Analysis of xx-mith-te3-00153274-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .23.5....4.7...2.6.89......2...7.16....6...7.7...1.5.4..1.426.7........5.7.56..1. initial

Autosolve

position: .23.5....4.7...2.6.89......2...7.16....6...7.7...1.5.4..1.426.7........5.7.56..1. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # F3: 1,3 => CTR => F3: 4,6,7
* CNT   1 HDP CHAINS /  21 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 # F3: 1,3 => CTR => F3: 4,6,7
* STA F3: 4,6,7
* CNT   1 HDP CHAINS /  44 HYP OPENED

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

Pair Reduction Position

position: .23.5....4.7...2.6.89......2...7.16....6...7.7...1.5.4..1.426.7........5.7.56..1. pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:14.121024

The following important HDP chains were detected:

* PRF # F1: 1,6 # I5: 8,9 => SOL
* STA # F1: 1,6 + I5: 8,9
* CNT   1 HDP CHAINS /  67 HYP OPENED

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

Details

Positions

.23.5....4.7...2.6.89......2...7.16....6...7.7...1.5.4..1.426.7........5.7.56..1. initial
.23.5....4.7...2.6.89......2...7.16....6...7.7...1.5.4..1.426.7........5.7.56..1. autosolve
.23.5....4.7...2.6.89......2...7.16....6...7.7...1.5.4..1.426.7........5.7.56..1. pair_reduction
123456789457189236689237451248975163315624978796318524531842697862791345974563812 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A1: 1,6
B2: 1,5
E3: 2,3
I3: 1,3
C6: 6,8
B8: 4,6
C9: 2,4
D8: 1,7
F8: 1,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I1,I3: 1.. / I1 = 1  => 12 pairs (_) / I3 = 1  => 10 pairs (_)
A5,B5: 1.. / A5 = 1  => 11 pairs (_) / B5 = 1  => 13 pairs (_)
D8,F8: 1.. / D8 = 1  =>  7 pairs (_) / F8 = 1  => 11 pairs (_)
B2,B5: 1.. / B2 = 1  => 11 pairs (_) / B5 = 1  => 13 pairs (_)
D3,E3: 2.. / D3 = 2  => 12 pairs (_) / E3 = 2  =>  9 pairs (_)
E5,D6: 2.. / E5 = 2  => 12 pairs (_) / D6 = 2  =>  9 pairs (_)
I5,H6: 2.. / I5 = 2  =>  9 pairs (_) / H6 = 2  => 12 pairs (_)
C8,C9: 2.. / C8 = 2  => 12 pairs (_) / C9 = 2  =>  9 pairs (_)
H8,I9: 2.. / H8 = 2  =>  9 pairs (_) / I9 = 2  => 12 pairs (_)
E5,I5: 2.. / E5 = 2  => 12 pairs (_) / I5 = 2  =>  9 pairs (_)
D6,H6: 2.. / D6 = 2  =>  9 pairs (_) / H6 = 2  => 12 pairs (_)
C8,H8: 2.. / C8 = 2  => 12 pairs (_) / H8 = 2  =>  9 pairs (_)
C9,I9: 2.. / C9 = 2  =>  9 pairs (_) / I9 = 2  => 12 pairs (_)
D3,D6: 2.. / D3 = 2  => 12 pairs (_) / D6 = 2  =>  9 pairs (_)
E3,E5: 2.. / E3 = 2  =>  9 pairs (_) / E5 = 2  => 12 pairs (_)
H6,H8: 2.. / H6 = 2  => 12 pairs (_) / H8 = 2  =>  9 pairs (_)
I5,I9: 2.. / I5 = 2  =>  9 pairs (_) / I9 = 2  => 12 pairs (_)
C9,G9: 4.. / C9 = 4  => 12 pairs (_) / G9 = 4  =>  9 pairs (_)
B2,A3: 5.. / B2 = 5  => 13 pairs (_) / A3 = 5  => 11 pairs (_)
H2,H3: 5.. / H2 = 5  => 11 pairs (_) / H3 = 5  => 13 pairs (_)
C4,C5: 5.. / C4 = 5  => 11 pairs (_) / C5 = 5  => 10 pairs (_)
F4,F5: 5.. / F4 = 5  => 10 pairs (_) / F5 = 5  => 11 pairs (_)
A7,B7: 5.. / A7 = 5  => 13 pairs (_) / B7 = 5  => 11 pairs (_)
B2,H2: 5.. / B2 = 5  => 13 pairs (_) / H2 = 5  => 11 pairs (_)
A3,H3: 5.. / A3 = 5  => 11 pairs (_) / H3 = 5  => 13 pairs (_)
C4,F4: 5.. / C4 = 5  => 11 pairs (_) / F4 = 5  => 10 pairs (_)
C5,F5: 5.. / C5 = 5  => 10 pairs (_) / F5 = 5  => 11 pairs (_)
A3,A7: 5.. / A3 = 5  => 11 pairs (_) / A7 = 5  => 13 pairs (_)
B2,B7: 5.. / B2 = 5  => 13 pairs (_) / B7 = 5  => 11 pairs (_)
A1,A3: 6.. / A1 = 6  =>  9 pairs (_) / A3 = 6  => 11 pairs (_)
F1,F3: 6.. / F1 = 6  => 11 pairs (_) / F3 = 6  =>  9 pairs (_)
B6,C6: 6.. / B6 = 6  => 12 pairs (_) / C6 = 6  => 11 pairs (_)
B8,C8: 6.. / B8 = 6  => 11 pairs (_) / C8 = 6  => 12 pairs (_)
A1,F1: 6.. / A1 = 6  =>  9 pairs (_) / F1 = 6  => 11 pairs (_)
A3,F3: 6.. / A3 = 6  => 11 pairs (_) / F3 = 6  =>  9 pairs (_)
B6,B8: 6.. / B6 = 6  => 12 pairs (_) / B8 = 6  => 11 pairs (_)
C6,C8: 6.. / C6 = 6  => 11 pairs (_) / C8 = 6  => 12 pairs (_)
G1,G3: 7.. / G1 = 7  => 10 pairs (_) / G3 = 7  =>  9 pairs (_)
D8,F8: 7.. / D8 = 7  => 11 pairs (_) / F8 = 7  =>  7 pairs (_)
* DURATION: 0:00:11.732138  START: 15:11:40.033834  END: 15:11:51.765972 2025-04-05
* CP COUNT: (39)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:13.924070  START: 15:12:02.429690  END: 15:12:16.353760 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00153274-base-pr-002.dot
* REASONING
* PRF # F1: 1,6 # I5: 8,9 => SOL
* STA # F1: 1,6 + I5: 8,9
* CNT   1 HDP CHAINS /  67 HYP OPENED

Header Info

rating: 42169; r2: 756307; index: 153274

Solution

position: 123456789457189236689237451248975163315624978796318524531842697862791345974563812 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 # A3: 1,6 => UNS
* INC # A3: 5 => UNS
* INC # F1: 1,6 => UNS
* INC # F1: 4,7,8,9 => UNS
* INC # A3: 1,5 => UNS
* INC # A3: 6 => UNS
* INC # D3: 2,3 => UNS
* INC # D3: 1,4,7 => UNS
* INC # E5: 2,3 => UNS
* INC # E5: 8,9 => UNS
* INC # D3: 1,3 => UNS
* DIS # F3: 1,3 => CTR => F3: 4,6,7
* INC # F3: 4,6,7 => UNS
* INC # C8: 4,6 => UNS
* INC # C8: 2 => UNS
* INC # C8: 2,4 => UNS
* INC # C8: 6 => UNS
* INC # D1: 1,7 => UNS
* INC # D3: 1,7 => UNS
* INC # F1: 1,7 => UNS
* INC # F3: 1,7 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,6 => UNS
* INC # A3: 5 => UNS
* INC # F1: 1,6 => UNS
* INC # F1: 4,7,8,9 => UNS
* INC # A3: 1,5 => UNS
* INC # A3: 6 => UNS
* INC # D3: 2,3 => UNS
* INC # D3: 1,4,7 => UNS
* INC # E5: 2,3 => UNS
* INC # E5: 8,9 => UNS
* INC # D3: 1,3 => UNS
* DIS # F3: 1,3 => CTR => F3: 4,6,7
* INC F3: 4,6,7 # D3: 1,3 => UNS
* INC F3: 4,6,7 # D3: 2,4,7 => UNS
* INC F3: 4,6,7 # D3: 1,3 => UNS
* INC F3: 4,6,7 # D3: 2,4,7 => UNS
* INC F3: 4,6,7 # C8: 4,6 => UNS
* INC F3: 4,6,7 # C8: 2 => UNS
* INC F3: 4,6,7 # C8: 2,4 => UNS
* INC F3: 4,6,7 # C8: 6 => UNS
* INC F3: 4,6,7 # D1: 1,7 => UNS
* INC F3: 4,6,7 # D3: 1,7 => UNS
* INC F3: 4,6,7 # F1: 1,7 => UNS
* INC F3: 4,6,7 # F1: 4,6,8,9 => UNS
* INC F3: 4,6,7 # A3: 1,6 => UNS
* INC F3: 4,6,7 # A3: 5 => UNS
* INC F3: 4,6,7 # F1: 1,6 => UNS
* INC F3: 4,6,7 # F1: 4,7,8,9 => UNS
* INC F3: 4,6,7 # A3: 1,5 => UNS
* INC F3: 4,6,7 # A3: 6 => UNS
* INC F3: 4,6,7 # D3: 2,3 => UNS
* INC F3: 4,6,7 # D3: 1,4,7 => UNS
* INC F3: 4,6,7 # E5: 2,3 => UNS
* INC F3: 4,6,7 # E5: 8,9 => UNS
* INC F3: 4,6,7 # D3: 1,3 => UNS
* INC F3: 4,6,7 # D3: 2,4,7 => UNS
* INC F3: 4,6,7 # C8: 4,6 => UNS
* INC F3: 4,6,7 # C8: 2 => UNS
* INC F3: 4,6,7 # C8: 2,4 => UNS
* INC F3: 4,6,7 # C8: 6 => UNS
* INC F3: 4,6,7 # D1: 1,7 => UNS
* INC F3: 4,6,7 # D3: 1,7 => UNS
* INC F3: 4,6,7 # F1: 1,7 => UNS
* INC F3: 4,6,7 # F1: 4,6,8,9 => UNS
* STA F3: 4,6,7
* CNT  44 HDP CHAINS /  44 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 1,6 => UNS
* INC # A3: 5 => UNS
* INC # F1: 1,6 => UNS
* INC # F1: 4,7,8,9 => UNS
* INC # A3: 1,5 => UNS
* INC # A3: 6 => UNS
* INC # D3: 2,3 => UNS
* INC # D3: 1,4,7 => UNS
* INC # E5: 2,3 => UNS
* INC # E5: 8,9 => UNS
* INC # D3: 1,3 => UNS
* INC # D3: 2,4,7 => UNS
* INC # C8: 4,6 => UNS
* INC # C8: 2 => UNS
* INC # C8: 2,4 => UNS
* INC # C8: 6 => UNS
* INC # D1: 1,7 => UNS
* INC # D3: 1,7 => UNS
* INC # F1: 1,7 => UNS
* INC # F1: 4,6,8,9 => UNS
* INC # A3: 1,6 # D3: 2,3 => UNS
* INC # A3: 1,6 # D3: 4,7 => UNS
* INC # A3: 1,6 # E5: 2,3 => UNS
* INC # A3: 1,6 # E5: 8,9 => UNS
* INC # A3: 1,6 # B4: 3,9 => UNS
* INC # A3: 1,6 # B6: 3,9 => UNS
* INC # A3: 1,6 # E5: 3,9 => UNS
* INC # A3: 1,6 # G5: 3,9 => UNS
* INC # A3: 1,6 # I5: 3,9 => UNS
* INC # A3: 1,6 # A8: 3,9 => UNS
* INC # A3: 1,6 # A9: 3,9 => UNS
* INC # A3: 1,6 # C4: 4,5 => UNS
* INC # A3: 1,6 # C4: 8 => UNS
* INC # A3: 1,6 # F4: 4,5 => UNS
* INC # A3: 1,6 # F4: 3,8,9 => UNS
* INC # A3: 1,6 # A8: 3,9 => UNS
* INC # A3: 1,6 # A9: 3,9 => UNS
* INC # A3: 1,6 # D7: 3,9 => UNS
* INC # A3: 1,6 # H7: 3,9 => UNS
* INC # A3: 1,6 # B4: 3,9 => UNS
* INC # A3: 1,6 # B6: 3,9 => UNS
* INC # A3: 1,6 # C8: 4,6 => UNS
* INC # A3: 1,6 # C8: 2 => UNS
* INC # A3: 1,6 # C8: 2,4 => UNS
* INC # A3: 1,6 # C8: 6 => UNS
* INC # A3: 1,6 => UNS
* INC # A3: 5 # D1: 1,7 => UNS
* INC # A3: 5 # D3: 1,7 => UNS
* INC # A3: 5 # C4: 4,5 => UNS
* INC # A3: 5 # C4: 8 => UNS
* INC # A3: 5 # C5: 4,5 => UNS
* INC # A3: 5 # C5: 8 => UNS
* INC # A3: 5 # D1: 1,7 => UNS
* INC # A3: 5 # D3: 1,7 => UNS
* INC # A3: 5 => UNS
* INC # F1: 1,6 # D3: 2,3 => UNS
* INC # F1: 1,6 # D3: 4,7 => UNS
* INC # F1: 1,6 # E5: 2,3 => UNS
* INC # F1: 1,6 # E5: 8,9 => UNS
* INC # F1: 1,6 # G1: 8,9 => UNS
* INC # F1: 1,6 # H1: 8,9 => UNS
* INC # F1: 1,6 # H2: 8,9 => UNS
* INC # F1: 1,6 # D1: 8,9 => UNS
* INC # F1: 1,6 # D1: 4,7 => UNS
* INC # F1: 1,6 # I4: 8,9 => UNS
* PRF # F1: 1,6 # I5: 8,9 => SOL
* STA # F1: 1,6 + I5: 8,9
* CNT  66 HDP CHAINS /  67 HYP OPENED