Analysis of zz-www.sudokuwiki.org-0268-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=268

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=268

position: 1....4....34.6....6..7.2..4..6.5..4....6.8....2..4.9..5..4.6..7....9.16....3....2 initial

Autosolve

position: 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H1: 3,8 => CTR => H1: 2,5,7
* PRF # F4: 3,7 => SOL
* DIS # C6: 3,7 => CTR => C6: 5,8
* DIS # H7: 3,8 => CTR => H7: 9
* CNT   4 HDP CHAINS /  22 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 # H1: 3,8 => CTR => H1: 2,5,7
* PRF H1: 2,5,7 # F4: 3,7 => SOL
* STA H1: 2,5,7 + F4: 3,7
* CNT   2 HDP CHAINS /  13 HYP OPENED

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

Details

Positions

1....4....34.6....6..7.2..4..6.5..4....6.8....2..4.9..5..4.6..7....9.16....3....2 initial
1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2 autosolve
187534629234869715659712834876953241491628573325147986512486397743295168968371452 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
E1: 3,8
D4: 2,9
E5: 2,7
F6: 3,7
F8: 5,7
G7: 3,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,E3: 1.. / F2 = 1  => 10 pairs (_) / E3 = 1  => 13 pairs (_)
E3,H3: 1.. / E3 = 1  => 13 pairs (_) / H3 = 1  => 10 pairs (_)
B4,I4: 1.. / B4 = 1  => 11 pairs (_) / I4 = 1  => 12 pairs (_)
F2,F9: 1.. / F2 = 1  => 10 pairs (_) / F9 = 1  => 13 pairs (_)
C1,A2: 2.. / C1 = 2  => 14 pairs (_) / A2 = 2  =>  6 pairs (_)
D4,E5: 2.. / D4 = 2  =>  7 pairs (_) / E5 = 2  =>  0 pairs (*)
E7,D8: 2.. / E7 = 2  =>  7 pairs (_) / D8 = 2  =>  0 pairs (*)
C1,H1: 2.. / C1 = 2  => 14 pairs (_) / H1 = 2  =>  6 pairs (_)
D4,G4: 2.. / D4 = 2  =>  7 pairs (_) / G4 = 2  =>  0 pairs (*)
C7,E7: 2.. / C7 = 2  =>  0 pairs (*) / E7 = 2  =>  0 pairs (X)
A2,A8: 2.. / A2 = 2  =>  6 pairs (_) / A8 = 2  => 14 pairs (_)
D4,D8: 2.. / D4 = 2  =>  7 pairs (_) / D8 = 2  =>  0 pairs (*)
E5,E7: 2.. / E5 = 2  =>  0 pairs (*) / E7 = 2  =>  0 pairs (X)
E1,E3: 3.. / E1 = 3  =>  6 pairs (_) / E3 = 3  => 10 pairs (_)
F4,F6: 3.. / F4 = 3  =>  0 pairs (*) / F6 = 3  =>  0 pairs (X)
A5,B5: 4.. / A5 = 4  =>  8 pairs (_) / B5 = 4  => 11 pairs (_)
A8,B8: 4.. / A8 = 4  => 11 pairs (_) / B8 = 4  =>  8 pairs (_)
A5,A8: 4.. / A5 = 4  =>  8 pairs (_) / A8 = 4  => 11 pairs (_)
B5,B8: 4.. / B5 = 4  => 11 pairs (_) / B8 = 4  =>  8 pairs (_)
I8,H9: 5.. / I8 = 5  => 19 pairs (_) / H9 = 5  => 10 pairs (_)
C6,H6: 5.. / C6 = 5  =>  7 pairs (_) / H6 = 5  =>  0 pairs (X)
F9,H9: 5.. / F9 = 5  => 19 pairs (_) / H9 = 5  => 10 pairs (_)
E5,E9: 7.. / E5 = 7  =>  7 pairs (_) / E9 = 7  =>  0 pairs (*)
B3,C3: 9.. / B3 = 9  =>  8 pairs (_) / C3 = 9  =>  9 pairs (_)
I1,I2: 9.. / I1 = 9  =>  7 pairs (_) / I2 = 9  =>  8 pairs (_)
D4,F4: 9.. / D4 = 9  =>  0 pairs (*) / F4 = 9  =>  0 pairs (X)
H7,H9: 9.. / H7 = 9  =>  8 pairs (_) / H9 = 9  =>  0 pairs (X)
D1,I1: 9.. / D1 = 9  =>  8 pairs (_) / I1 = 9  =>  7 pairs (_)
A5,A9: 9.. / A5 = 9  => 15 pairs (_) / A9 = 9  =>  8 pairs (_)
F2,F4: 9.. / F2 = 9  =>  0 pairs (*) / F4 = 9  =>  0 pairs (X)
* DURATION: 0:00:30.414139  START: 14:14:16.397546  END: 14:14:46.811685 2019-04-28
* CP COUNT: (30)
* SOLUTION FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E1,E5,F6,F8,G7)
* 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2
* PAIR E1: 3,8 BLK 2
E3: 3,8,1                                # reduction candidate for 3,8
E3: 1                                    # 13 pairs
E3: 3,8                                  # 10 pairs
* PAIR E1: 3,8 ROW 1
H1: 3,8,2,5,7                            # reduction candidate for 3,8
H1: 3,8 => CTR
* 172..463.834.6127.6..7328143.625974.4..6785237251439865..42639724389716596.31.4.2
H1: 2,5,7                                #  6 pairs
I1: 3,8,5,9                              # reduction candidate for 3,8
I1: 3,8                                  # 10 pairs
* PAIR E5: 2,7 ROW 5
G5: 2,7,3,5                              # reduction candidate for 2,7
G5: 2,7                                  #  7 pairs
H5: 2,7,1,3,5                            # reduction candidate for 2,7
H5: 2,7                                  # 10 pairs
* PAIR F6: 3,7 BLK 5
F4: 3,7,9                                # reduction candidate for 3,7
F4: 3,7 => SOLVED
* 187534629234869715659712834876953241491628573325147986512486397743295168968371452
F4: 9                                    #  7 pairs
* PAIR F6: 3,7 ROW 6
A6: 3,7,8                                # reduction candidate for 3,7
A6: 3,7                                  #  9 pairs
C6: 3,7,5,8                              # reduction candidate for 3,7
C6: 3,7 => CTR
* 17...46..234.61.7.6..7.2.1431625974894.678...8271439565..426..7...89716576.3154.2
C6: 5,8                                  #  7 pairs
H6: 3,7,5,8                              # reduction candidate for 3,7
H6: 3,7                                  # 12 pairs
* PAIR F8: 5,7 BLK 8
F9: 5,7,1                                # reduction candidate for 5,7
F9: 1                                    # 13 pairs
F9: 5,7                                  # 10 pairs
* PAIR G7: 3,8 BLK 9
H7: 3,8,9                                # reduction candidate for 3,8
H7: 3,8 => CTR
* 1....46..234.61...6..7.2.14..6.59.4.94.6.8....2.1439.65..4.6..74.329.165.6.3.5492
H7: 9                                    #  8 pairs
I8: 3,8,5                                # reduction candidate for 3,8
I8: 3,8                                  # 10 pairs
* PAIR G7: 3,8 ROW 7
C7: 3,8,1,2,9                            # reduction candidate for 3,8
C7: 3,8                                  # 16 pairs
C7: 1,2,9                                #  7 pairs
* PAIR G7: 3,8 COL G
G3: 3,8,5                                # reduction candidate for 3,8
G3: 3,8                                  #  8 pairs
G4: 3,8,2,7                              # reduction candidate for 3,8
G4: 3,8                                  # 21 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0268-base-pr-000.dot
* REASONING
* DIS # H1: 3,8 => CTR => H1: 2,5,7
* PRF # F4: 3,7 => SOL
* DIS # C6: 3,7 => CTR => C6: 5,8
* DIS # H7: 3,8 => CTR => H7: 9
* CNT   4 HDP CHAINS /  22 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (D4,E1,E5,F6,F8,G7)
* 1....46...34.6....6..7.2..4..6.5..4....6.8....2.14.9.65..4.6..7....9.16..6.3..4.2
* PAIR E1: 3,8 BLK 2
E3: 3,8,1                                # reduction candidate for 3,8
E3: 1                                    # 13 pairs
E3: 3,8                                  # 10 pairs
* PAIR E1: 3,8 ROW 1
H1: 3,8,2,5,7                            # reduction candidate for 3,8
H1: 3,8 => CTR
* 172..463.834.6127.6..7328143.625974.4..6785237251439865..42639724389716596.31.4.2
I1: 3,8,5,9                              # reduction candidate for 3,8
I1: 3,8                                  # 10 pairs
* RESTART
* PAIR E1: 3,8 ROW 1
I1: 3,8,5,9                              # reduction candidate for 3,8
I1: 3,8                                  # 10 pairs
I1: 5,9                                  #  7 pairs
* PAIR RESTART
* PAIR E1: 3,8 BLK 2
E3: 3,8,1                                # reduction candidate for 3,8
E3: 1                                    # 14 pairs
E3: 3,8                                  # 10 pairs
* PAIR E1: 3,8 ROW 1
I1: 3,8,5,9                              # reduction candidate for 3,8
I1: 3,8                                  # 10 pairs
I1: 5,9                                  #  7 pairs
* PAIR E5: 2,7 ROW 5
G5: 2,7,3,5                              # reduction candidate for 2,7
G5: 2,7                                  #  8 pairs
H5: 2,7,1,3,5                            # reduction candidate for 2,7
H5: 2,7                                  # 10 pairs
* PAIR F6: 3,7 BLK 5
F4: 3,7,9                                # reduction candidate for 3,7
F4: 3,7 => SOLVED
* 187534629234869715659712834876953241491628573325147986512486397743295168968371452
* DURATION: 0:00:08.098779  START: 14:14:58.963248  END: 14:15:07.062027 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0268-base-pr-001.dot
* REASONING
* DIS # H1: 3,8 => CTR => H1: 2,5,7
* PRF H1: 2,5,7 # F4: 3,7 => SOL
* STA H1: 2,5,7 + F4: 3,7
* CNT   2 HDP CHAINS /  13 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=268

Solution

position: 187534629234869715659712834876953241491628573325147986512486397743295168968371452 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 # E3: 3,8 => UNS
* INC # E3: 1 => UNS
* DIS # H1: 3,8 => CTR => H1: 2,5,7
* INC # H1: 2,5,7 => UNS
* INC # I1: 3,8 => UNS
* INC # G5: 2,7 => UNS
* INC # H5: 2,7 => UNS
* PRF # F4: 3,7 => SOL
* INC # F4: 9 => UNS
* INC # A6: 3,7 => UNS
* DIS # C6: 3,7 => CTR => C6: 5,8
* INC # C6: 5,8 => UNS
* INC # H6: 3,7 => UNS
* INC # F9: 5,7 => UNS
* INC # F9: 1 => UNS
* DIS # H7: 3,8 => CTR => H7: 9
* INC # H7: 9 => UNS
* INC # I8: 3,8 => UNS
* INC # C7: 3,8 => UNS
* INC # C7: 1,2,9 => UNS
* INC # G3: 3,8 => UNS
* INC # G4: 3,8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 3,8 => UNS
* INC # E3: 1 => UNS
* DIS # H1: 3,8 => CTR => H1: 2,5,7
* INC H1: 2,5,7 # I1: 3,8 => UNS
* INC H1: 2,5,7 # I1: 3,8 => UNS
* INC H1: 2,5,7 # I1: 5,9 => UNS
* INC H1: 2,5,7 # E3: 3,8 => UNS
* INC H1: 2,5,7 # E3: 1 => UNS
* INC H1: 2,5,7 # I1: 3,8 => UNS
* INC H1: 2,5,7 # I1: 5,9 => UNS
* INC H1: 2,5,7 # G5: 2,7 => UNS
* INC H1: 2,5,7 # H5: 2,7 => UNS
* PRF H1: 2,5,7 # F4: 3,7 => SOL
* STA H1: 2,5,7 + F4: 3,7
* CNT  13 HDP CHAINS /  13 HYP OPENED