Analysis of xx-ph-00016560-Kz1_b-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 98.7.....76..5......4..67..8....96.....3...2.....6...1.7...48.....1....3....2..5. initial

Autosolve

position: 98.7.....76..5......4..67..8....96.....3...2.....6...1.7...48.....1....3....2..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: 0:00:38.795982

The following important HDP chains were detected:

* DIS # C7: 3,9 # A7: 5,6 => CTR => A7: 1,2
* DIS # C7: 3,9 + A7: 1,2 # C9: 3,9 => CTR => C9: 1,8
* PRF # C7: 3,9 + A7: 1,2 + C9: 1,8 # F5: 7,8 => SOL
* STA # C7: 3,9 + A7: 1,2 + C9: 1,8 + F5: 7,8
* CNT   3 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

98.7.....76..5......4..67..8....96.....3...2.....6...1.7...48.....1....3....2..5. initial
98.7.....76..5......4..67..8....96.....3...2.....6...1.7...48.....1....3....2..5. autosolve
985731246761452389234986715857219634619347528342865971173594862526178493498623157 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (1)
E7: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H7,G9: 1.. / H7 = 1  =>  2 pairs (_) / G9 = 1  =>  2 pairs (_)
I7,G8: 2.. / I7 = 2  =>  2 pairs (_) / G8 = 2  =>  2 pairs (_)
E7,F9: 3.. / E7 = 3  =>  2 pairs (_) / F9 = 3  =>  7 pairs (_)
E1,D2: 4.. / E1 = 4  =>  2 pairs (_) / D2 = 4  =>  3 pairs (_)
D7,F8: 5.. / D7 = 5  =>  3 pairs (_) / F8 = 5  =>  2 pairs (_)
H1,I1: 6.. / H1 = 6  =>  2 pairs (_) / I1 = 6  =>  2 pairs (_)
A5,C5: 6.. / A5 = 6  =>  1 pairs (_) / C5 = 6  =>  1 pairs (_)
D7,D9: 6.. / D7 = 6  =>  7 pairs (_) / D9 = 6  =>  2 pairs (_)
H8,I9: 7.. / H8 = 7  =>  4 pairs (_) / I9 = 7  =>  3 pairs (_)
F9,I9: 7.. / F9 = 7  =>  4 pairs (_) / I9 = 7  =>  3 pairs (_)
I5,H6: 8.. / I5 = 8  =>  1 pairs (_) / H6 = 8  =>  1 pairs (_)
C8,C9: 8.. / C8 = 8  =>  3 pairs (_) / C9 = 8  =>  3 pairs (_)
* DURATION: 0:00:09.777414  START: 08:41:57.635982  END: 08:42:07.413396 2020-11-19
* CP COUNT: (12)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:38.628112  START: 08:42:11.552594  END: 08:42:50.180706 2020-11-19
* SOLUTION FOUND
* SAVE PR GRAPH xx-ph-00016560-Kz1_b-base-pr-002.dot
* REASONING
* DIS # C7: 3,9 # A7: 5,6 => CTR => A7: 1,2
* DIS # C7: 3,9 + A7: 1,2 # C9: 3,9 => CTR => C9: 1,8
* PRF # C7: 3,9 + A7: 1,2 + C9: 1,8 # F5: 7,8 => SOL
* STA # C7: 3,9 + A7: 1,2 + C9: 1,8 + F5: 7,8
* CNT   3 HDP CHAINS /  31 HYP OPENED

Header Info

16560;Kz1 b;GP;23;11.30;11.30;11.30

Solution

position: 985731246761452389234986715857219634619347528342865971173594862526178493498623157 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 # C7: 3,9 => UNS
* INC # C7: 1,2,5,6 => UNS
* INC # E3: 3,9 => UNS
* INC # E3: 1,8 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C7: 3,9 => UNS
* INC # C7: 1,2,5,6 => UNS
* INC # E3: 3,9 => UNS
* INC # E3: 1,8 => UNS
* CNT   4 HDP CHAINS /   4 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C7: 3,9 => UNS
* INC # C7: 1,2,5,6 => UNS
* INC # E3: 3,9 => UNS
* INC # E3: 1,8 => UNS
* INC # C7: 3,9 # B9: 3,9 => UNS
* INC # C7: 3,9 # C9: 3,9 => UNS
* INC # C7: 3,9 # C6: 3,9 => UNS
* INC # C7: 3,9 # C6: 2,5,7 => UNS
* DIS # C7: 3,9 # A7: 5,6 => CTR => A7: 1,2
* INC # C7: 3,9 + A7: 1,2 # H1: 1,6 => UNS
* INC # C7: 3,9 + A7: 1,2 # H1: 3,4 => UNS
* INC # C7: 3,9 + A7: 1,2 # I1: 2,6 => UNS
* INC # C7: 3,9 + A7: 1,2 # I1: 4,5 => UNS
* INC # C7: 3,9 + A7: 1,2 # D6: 2,4 => UNS
* INC # C7: 3,9 + A7: 1,2 # D6: 8 => UNS
* INC # C7: 3,9 + A7: 1,2 # B4: 2,4 => UNS
* INC # C7: 3,9 + A7: 1,2 # B4: 1,3,5 => UNS
* INC # C7: 3,9 + A7: 1,2 # D2: 2,4 => UNS
* INC # C7: 3,9 + A7: 1,2 # D2: 8,9 => UNS
* INC # C7: 3,9 + A7: 1,2 # A3: 1,2 => UNS
* INC # C7: 3,9 + A7: 1,2 # A3: 3,5 => UNS
* INC # C7: 3,9 + A7: 1,2 # B9: 3,9 => UNS
* DIS # C7: 3,9 + A7: 1,2 # C9: 3,9 => CTR => C9: 1,8
* INC # C7: 3,9 + A7: 1,2 + C9: 1,8 # B9: 3,9 => UNS
* INC # C7: 3,9 + A7: 1,2 + C9: 1,8 # B9: 1,4 => UNS
* INC # C7: 3,9 + A7: 1,2 + C9: 1,8 # C6: 3,9 => UNS
* INC # C7: 3,9 + A7: 1,2 + C9: 1,8 # C6: 2,5,7 => UNS
* INC # C7: 3,9 + A7: 1,2 + C9: 1,8 # E8: 7,8 => UNS
* INC # C7: 3,9 + A7: 1,2 + C9: 1,8 # F9: 7,8 => UNS
* PRF # C7: 3,9 + A7: 1,2 + C9: 1,8 # F5: 7,8 => SOL
* STA # C7: 3,9 + A7: 1,2 + C9: 1,8 + F5: 7,8
* CNT  30 HDP CHAINS /  31 HYP OPENED