Analysis of zz-www.sudokuwiki.org-0099-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=99

level: hard

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=99

position: .5.......9...8..14.....4..7..1..6...83..7..49...2..6..3..9.....54..1...3.......5. initial

Autosolve

position: .54......9...8..14.....4..7..1..6..5836.7.249..52..6.13..9.....54..1...3..9....5. 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: 0:00:29.735597

The following important HDP chains were detected:

* DIS # G3: 3,5 # H1: 8,9 => CTR => H1: 2,6
* DIS # G3: 3,5 + H1: 2,6 # G8: 7 => CTR => G8: 8,9
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 6 => CTR => D3: 1,5
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 # D1: 6,7 => CTR => D1: 3
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 + D1: 3 => CTR => G3: 9
* DIS G3: 9 # A1: 7 => CTR => A1: 1,2
* DIS G3: 9 + A1: 1,2 # H1: 3,8 => CTR => H1: 2
* PRF G3: 9 + A1: 1,2 + H1: 2 => SOL
* STA G3: 9 + A1: 1,2 + H1: 2
* CNT   8 HDP CHAINS /  20 HYP OPENED

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

Details

Positions

.5.......9...8..14.....4..7..1..6...83..7..49...2..6..3..9.....54..1...3.......5. initial
.54......9...8..14.....4..7..1..6..5836.7.249..52..6.13..9.....54..1...3..9....5. autosolve
154769328967382514283154967421896735836571249795243681318925476542617893679438152 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
G2: 3,5
A6: 4,7
B6: 7,9
D5: 1,5
F5: 1,5
G7: 1,4
G9: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,F5: 1.. / D5 = 1  =>  0 pairs (X) / F5 = 1  =>  5 pairs (_)
G7,G9: 1.. / G7 = 1  =>  0 pairs (X) / G9 = 1  =>  6 pairs (_)
B7,G7: 1.. / B7 = 1  =>  6 pairs (_) / G7 = 1  =>  0 pairs (X)
F1,F5: 1.. / F1 = 1  =>  0 pairs (X) / F5 = 1  =>  5 pairs (_)
A4,B4: 2.. / A4 = 2  => 10 pairs (_) / B4 = 2  => 14 pairs (_)
C2,C3: 3.. / C2 = 3  => 12 pairs (_) / C3 = 3  =>  9 pairs (_)
A4,A6: 4.. / A4 = 4  => 13 pairs (_) / A6 = 4  =>  8 pairs (_)
G7,G9: 4.. / G7 = 4  =>  6 pairs (_) / G9 = 4  =>  0 pairs (X)
A6,E6: 4.. / A6 = 4  =>  8 pairs (_) / E6 = 4  => 13 pairs (_)
E7,G7: 4.. / E7 = 4  =>  0 pairs (X) / G7 = 4  =>  6 pairs (_)
D4,D9: 4.. / D4 = 4  =>  0 pairs (X) / D9 = 4  => 12 pairs (_)
G2,G3: 5.. / G2 = 5  =>  7 pairs (_) / G3 = 5  =>  0 pairs (X)
D5,F5: 5.. / D5 = 5  =>  5 pairs (_) / F5 = 5  =>  0 pairs (X)
E7,F7: 5.. / E7 = 5  => 11 pairs (_) / F7 = 5  =>  6 pairs (_)
E3,E7: 5.. / E3 = 5  =>  6 pairs (_) / E7 = 5  => 11 pairs (_)
B2,D2: 6.. / B2 = 6  => 10 pairs (_) / D2 = 6  =>  0 pairs (X)
D8,H8: 6.. / D8 = 6  => 13 pairs (_) / H8 = 6  =>  0 pairs (X)
G4,G8: 7.. / G4 = 7  => 12 pairs (_) / G8 = 7  => 16 pairs (_)
B3,C3: 8.. / B3 = 8  =>  8 pairs (_) / C3 = 8  => 14 pairs (_)
D4,F6: 8.. / D4 = 8  => 14 pairs (_) / F6 = 8  => 11 pairs (_)
F6,H6: 8.. / F6 = 8  => 11 pairs (_) / H6 = 8  => 14 pairs (_)
B4,B6: 9.. / B4 = 9  => 10 pairs (_) / B6 = 9  => 10 pairs (_)
G8,H8: 9.. / G8 = 9  => 13 pairs (_) / H8 = 9  => 14 pairs (_)
B4,E4: 9.. / B4 = 9  => 10 pairs (_) / E4 = 9  => 10 pairs (_)
F1,F6: 9.. / F1 = 9  =>  9 pairs (_) / F6 = 9  =>  0 pairs (X)
* DURATION: 0:00:35.568661  START: 18:53:57.143118  END: 18:54:32.711779 2017-04-30
* CP COUNT: (25)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:29.538472  START: 18:54:47.848675  END: 18:55:17.387147 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0099-base-pr-002.dot
* REASONING
* DIS # G3: 3,5 # H1: 8,9 => CTR => H1: 2,6
* DIS # G3: 3,5 + H1: 2,6 # G8: 7 => CTR => G8: 8,9
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 6 => CTR => D3: 1,5
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 # D1: 6,7 => CTR => D1: 3
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 + D1: 3 => CTR => G3: 9
* DIS G3: 9 # A1: 7 => CTR => A1: 1,2
* DIS G3: 9 + A1: 1,2 # H1: 3,8 => CTR => H1: 2
* PRF G3: 9 + A1: 1,2 + H1: 2 => SOL
* STA G3: 9 + A1: 1,2 + H1: 2
* CNT   8 HDP CHAINS /  20 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=99

Solution

position: 154769328967382514283154967421896735836571249795243681318925476542617893679438152 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: 3,5 => UNS
* INC # G3: 9 => UNS
* INC # D2: 3,5 => UNS
* INC # F2: 3,5 => UNS
* INC # A4: 4,7 => UNS
* INC # A4: 2 => UNS
* INC # B4: 7,9 => UNS
* INC # B4: 2 => UNS
* INC # D3: 1,5 => UNS
* INC # D3: 3,6 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 3,5 => UNS
* INC # G3: 9 => UNS
* INC # D2: 3,5 => UNS
* INC # F2: 3,5 => UNS
* INC # A4: 4,7 => UNS
* INC # A4: 2 => UNS
* INC # B4: 7,9 => UNS
* INC # B4: 2 => UNS
* INC # D3: 1,5 => UNS
* INC # D3: 3,6 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 3,5 => UNS
* INC # G3: 9 => UNS
* INC # D2: 3,5 => UNS
* INC # F2: 3,5 => UNS
* INC # A4: 4,7 => UNS
* INC # A4: 2 => UNS
* INC # B4: 7,9 => UNS
* INC # B4: 2 => UNS
* INC # D3: 1,5 => UNS
* INC # D3: 3,6 => UNS
* DIS # G3: 3,5 # H1: 8,9 => CTR => H1: 2,6
* INC # G3: 3,5 + H1: 2,6 # G8: 8,9 => UNS
* DIS # G3: 3,5 + H1: 2,6 # G8: 7 => CTR => G8: 8,9
* INC # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 1,5 => UNS
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 # D3: 6 => CTR => D3: 1,5
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 # D1: 6,7 => CTR => D1: 3
* DIS # G3: 3,5 + H1: 2,6 + G8: 8,9 + D3: 1,5 + D1: 3 => CTR => G3: 9
* INC G3: 9 # A1: 1,2 => UNS
* DIS G3: 9 # A1: 7 => CTR => A1: 1,2
* DIS G3: 9 + A1: 1,2 # H1: 3,8 => CTR => H1: 2
* PRF G3: 9 + A1: 1,2 + H1: 2 => SOL
* STA G3: 9 + A1: 1,2 + H1: 2
* CNT  21 HDP CHAINS /  20 HYP OPENED