Analysis of zz-www.sudokuwiki.org-0054-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=54

level: hard

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=54

position: 9...53....4.....65..67..1..3..2......6..4..8......1..6..2..87..48.....1.....9...8 initial

Autosolve

position: 9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # D9: 3,5 => CTR => D9: 1,4
* CNT   1 HDP CHAINS /  13 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 # D9: 3,5 => CTR => D9: 1,4
* STA D9: 1,4
* CNT   1 HDP CHAINS /  28 HYP OPENED

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

Pair Reduction Position

position: 9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:56.198861

The following important HDP chains were detected:

* DIS # C4: 4,5,7,9 # H6: 4,7 => CTR => H6: 2,3,9
* DIS # C4: 4,5,7,9 + H6: 2,3,9 # H6: 3,9 => CTR => H6: 2
* DIS # C4: 4,5,7,9 + H6: 2,3,9 + H6: 2 => CTR => C4: 1,8
* PRF C4: 1,8 # E2: 1 # A3: 5 => SOL
* STA C4: 1,8 # E2: 1 + A3: 5
* CNT   4 HDP CHAINS /  54 HYP OPENED

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

Details

Positions

9...53....4.....65..67..1..3..2......6..4..8......1..6..2..87..48.....1.....9...8 initial
9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 autosolve
9..653....4.....65..67.41..3..2......6..4..8......1..6..2..87..48.....1.....9...8 pair_reduction
921653874847912365536784192378265941165349287294871536612438759489527613753196428 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
B1: 1,2
C1: 1,8
F2: 2,9
E3: 2,8
D8: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 1.. / B1 = 1  =>  0 pairs (X) / C1 = 1  =>  9 pairs (_)
D2,E2: 1.. / D2 = 1  => 23 pairs (_) / E2 = 1  =>  9 pairs (_)
I4,I5: 1.. / I4 = 1  =>  5 pairs (_) / I5 = 1  =>  7 pairs (_)
E2,E7: 1.. / E2 = 1  =>  9 pairs (_) / E7 = 1  => 23 pairs (_)
C2,B3: 3.. / C2 = 3  =>  9 pairs (_) / B3 = 3  => 14 pairs (_)
C2,G2: 3.. / C2 = 3  =>  9 pairs (_) / G2 = 3  => 14 pairs (_)
C4,C6: 4.. / C4 = 4  => 17 pairs (_) / C6 = 4  =>  5 pairs (_)
D7,D9: 4.. / D7 = 4  =>  8 pairs (_) / D9 = 4  =>  6 pairs (_)
A3,B3: 5.. / A3 = 5  => 14 pairs (_) / B3 = 5  =>  9 pairs (_)
E4,F4: 6.. / E4 = 6  => 13 pairs (_) / F4 = 6  =>  6 pairs (_)
A7,A9: 6.. / A7 = 6  =>  7 pairs (_) / A9 = 6  => 11 pairs (_)
G8,G9: 6.. / G8 = 6  =>  5 pairs (_) / G9 = 6  =>  8 pairs (_)
A7,E7: 6.. / A7 = 6  =>  7 pairs (_) / E7 = 6  => 11 pairs (_)
A2,C2: 7.. / A2 = 7  =>  6 pairs (_) / C2 = 7  => 14 pairs (_)
H1,I1: 7.. / H1 = 7  =>  8 pairs (_) / I1 = 7  =>  6 pairs (_)
G1,G2: 8.. / G1 = 8  =>  9 pairs (_) / G2 = 8  =>  0 pairs (X)
C1,G1: 8.. / C1 = 8  =>  0 pairs (X) / G1 = 8  =>  9 pairs (_)
A3,E3: 8.. / A3 = 8  => 15 pairs (_) / E3 = 8  => 14 pairs (_)
C4,E4: 8.. / C4 = 8  => 11 pairs (_) / E4 = 8  => 17 pairs (_)
D2,D6: 8.. / D2 = 8  => 16 pairs (_) / D6 = 8  => 13 pairs (_)
D2,F2: 9.. / D2 = 9  =>  0 pairs (*) / F2 = 9  =>  0 pairs (X)
H3,I3: 9.. / H3 = 9  =>  6 pairs (_) / I3 = 9  =>  8 pairs (_)
B7,C8: 9.. / B7 = 9  =>  6 pairs (_) / C8 = 9  =>  6 pairs (_)
* DURATION: 0:00:26.832596  START: 18:33:06.771822  END: 18:33:33.604418 2017-04-30
* CP COUNT: (23)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:55.864938  START: 18:34:08.959223  END: 18:35:04.824161 2017-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0054-base-pr-002.dot
* REASONING
* DIS # C4: 4,5,7,9 # H6: 4,7 => CTR => H6: 2,3,9
* DIS # C4: 4,5,7,9 + H6: 2,3,9 # H6: 3,9 => CTR => H6: 2
* DIS # C4: 4,5,7,9 + H6: 2,3,9 + H6: 2 => CTR => C4: 1,8
* PRF C4: 1,8 # E2: 1 # A3: 5 => SOL
* STA C4: 1,8 # E2: 1 + A3: 5
* CNT   4 HDP CHAINS /  54 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=54

Solution

position: 921653874847912365536784192378265941165349287294871536612438759489527613753196428 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 # C4: 1,8 => UNS
* INC # C4: 4,5,7,9 => UNS
* INC # E2: 2,8 => UNS
* INC # E2: 1 => UNS
* INC # A3: 2,8 => UNS
* INC # A3: 5 => UNS
* INC # D7: 3,5 => UNS
* DIS # D9: 3,5 => CTR => D9: 1,4
* INC # D9: 1,4 => UNS
* INC # C8: 3,5 => UNS
* INC # G8: 3,5 => UNS
* INC # D5: 3,5 => UNS
* INC # D6: 3,5 => UNS
* CNT  13 HDP CHAINS /  13 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 1,8 => UNS
* INC # C4: 4,5,7,9 => UNS
* INC # E2: 2,8 => UNS
* INC # E2: 1 => UNS
* INC # A3: 2,8 => UNS
* INC # A3: 5 => UNS
* INC # D7: 3,5 => UNS
* DIS # D9: 3,5 => CTR => D9: 1,4
* INC D9: 1,4 # D7: 3,5 => UNS
* INC D9: 1,4 # D7: 1,4 => UNS
* INC D9: 1,4 # C8: 3,5 => UNS
* INC D9: 1,4 # G8: 3,5 => UNS
* INC D9: 1,4 # D5: 3,5 => UNS
* INC D9: 1,4 # D6: 3,5 => UNS
* INC D9: 1,4 # C4: 1,8 => UNS
* INC D9: 1,4 # C4: 4,5,7,9 => UNS
* INC D9: 1,4 # E2: 2,8 => UNS
* INC D9: 1,4 # E2: 1 => UNS
* INC D9: 1,4 # A3: 2,8 => UNS
* INC D9: 1,4 # A3: 5 => UNS
* INC D9: 1,4 # D7: 3,5 => UNS
* INC D9: 1,4 # D7: 1,4 => UNS
* INC D9: 1,4 # C8: 3,5 => UNS
* INC D9: 1,4 # G8: 3,5 => UNS
* INC D9: 1,4 # D5: 3,5 => UNS
* INC D9: 1,4 # D6: 3,5 => UNS
* INC D9: 1,4 # D7: 1,4 => UNS
* INC D9: 1,4 # D7: 3,5 => UNS
* STA D9: 1,4
* CNT  28 HDP CHAINS /  28 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 1,8 => UNS
* INC # C4: 4,5,7,9 => UNS
* INC # E2: 2,8 => UNS
* INC # E2: 1 => UNS
* INC # A3: 2,8 => UNS
* INC # A3: 5 => UNS
* INC # D7: 3,5 => UNS
* INC # D7: 1,4 => UNS
* INC # C8: 3,5 => UNS
* INC # G8: 3,5 => UNS
* INC # D5: 3,5 => UNS
* INC # D6: 3,5 => UNS
* INC # D7: 1,4 => UNS
* INC # D7: 3,5 => UNS
* INC # C4: 1,8 # C8: 3,7 => UNS
* INC # C4: 1,8 # C9: 3,7 => UNS
* INC # C4: 1,8 # E2: 2,8 => UNS
* INC # C4: 1,8 # E2: 1 => UNS
* INC # C4: 1,8 # A3: 2,8 => UNS
* INC # C4: 1,8 # A3: 5 => UNS
* INC # C4: 1,8 # D7: 3,5 => UNS
* INC # C4: 1,8 # D7: 1,4 => UNS
* INC # C4: 1,8 # C8: 3,5 => UNS
* INC # C4: 1,8 # G8: 3,5 => UNS
* INC # C4: 1,8 # D5: 3,5 => UNS
* INC # C4: 1,8 # D6: 3,5 => UNS
* INC # C4: 1,8 # D7: 1,4 => UNS
* INC # C4: 1,8 # D7: 3,5 => UNS
* INC # C4: 1,8 => UNS
* DIS # C4: 4,5,7,9 # H6: 4,7 => CTR => H6: 2,3,9
* DIS # C4: 4,5,7,9 + H6: 2,3,9 # H6: 3,9 => CTR => H6: 2
* DIS # C4: 4,5,7,9 + H6: 2,3,9 + H6: 2 => CTR => C4: 1,8
* INC C4: 1,8 # C8: 3,7 => UNS
* INC C4: 1,8 # C9: 3,7 => UNS
* INC C4: 1,8 # E2: 2,8 => UNS
* INC C4: 1,8 # E2: 1 => UNS
* INC C4: 1,8 # A3: 2,8 => UNS
* INC C4: 1,8 # A3: 5 => UNS
* INC C4: 1,8 # D7: 3,5 => UNS
* INC C4: 1,8 # D7: 1,4 => UNS
* INC C4: 1,8 # C8: 3,5 => UNS
* INC C4: 1,8 # G8: 3,5 => UNS
* INC C4: 1,8 # D5: 3,5 => UNS
* INC C4: 1,8 # D6: 3,5 => UNS
* INC C4: 1,8 # D7: 1,4 => UNS
* INC C4: 1,8 # D7: 3,5 => UNS
* INC C4: 1,8 # E2: 2,8 => UNS
* INC C4: 1,8 # E2: 1 # C8: 3,7 => UNS
* INC C4: 1,8 # E2: 1 # C9: 3,7 => UNS
* INC C4: 1,8 # E2: 1 # D6: 8,9 => UNS
* INC C4: 1,8 # E2: 1 # D6: 3,5 => UNS
* INC C4: 1,8 # E2: 1 # A3: 2,8 => UNS
* PRF C4: 1,8 # E2: 1 # A3: 5 => SOL
* STA C4: 1,8 # E2: 1 + A3: 5
* CNT  53 HDP CHAINS /  54 HYP OPENED