Analysis of zz-www.sudokuwiki.org-0273-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=273

level: hard

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=273

position: ...1..53.5...9...2.8..6..4...45.....2.......7.....68...3..2..6.8...5...3.75..4... initial

Autosolve

position: ...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.4.3..2..658...5...3.75..4... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # A7: 1,9 => CTR => A7: 4
* CNT   1 HDP CHAINS /  18 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 # A7: 1,9 => CTR => A7: 4
* STA A7: 4
* CNT   1 HDP CHAINS /  33 HYP OPENED

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

Pair Reduction Position

position: ...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.443..2..658...5.4.3.75..4... pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:01:03.983832

The following important HDP chains were detected:

* DIS # G3: 1,9 # G9: 1,9 => CTR => G9: 2
* DIS # G3: 1,9 + G9: 2 # B8: 1,9 => CTR => B8: 2,6
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 # C6: 1,9 => CTR => C6: 3,7
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E5: 1,3 => CTR => E5: 4
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 3 => CTR => C2: 1,6
* PRF # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 # B4: 1,6 => SOL
* STA # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 + B4: 1,6
* CNT   6 HDP CHAINS /  54 HYP OPENED

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

Details

Positions

...1..53.5...9...2.8..6..4...45.....2.......7.....68...3..2..6.8...5...3.75..4... initial
...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.4.3..2..658...5...3.75..4... autosolve
...1..53.5...9...2.8..65.4...45.....2.8.....7.....68.443..2..658...5.4.3.75..4... pair_reduction
947182536561493782382765941614578329258349617793216854439827165826951473175634298 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
I3: 1,9
C7: 1,9
E9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F1,D3: 2.. / F1 = 2  =>  4 pairs (_) / D3 = 2  =>  9 pairs (_)
F4,D6: 2.. / F4 = 2  =>  9 pairs (_) / D6 = 2  =>  4 pairs (_)
B8,C8: 2.. / B8 = 2  =>  3 pairs (_) / C8 = 2  => 11 pairs (_)
G9,H9: 2.. / G9 = 2  =>  3 pairs (_) / H9 = 2  =>  0 pairs (X)
C3,D3: 2.. / C3 = 2  =>  4 pairs (_) / D3 = 2  =>  9 pairs (_)
D6,H6: 2.. / D6 = 2  =>  4 pairs (_) / H6 = 2  =>  9 pairs (_)
B1,B8: 2.. / B1 = 2  => 11 pairs (_) / B8 = 2  =>  3 pairs (_)
D3,D6: 2.. / D3 = 2  =>  9 pairs (_) / D6 = 2  =>  4 pairs (_)
F1,F4: 2.. / F1 = 2  =>  4 pairs (_) / F4 = 2  =>  9 pairs (_)
G4,G9: 2.. / G4 = 2  =>  0 pairs (X) / G9 = 2  =>  3 pairs (_)
G4,G5: 3.. / G4 = 3  =>  4 pairs (_) / G5 = 3  => 13 pairs (_)
D9,E9: 3.. / D9 = 3  => 12 pairs (_) / E9 = 3  =>  6 pairs (_)
E1,D2: 4.. / E1 = 4  =>  7 pairs (_) / D2 = 4  => 10 pairs (_)
D5,E5: 4.. / D5 = 4  =>  7 pairs (_) / E5 = 4  => 10 pairs (_)
A7,B8: 4.. / A7 = 4  =>  3 pairs (_) / B8 = 4  =>  0 pairs (X)
G7,G8: 4.. / G7 = 4  =>  0 pairs (X) / G8 = 4  =>  3 pairs (_)
B2,D2: 4.. / B2 = 4  =>  7 pairs (_) / D2 = 4  => 10 pairs (_)
A7,G7: 4.. / A7 = 4  =>  3 pairs (_) / G7 = 4  =>  0 pairs (X)
B8,G8: 4.. / B8 = 4  =>  0 pairs (X) / G8 = 4  =>  3 pairs (_)
A1,A7: 4.. / A1 = 4  =>  0 pairs (X) / A7 = 4  =>  3 pairs (_)
D2,D5: 4.. / D2 = 4  => 10 pairs (_) / D5 = 4  =>  7 pairs (_)
E1,E5: 4.. / E1 = 4  =>  7 pairs (_) / E5 = 4  => 10 pairs (_)
B5,B6: 5.. / B5 = 5  =>  0 pairs (*) / B6 = 5  =>  0 pairs (X)
H5,H6: 5.. / H5 = 5  =>  3 pairs (_) / H6 = 5  =>  0 pairs (*)
B5,H5: 5.. / B5 = 5  =>  0 pairs (*) / H5 = 5  =>  0 pairs (X)
B6,H6: 5.. / B6 = 5  =>  3 pairs (_) / H6 = 5  =>  0 pairs (*)
I1,G2: 6.. / I1 = 6  => 15 pairs (_) / G2 = 6  =>  6 pairs (_)
D8,D9: 6.. / D8 = 6  =>  5 pairs (_) / D9 = 6  =>  9 pairs (_)
B5,G5: 6.. / B5 = 6  =>  5 pairs (_) / G5 = 6  => 16 pairs (_)
A9,D9: 6.. / A9 = 6  =>  5 pairs (_) / D9 = 6  =>  9 pairs (_)
I1,I4: 6.. / I1 = 6  => 15 pairs (_) / I4 = 6  =>  6 pairs (_)
H2,H8: 7.. / H2 = 7  => 15 pairs (_) / H8 = 7  =>  8 pairs (_)
I1,H2: 8.. / I1 = 8  =>  9 pairs (_) / H2 = 8  => 11 pairs (_)
E4,F4: 8.. / E4 = 8  =>  4 pairs (_) / F4 = 8  => 21 pairs (_)
D7,F7: 8.. / D7 = 8  =>  3 pairs (_) / F7 = 8  => 14 pairs (_)
H9,I9: 8.. / H9 = 8  =>  9 pairs (_) / I9 = 8  => 11 pairs (_)
D2,D7: 8.. / D2 = 8  => 14 pairs (_) / D7 = 8  =>  3 pairs (_)
E1,E4: 8.. / E1 = 8  => 21 pairs (_) / E4 = 8  =>  4 pairs (_)
H2,H9: 8.. / H2 = 8  => 11 pairs (_) / H9 = 8  =>  9 pairs (_)
I1,I9: 8.. / I1 = 8  =>  9 pairs (_) / I9 = 8  => 11 pairs (_)
* DURATION: 0:00:35.982938  START: 14:29:33.221092  END: 14:30:09.204030 2019-04-28
* CP COUNT: (40)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:01:03.720970  START: 14:30:39.703706  END: 14:31:43.424676 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0273-base-pr-002.dot
* REASONING
* DIS # G3: 1,9 # G9: 1,9 => CTR => G9: 2
* DIS # G3: 1,9 + G9: 2 # B8: 1,9 => CTR => B8: 2,6
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 # C6: 1,9 => CTR => C6: 3,7
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E5: 1,3 => CTR => E5: 4
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 3 => CTR => C2: 1,6
* PRF # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 # B4: 1,6 => SOL
* STA # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 + B4: 1,6
* CNT   6 HDP CHAINS /  54 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=273

Solution

position: 947182536561493782382765941614578329258349617793216854439827165826951473175634298 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 # G3: 1,9 => UNS
* INC # G3: 7 => UNS
* INC # A3: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # I4: 1,9 => UNS
* INC # I9: 1,9 => UNS
* DIS # A7: 1,9 => CTR => A7: 4
* INC # A7: 4 => UNS
* INC # B8: 1,9 => UNS
* INC # C8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # F7: 1,9 => UNS
* INC # G7: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # C6: 1,9 => UNS
* INC # E4: 1,3 => UNS
* INC # E5: 1,3 => UNS
* INC # E6: 1,3 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 1,9 => UNS
* INC # G3: 7 => UNS
* INC # A3: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # I4: 1,9 => UNS
* INC # I9: 1,9 => UNS
* DIS # A7: 1,9 => CTR => A7: 4
* INC A7: 4 # B8: 1,9 => UNS
* INC A7: 4 # C8: 1,9 => UNS
* INC A7: 4 # A9: 1,9 => UNS
* INC A7: 4 # F7: 1,9 => UNS
* INC A7: 4 # G7: 1,9 => UNS
* INC A7: 4 # C3: 1,9 => UNS
* INC A7: 4 # C6: 1,9 => UNS
* INC A7: 4 # E4: 1,3 => UNS
* INC A7: 4 # E5: 1,3 => UNS
* INC A7: 4 # E6: 1,3 => UNS
* INC A7: 4 # G3: 1,9 => UNS
* INC A7: 4 # G3: 7 => UNS
* INC A7: 4 # A3: 1,9 => UNS
* INC A7: 4 # C3: 1,9 => UNS
* INC A7: 4 # I4: 1,9 => UNS
* INC A7: 4 # I9: 1,9 => UNS
* INC A7: 4 # B8: 1,9 => UNS
* INC A7: 4 # C8: 1,9 => UNS
* INC A7: 4 # A9: 1,9 => UNS
* INC A7: 4 # F7: 1,9 => UNS
* INC A7: 4 # G7: 1,9 => UNS
* INC A7: 4 # C3: 1,9 => UNS
* INC A7: 4 # C6: 1,9 => UNS
* INC A7: 4 # E4: 1,3 => UNS
* INC A7: 4 # E5: 1,3 => UNS
* INC A7: 4 # E6: 1,3 => UNS
* STA A7: 4
* CNT  33 HDP CHAINS /  33 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 1,9 => UNS
* INC # G3: 7 => UNS
* INC # A3: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # I4: 1,9 => UNS
* INC # I9: 1,9 => UNS
* INC # B8: 1,9 => UNS
* INC # C8: 1,9 => UNS
* INC # A9: 1,9 => UNS
* INC # F7: 1,9 => UNS
* INC # G7: 1,9 => UNS
* INC # C3: 1,9 => UNS
* INC # C6: 1,9 => UNS
* INC # E4: 1,3 => UNS
* INC # E5: 1,3 => UNS
* INC # E6: 1,3 => UNS
* INC # G3: 1,9 # C3: 3,7 => UNS
* INC # G3: 1,9 # C3: 2 => UNS
* INC # G3: 1,9 # D3: 3,7 => UNS
* INC # G3: 1,9 # D3: 2 => UNS
* INC # G3: 1,9 # A4: 3,7 => UNS
* INC # G3: 1,9 # A6: 3,7 => UNS
* INC # G3: 1,9 # D2: 3,8 => UNS
* INC # G3: 1,9 # D2: 4 => UNS
* INC # G3: 1,9 # F4: 3,8 => UNS
* INC # G3: 1,9 # F4: 1,2,7,9 => UNS
* INC # G3: 1,9 # G4: 1,9 => UNS
* INC # G3: 1,9 # G5: 1,9 => UNS
* INC # G3: 1,9 # G7: 1,9 => UNS
* DIS # G3: 1,9 # G9: 1,9 => CTR => G9: 2
* INC # G3: 1,9 + G9: 2 # G4: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 # G5: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 # G7: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 # I4: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 # I9: 1,9 => UNS
* DIS # G3: 1,9 + G9: 2 # B8: 1,9 => CTR => B8: 2,6
* INC # G3: 1,9 + G9: 2 + B8: 2,6 # C8: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 # A9: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 # F7: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 # G7: 1,9 => UNS
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 # C6: 1,9 => CTR => C6: 3,7
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # C8: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # A9: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # F7: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # G7: 1,9 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E4: 1,3 => UNS
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 # E5: 1,3 => CTR => E5: 4
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # E6: 1,3 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # E4: 1,3 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # E6: 1,3 => UNS
* INC # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 1,6 => UNS
* DIS # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 # C2: 3 => CTR => C2: 1,6
* PRF # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 # B4: 1,6 => SOL
* STA # G3: 1,9 + G9: 2 + B8: 2,6 + C6: 3,7 + E5: 4 + C2: 1,6 + B4: 1,6
* CNT  53 HDP CHAINS /  54 HYP OPENED