Analysis of xx-ph-00028052-2011_12-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....6...9......5..49..4....58....6....3.....2...1.6...85....4.3...7...1...2. initial

Autosolve

position: 98.7.....64..9......5..49..4....58....6....3.....2...1.6...85....4.3...7...1...2. 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: 0:00:15.763389

The following important HDP chains were detected:

* PRF # E9: 4,7 # F8: 2 => SOL
* STA # E9: 4,7 + F8: 2
* CNT   1 HDP CHAINS /  21 HYP OPENED

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

Details

Positions

98.7.....6...9......5..49..4....58....6....3.....2...1.6...85....4.3...7...1...2. initial
98.7.....64..9......5..49..4....58....6....3.....2...1.6...85....4.3...7...1...2. autosolve
983751246647293158215684973471365892826419735539827461362978514194532687758146329 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (2)
E7: 4,7
G8: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E1,D2: 5.. / E1 = 5  =>  2 pairs (_) / D2 = 5  =>  7 pairs (_)
I5,H6: 5.. / I5 = 5  =>  2 pairs (_) / H6 = 5  =>  2 pairs (_)
D8,E9: 5.. / D8 = 5  =>  2 pairs (_) / E9 = 5  =>  7 pairs (_)
D2,D8: 5.. / D2 = 5  =>  7 pairs (_) / D8 = 5  =>  2 pairs (_)
E1,E9: 5.. / E1 = 5  =>  2 pairs (_) / E9 = 5  =>  7 pairs (_)
H8,I9: 8.. / H8 = 8  =>  2 pairs (_) / I9 = 8  =>  2 pairs (_)
A8,H8: 8.. / A8 = 8  =>  2 pairs (_) / H8 = 8  =>  2 pairs (_)
C6,C9: 8.. / C6 = 8  =>  2 pairs (_) / C9 = 8  =>  2 pairs (_)
E3,E5: 8.. / E3 = 8  =>  2 pairs (_) / E5 = 8  =>  5 pairs (_)
* DURATION: 0:00:05.412203  START: 22:04:35.399608  END: 22:04:40.811811 2020-12-09
* CP COUNT: (9)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:15.621218  START: 22:04:46.726761  END: 22:05:02.347979 2020-12-09
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00028052-2011_12-base-pr-002.dot
* REASONING
* PRF # E9: 4,7 # F8: 2 => SOL
* STA # E9: 4,7 + F8: 2
* CNT   1 HDP CHAINS /  21 HYP OPENED

Header Info

28052;2011_12;GP;23;11.30;1.20;1.20

Solution

position: 983751246647293158215684973471365892826419735539827461362978514194532687758146329 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 # E9: 4,7 => UNS
* INC # E9: 5,6 => UNS
* INC # E5: 4,7 => UNS
* INC # E5: 1,8 => UNS
* INC # H8: 1,6 => UNS
* INC # H8: 8,9 => UNS
* INC # G1: 1,6 => UNS
* INC # G1: 2,3,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E9: 4,7 => UNS
* INC # E9: 5,6 => UNS
* INC # E5: 4,7 => UNS
* INC # E5: 1,8 => UNS
* INC # H8: 1,6 => UNS
* INC # H8: 8,9 => UNS
* INC # G1: 1,6 => UNS
* INC # G1: 2,3,4 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E9: 4,7 => UNS
* INC # E9: 5,6 => UNS
* INC # E5: 4,7 => UNS
* INC # E5: 1,8 => UNS
* INC # H8: 1,6 => UNS
* INC # H8: 8,9 => UNS
* INC # G1: 1,6 => UNS
* INC # G1: 2,3,4 => UNS
* INC # E9: 4,7 # E3: 1,6 => UNS
* INC # E9: 4,7 # E3: 8 => UNS
* INC # E9: 4,7 # A5: 1,8 => UNS
* INC # E9: 4,7 # A5: 2,5,7 => UNS
* INC # E9: 4,7 # E3: 1,8 => UNS
* INC # E9: 4,7 # E3: 6 => UNS
* INC # E9: 4,7 # F8: 2,9 => UNS
* INC # E9: 4,7 # F8: 6 => UNS
* INC # E9: 4,7 # C7: 2,9 => UNS
* INC # E9: 4,7 # C7: 1,3,7 => UNS
* INC # E9: 4,7 # F8: 6,9 => UNS
* PRF # E9: 4,7 # F8: 2 => SOL
* STA # E9: 4,7 + F8: 2
* CNT  20 HDP CHAINS /  21 HYP OPENED