Analysis of zz-www.sudokuwiki.org-0345-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=345

level: hard

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=345

position: ........1.....2.3.....3.42...42..56...6..4....1.8.......5..63...8.7....99..1..... initial

Autosolve

position: ........1.....2.3.....3.42...42..56...63.4....1.86......5..63...8.7....99..1..... 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: 0:00:24.468446

The following important HDP chains were detected:

* DIS # E7: 4,9 # C9: 2,7 => CTR => C9: 3
* DIS # E7: 4,9 + C9: 3 # B1: 2,7 => CTR => B1: 3,4,5,6,9
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 1 => CTR => A7: 2,7
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 # B5: 2,7 => CTR => B5: 5,9
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 # A1: 4,6 => CTR => A1: 2,3,5
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 # A2: 4,6 => CTR => A2: 1
* PRF # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 + A2: 1 => SOL
* STA E7: 4,9
* CNT   7 HDP CHAINS /  20 HYP OPENED

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

Details

Positions

........1.....2.3.....3.42...42..56...6..4....1.8.......5..63...8.7....99..1..... initial
........1.....2.3.....3.42...42..56...63.4....1.86......5..63...8.7....99..1..... autosolve
352647891149582736678931425834219567596374182217865943725496318481723659963158274 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
D7: 4,9
F8: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E2,F3: 1.. / E2 = 1  =>  3 pairs (_) / F3 = 1  =>  3 pairs (_)
E4,F4: 1.. / E4 = 1  =>  3 pairs (_) / F4 = 1  =>  3 pairs (_)
G5,H5: 1.. / G5 = 1  =>  3 pairs (_) / H5 = 1  =>  5 pairs (_)
A7,H7: 1.. / A7 = 1  =>  3 pairs (_) / H7 = 1  =>  4 pairs (_)
E2,E4: 1.. / E2 = 1  =>  3 pairs (_) / E4 = 1  =>  3 pairs (_)
F3,F4: 1.. / F3 = 1  =>  3 pairs (_) / F4 = 1  =>  3 pairs (_)
G5,G8: 1.. / G5 = 1  =>  3 pairs (_) / G8 = 1  =>  5 pairs (_)
I4,I6: 3.. / I4 = 3  =>  3 pairs (_) / I6 = 3  =>  4 pairs (_)
F8,F9: 3.. / F8 = 3  =>  3 pairs (_) / F9 = 3  =>  5 pairs (_)
H6,I6: 4.. / H6 = 4  =>  3 pairs (_) / I6 = 4  =>  4 pairs (_)
E5,F6: 5.. / E5 = 5  =>  5 pairs (_) / F6 = 5  =>  4 pairs (_)
A6,F6: 5.. / A6 = 5  =>  5 pairs (_) / F6 = 5  =>  4 pairs (_)
A8,B9: 6.. / A8 = 6  =>  3 pairs (_) / B9 = 6  =>  2 pairs (_)
A8,G8: 6.. / A8 = 6  =>  3 pairs (_) / G8 = 6  =>  2 pairs (_)
A4,A5: 8.. / A4 = 8  =>  3 pairs (_) / A5 = 8  =>  5 pairs (_)
A4,I4: 8.. / A4 = 8  =>  3 pairs (_) / I4 = 8  =>  5 pairs (_)
D7,E7: 9.. / D7 = 9  =>  2 pairs (_) / E7 = 9  =>  8 pairs (_)
* DURATION: 0:00:12.353350  START: 19:09:23.439806  END: 19:09:35.793156 2019-04-28
* CP COUNT: (17)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:24.275807  START: 19:09:41.269823  END: 19:10:05.545630 2019-04-28
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0345-base-pr-002.dot
* REASONING
* DIS # E7: 4,9 # C9: 2,7 => CTR => C9: 3
* DIS # E7: 4,9 + C9: 3 # B1: 2,7 => CTR => B1: 3,4,5,6,9
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 1 => CTR => A7: 2,7
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 # B5: 2,7 => CTR => B5: 5,9
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 # A1: 4,6 => CTR => A1: 2,3,5
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 # A2: 4,6 => CTR => A2: 1
* PRF # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 + A2: 1 => SOL
* STA E7: 4,9
* CNT   7 HDP CHAINS /  20 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=345

Solution

position: 352647891149582736678931425834219567596374182217865943725496318481723659963158274 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 # E7: 4,9 => UNS
* INC # E7: 2,8 => UNS
* INC # D1: 4,9 => UNS
* INC # D2: 4,9 => UNS
* INC # F9: 3,5 => UNS
* INC # F9: 8 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E7: 4,9 => UNS
* INC # E7: 2,8 => UNS
* INC # D1: 4,9 => UNS
* INC # D2: 4,9 => UNS
* INC # F9: 3,5 => UNS
* INC # F9: 8 => UNS
* CNT   6 HDP CHAINS /   6 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E7: 4,9 => UNS
* INC # E7: 2,8 => UNS
* INC # D1: 4,9 => UNS
* INC # D2: 4,9 => UNS
* INC # F9: 3,5 => UNS
* INC # F9: 8 => UNS
* INC # E7: 4,9 # A7: 2,7 => UNS
* DIS # E7: 4,9 # C9: 2,7 => CTR => C9: 3
* INC # E7: 4,9 + C9: 3 # A7: 2,7 => UNS
* INC # E7: 4,9 + C9: 3 # A7: 1 => UNS
* DIS # E7: 4,9 + C9: 3 # B1: 2,7 => CTR => B1: 3,4,5,6,9
* INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # B5: 2,7 => UNS
* INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # B5: 2,7 => UNS
* INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # B5: 5,9 => UNS
* INC # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 2,7 => UNS
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 # A7: 1 => CTR => A7: 2,7
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 # B5: 2,7 => CTR => B5: 5,9
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 # A1: 4,6 => CTR => A1: 2,3,5
* DIS # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 # A2: 4,6 => CTR => A2: 1
* PRF # E7: 4,9 + C9: 3 + B1: 3,4,5,6,9 + A7: 2,7 + B5: 5,9 + A1: 2,3,5 + A2: 1 => SOL
* STA E7: 4,9
* CNT  20 HDP CHAINS /  20 HYP OPENED