Analysis of zz-www.sudokuwiki.org-0052-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=52

level: hard

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=52

position: ..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......56..9..62.. initial

Autosolve

position: ..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......565.9..62.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:28.712473

The following important HDP chains were detected:

* DIS # A3: 6,9 # H1: 6,9 => CTR => H1: 4,7
* DIS # A3: 6,9 + H1: 4,7 => CTR => A3: 2
* PRF A3: 2 # C2: 3 => SOL
* STA A3: 2 + C2: 3
* CNT   3 HDP CHAINS /  30 HYP OPENED

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

Details

Positions

..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......56..9..62.. initial
..12..8..75......2..4.3...1...56..3.3..4.9..8.9..83...1...5.7..8......565.9..62.. autosolve
961245873753198462284637591418562937375419628692783145126354789847921356539876214 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
A1: 6,9
B1: 3,6
A4: 2,4
D6: 1,7
I9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B4,B5: 1.. / B4 = 1  =>  0 pairs (*) / B5 = 1  =>  0 pairs (X)
G8,H9: 1.. / G8 = 1  => 15 pairs (_) / H9 = 1  =>  9 pairs (_)
A3,B3: 2.. / A3 = 2  =>  7 pairs (_) / B3 = 2  => 22 pairs (_)
F4,E5: 2.. / F4 = 2  => 13 pairs (_) / E5 = 2  =>  7 pairs (_)
H5,H6: 2.. / H5 = 2  => 13 pairs (_) / H6 = 2  =>  6 pairs (_)
E5,E8: 2.. / E5 = 2  =>  7 pairs (_) / E8 = 2  => 13 pairs (_)
B1,C2: 3.. / B1 = 3  =>  6 pairs (_) / C2 = 3  =>  0 pairs (*)
I1,G2: 3.. / I1 = 3  =>  0 pairs (*) / G2 = 3  =>  0 pairs (X)
B1,I1: 3.. / B1 = 3  =>  6 pairs (_) / I1 = 3  =>  0 pairs (*)
C2,G2: 3.. / C2 = 3  =>  0 pairs (*) / G2 = 3  =>  0 pairs (X)
G2,G8: 3.. / G2 = 3  =>  6 pairs (_) / G8 = 3  =>  0 pairs (*)
A4,A6: 4.. / A4 = 4  =>  7 pairs (_) / A6 = 4  =>  0 pairs (X)
F1,F3: 5.. / F1 = 5  =>  7 pairs (_) / F3 = 5  => 11 pairs (_)
I1,G3: 5.. / I1 = 5  => 11 pairs (_) / G3 = 5  =>  7 pairs (_)
C5,C6: 5.. / C5 = 5  =>  6 pairs (_) / C6 = 5  => 11 pairs (_)
F1,I1: 5.. / F1 = 5  =>  7 pairs (_) / I1 = 5  => 11 pairs (_)
F3,G3: 5.. / F3 = 5  => 11 pairs (_) / G3 = 5  =>  7 pairs (_)
C5,G5: 5.. / C5 = 5  =>  6 pairs (_) / G5 = 5  => 11 pairs (_)
I1,I6: 5.. / I1 = 5  => 11 pairs (_) / I6 = 5  =>  7 pairs (_)
D2,D3: 6.. / D2 = 6  =>  7 pairs (_) / D3 = 6  =>  9 pairs (_)
B7,C7: 6.. / B7 = 6  =>  8 pairs (_) / C7 = 6  =>  6 pairs (_)
C2,B3: 8.. / C2 = 8  => 11 pairs (_) / B3 = 8  =>  8 pairs (_)
B4,C4: 8.. / B4 = 8  => 11 pairs (_) / C4 = 8  =>  8 pairs (_)
H7,H9: 8.. / H7 = 8  =>  9 pairs (_) / H9 = 8  => 15 pairs (_)
D9,H9: 8.. / D9 = 8  =>  9 pairs (_) / H9 = 8  => 15 pairs (_)
B3,B4: 8.. / B3 = 8  =>  8 pairs (_) / B4 = 8  => 11 pairs (_)
C2,C4: 8.. / C2 = 8  => 11 pairs (_) / C4 = 8  =>  8 pairs (_)
A1,A3: 9.. / A1 = 9  =>  6 pairs (_) / A3 = 9  =>  0 pairs (X)
G4,I4: 9.. / G4 = 9  =>  8 pairs (_) / I4 = 9  => 13 pairs (_)
* DURATION: 0:00:34.062659  START: 18:31:21.091504  END: 18:31:55.154163 2017-04-30
* CP COUNT: (29)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:28.463482  START: 18:32:22.898077  END: 18:32:51.361559 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0052-base-pr-002.dot
* REASONING
* DIS # A3: 6,9 # H1: 6,9 => CTR => H1: 4,7
* DIS # A3: 6,9 + H1: 4,7 => CTR => A3: 2
* PRF A3: 2 # C2: 3 => SOL
* STA A3: 2 + C2: 3
* CNT   3 HDP CHAINS /  30 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=52

Solution

position: 961245873753198462284637591418562937375419628692783145126354789847921356539876214 solved
Solution

See section Deep 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 # A3: 6,9 => UNS
* INC # A3: 2 => UNS
* INC # H1: 6,9 => UNS
* INC # H1: 4,7 => UNS
* INC # C2: 3,6 => UNS
* INC # C2: 8 => UNS
* INC # B7: 3,6 => UNS
* INC # B7: 2,4 => UNS
* INC # A6: 2,4 => UNS
* INC # A6: 6 => UNS
* INC # F4: 1,7 => UNS
* INC # E5: 1,7 => UNS
* INC # H6: 1,7 => UNS
* INC # H6: 2,4,6 => UNS
* INC # D8: 1,7 => UNS
* INC # D9: 1,7 => UNS
* INC # I7: 3,4 => UNS
* INC # G8: 3,4 => UNS
* INC # B9: 3,4 => UNS
* INC # B9: 7 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 5,7,9 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 6,9 => UNS
* INC # A3: 2 => UNS
* INC # H1: 6,9 => UNS
* INC # H1: 4,7 => UNS
* INC # C2: 3,6 => UNS
* INC # C2: 8 => UNS
* INC # B7: 3,6 => UNS
* INC # B7: 2,4 => UNS
* INC # A6: 2,4 => UNS
* INC # A6: 6 => UNS
* INC # F4: 1,7 => UNS
* INC # E5: 1,7 => UNS
* INC # H6: 1,7 => UNS
* INC # H6: 2,4,6 => UNS
* INC # D8: 1,7 => UNS
* INC # D9: 1,7 => UNS
* INC # I7: 3,4 => UNS
* INC # G8: 3,4 => UNS
* INC # B9: 3,4 => UNS
* INC # B9: 7 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 5,7,9 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 6,9 => UNS
* INC # A3: 2 => UNS
* INC # H1: 6,9 => UNS
* INC # H1: 4,7 => UNS
* INC # C2: 3,6 => UNS
* INC # C2: 8 => UNS
* INC # B7: 3,6 => UNS
* INC # B7: 2,4 => UNS
* INC # A6: 2,4 => UNS
* INC # A6: 6 => UNS
* INC # F4: 1,7 => UNS
* INC # E5: 1,7 => UNS
* INC # H6: 1,7 => UNS
* INC # H6: 2,4,6 => UNS
* INC # D8: 1,7 => UNS
* INC # D9: 1,7 => UNS
* INC # I7: 3,4 => UNS
* INC # G8: 3,4 => UNS
* INC # B9: 3,4 => UNS
* INC # B9: 7 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 5,7,9 => UNS
* DIS # A3: 6,9 # H1: 6,9 => CTR => H1: 4,7
* DIS # A3: 6,9 + H1: 4,7 => CTR => A3: 2
* INC A3: 2 # C2: 3,6 => UNS
* INC A3: 2 # C2: 8 => UNS
* INC A3: 2 # B7: 3,6 => UNS
* INC A3: 2 # B7: 2,4 => UNS
* INC A3: 2 # C2: 6,8 => UNS
* PRF A3: 2 # C2: 3 => SOL
* STA A3: 2 + C2: 3
* CNT  30 HDP CHAINS /  30 HYP OPENED