30 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 # A1: 1,3 => CTR => A1: 4
* PRF A1: 4 # C2: 1,3 => SOL
* STA A1: 4 + C2: 1,3
* CNT   2 HDP CHAINS /   3 HYP OPENED

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

Details

Positions

.7...6.8..9.4...7...2...1.....2..9..5...1...6..4..8.......7.5...8...9.2..6.5...9. initial
.7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9. autosolve
473196285891425673652783149736254918528917436914368752349872561185649327267531894 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
C1: 1,3
F3: 3,7
B4: 1,3
B5: 2,3
H5: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,F2: 1.. / D1 = 1  => 13 pairs (_) / F2 = 1  =>  9 pairs (_)
B4,B6: 1.. / B4 = 1  =>  5 pairs (_) / B6 = 1  =>  4 pairs (_)
B5,B6: 2.. / B5 = 2  =>  5 pairs (_) / B6 = 2  =>  0 pairs (X)
A7,A9: 2.. / A7 = 2  => 13 pairs (_) / A9 = 2  =>  5 pairs (_)
B5,G5: 2.. / B5 = 2  =>  5 pairs (_) / G5 = 2  =>  0 pairs (X)
A7,F7: 2.. / A7 = 2  => 13 pairs (_) / F7 = 2  =>  5 pairs (_)
A1,A3: 4.. / A1 = 4  =>  6 pairs (_) / A3 = 4  =>  0 pairs (X)
I1,I2: 5.. / I1 = 5  => 12 pairs (_) / I2 = 5  =>  6 pairs (_)
H4,H6: 5.. / H4 = 5  =>  0 pairs (X) / H6 = 5  =>  5 pairs (_)
E1,I1: 5.. / E1 = 5  =>  6 pairs (_) / I1 = 5  => 12 pairs (_)
E6,H6: 5.. / E6 = 5  =>  0 pairs (X) / H6 = 5  =>  5 pairs (_)
F2,F4: 5.. / F2 = 5  =>  0 pairs (*) / F4 = 5  =>  0 pairs (X)
G2,H3: 6.. / G2 = 6  => 11 pairs (_) / H3 = 6  => 22 pairs (_)
H7,G8: 6.. / H7 = 6  => 11 pairs (_) / G8 = 6  => 22 pairs (_)
A3,H3: 6.. / A3 = 6  => 11 pairs (_) / H3 = 6  => 22 pairs (_)
D7,H7: 6.. / D7 = 6  => 22 pairs (_) / H7 = 6  => 11 pairs (_)
C2,C4: 6.. / C2 = 6  => 20 pairs (_) / C4 = 6  =>  7 pairs (_)
G2,G8: 6.. / G2 = 6  => 11 pairs (_) / G8 = 6  => 22 pairs (_)
H3,H7: 6.. / H3 = 6  => 22 pairs (_) / H7 = 6  => 11 pairs (_)
D3,F3: 7.. / D3 = 7  =>  0 pairs (*) / F3 = 7  =>  0 pairs (X)
I4,G5: 8.. / I4 = 8  =>  0 pairs (*) / G5 = 8  =>  0 pairs (X)
D7,E9: 8.. / D7 = 8  => 12 pairs (_) / E9 = 8  => 10 pairs (_)
C5,G5: 8.. / C5 = 8  =>  0 pairs (*) / G5 = 8  =>  0 pairs (X)
D7,I7: 8.. / D7 = 8  => 12 pairs (_) / I7 = 8  => 10 pairs (_)
D3,D7: 8.. / D3 = 8  => 10 pairs (_) / D7 = 8  => 12 pairs (_)
G5,G9: 8.. / G5 = 8  =>  8 pairs (_) / G9 = 8  =>  0 pairs (*)
I1,I3: 9.. / I1 = 9  =>  9 pairs (_) / I3 = 9  => 10 pairs (_)
C5,A6: 9.. / C5 = 9  => 12 pairs (_) / A6 = 9  => 12 pairs (_)
A7,C7: 9.. / A7 = 9  => 12 pairs (_) / C7 = 9  => 12 pairs (_)
C5,D5: 9.. / C5 = 9  => 12 pairs (_) / D5 = 9  => 12 pairs (_)
A6,A7: 9.. / A6 = 9  => 12 pairs (_) / A7 = 9  => 12 pairs (_)
C5,C7: 9.. / C5 = 9  => 12 pairs (_) / C7 = 9  => 12 pairs (_)
* DURATION: 0:00:43.419144  START: 04:12:27.690307  END: 04:13:11.109451 2017-05-01
* CP COUNT: (32)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,C1,F3,H5)
* .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9.
* PAIR C1: 1,3 BLK 1
A1: 1,3,4                                # reduction candidate for 1,3
A1: 1,3 => CTR
* .7.9.6.8..9.4.1.7.452837169...2.59..52971.8.6..4398.5.94.6725.8.8514962.267583491
A1: 4                                    #  6 pairs
A2: 1,3,6,8                              # reduction candidate for 1,3
A2: 1,3                                  #  9 pairs
C2: 1,3,6,8                              # reduction candidate for 1,3
C2: 1,3 => SOLVED
* 473196285891425673652783149736254918528917436914368752349872561185649327267531894
C2: 6,8                                  #  6 pairs
* PAIR C1: 1,3 ROW 1
D1: 1,3,9                                # reduction candidate for 1,3
D1: 9                                    # 19 pairs
D1: 1,3                                  # 11 pairs
* PAIR C1: 1,3 COL C
C7: 1,3,9                                # reduction candidate for 1,3
C7: 1,3                                  # 12 pairs
C9: 1,3,7                                # reduction candidate for 1,3
C9: 1,3                                  # 15 pairs
* PAIR F3: 3,7 BLK 2
D3: 3,7,8,9                              # reduction candidate for 3,7
D3: 3,7 => SOLVED
* 473196285891425673652783149736254918528917436914368752349872561185649327267531894
D3: 8,9                                  #  8 pairs
* PAIR F3: 3,7 COL F
F4: 3,7,4,5                              # reduction candidate for 3,7
F4: 3,7 => CTR
* 473196285.9.425673652783149..62.79..5279148369.4..87.2.4987.561185..9.2..6.5...9.
F4: 4,5                                  #  6 pairs
F5: 3,7,4                                # reduction candidate for 3,7
F5: 3,7                                  #  8 pairs
* PAIR B4: 1,3 BLK 4
B6: 1,3,2                                # reduction candidate for 1,3
B6: 2 => CTR
* .7...6.8..9.4...7..52...1...1.2..9.8538917246924..8....4987.56..85..9.2..6.5..89.
B6: 1,3                                  #  5 pairs
* PAIR B4: 1,3 ROW 4
H4: 1,3,4,5                              # reduction candidate for 1,3
H4: 1,3                                  #  6 pairs
I4: 1,3,4,7,8                            # reduction candidate for 1,3
I4: 1,3                                  # 14 pairs
* PAIR B5: 2,3 BLK 4
B6: 2,3,1                                # reduction candidate for 2,3
B6: 2,3                                  #  5 pairs
B6: 1                                    #  4 pairs
* PAIR B5: 2,3 ROW 5
G5: 2,3,4,7,8                            # reduction candidate for 2,3
G5: 2,3 => CTR
* .7...6.8..9.4...7..52...1.....2..9.85.8917.469.4..8....4987.56..85..9.2..6.5..89.
G5: 4,7,8                                #  5 pairs
* PAIR H5: 3,4 BLK 6
H4: 3,4,1,5                              # reduction candidate for 3,4
H4: 3,4                                  # 25 pairs
I4: 3,4,1,7,8                            # reduction candidate for 3,4
I4: 3,4                                  # 15 pairs
G5: 3,4,2,7,8                            # reduction candidate for 3,4
G5: 3,4 => SOLVED
* 473196285891425673652783149736254918528917436914368752349872561185649327267531894
G5: 2,7,8                                #  5 pairs
* PAIR H5: 3,4 ROW 5
F5: 3,4,7                                # reduction candidate for 3,4
F5: 7 => SOLVED
* 473196285891425673652783149736254918528917436914368752349872561185649327267531894
F5: 3,4                                  #  8 pairs
* PAIR H5: 3,4 COL H
H3: 3,4,6                                # reduction candidate for 3,4
H3: 6                                    # 22 pairs
H3: 3,4                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0040-base-pr-000.dot
* REASONING
* DIS # A1: 1,3 => CTR => A1: 4
* PRF # C2: 1,3 => SOL
* PRF # D3: 3,7 => SOL
* DIS # F4: 3,7 => CTR => F4: 4,5
* DIS # B6: 2 => CTR => B6: 1,3
* DIS # G5: 2,3 => CTR => G5: 4,7,8
* PRF # G5: 3,4 => SOL
* PRF # F5: 7 => SOL
* CNT   8 HDP CHAINS /  30 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B4,B5,C1,F3,H5)
* .7...6.8..9.4...7..52...1.....2..9..5...1...6..4..8....4..7.5...85..9.2..6.5...9.
* PAIR C1: 1,3 BLK 1
A1: 1,3,4                                # reduction candidate for 1,3
A1: 1,3 => CTR
* .7.9.6.8..9.4.1.7.452837169...2.59..52971.8.6..4398.5.94.6725.8.8514962.267583491
A2: 1,3,6,8                              # reduction candidate for 1,3
A2: 1,3                                  #  9 pairs
C2: 1,3,6,8                              # reduction candidate for 1,3
C2: 1,3 => SOLVED
* 473196285891425673652783149736254918528917436914368752349872561185649327267531894
* DURATION: 0:00:04.177925  START: 04:13:34.793385  END: 04:13:38.971310 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0040-base-pr-001.dot
* REASONING
* DIS # A1: 1,3 => CTR => A1: 4
* PRF A1: 4 # C2: 1,3 => SOL
* STA A1: 4 + C2: 1,3
* CNT   2 HDP CHAINS /   3 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=40

Solution

position: 473196285891425673652783149736254918528917436914368752349872561185649327267531894 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 # A1: 1,3 => CTR => A1: 4
* INC # A1: 4 => UNS
* INC # A2: 1,3 => UNS
* PRF # C2: 1,3 => SOL
* INC # C2: 6,8 => UNS
* INC # D1: 1,3 => UNS
* INC # D1: 9 => UNS
* INC # C7: 1,3 => UNS
* INC # C9: 1,3 => UNS
* PRF # D3: 3,7 => SOL
* INC # D3: 8,9 => UNS
* DIS # F4: 3,7 => CTR => F4: 4,5
* INC # F4: 4,5 => UNS
* INC # F5: 3,7 => UNS
* INC # B6: 1,3 => UNS
* DIS # B6: 2 => CTR => B6: 1,3
* INC # H4: 1,3 => UNS
* INC # I4: 1,3 => UNS
* INC # B6: 2,3 => UNS
* INC # B6: 1 => UNS
* DIS # G5: 2,3 => CTR => G5: 4,7,8
* INC # G5: 4,7,8 => UNS
* INC # H4: 3,4 => UNS
* INC # I4: 3,4 => UNS
* PRF # G5: 3,4 => SOL
* INC # G5: 2,7,8 => UNS
* INC # F5: 3,4 => UNS
* PRF # F5: 7 => SOL
* INC # H3: 3,4 => UNS
* INC # H3: 6 => UNS
* CNT  30 HDP CHAINS /  30 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # A1: 1,3 => CTR => A1: 4
* INC A1: 4 # A2: 1,3 => UNS
* PRF A1: 4 # C2: 1,3 => SOL
* STA A1: 4 + C2: 1,3
* CNT   3 HDP CHAINS /   3 HYP OPENED