Analysis of xx-mith-te3-00006468-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: ....56..9..6...1.37.8.....42...978.6..9......8.7..59.2..596....6.2.78.9....5.2... initial

Autosolve

position: ....56..9..6...1.37.8.....42...978.6.69......8.76.59.2..596....6.2.78.9.9..5.2... autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:07.840522

The following important HDP chains were detected:

* PRF # B2: 4,5 # B4: 1,3 => SOL
* STA # B2: 4,5 + B4: 1,3
* CNT   1 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

`....56..9..6...1.37.8.....42...978.6..9......8.7..59.2..596....6.2.78.9....5.2...`	initial
`....56..9..6...1.37.8.....42...978.6.69......8.76.59.2..596....6.2.78.9.9..5.2...`	autosolve
`123456789456789123798213564214397856569821437837645912385964271642178395971532648`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A2: 4,5
F2: 4,9
G1: 2,7
D5: 2,8
E5: 2,8
B7: 7,8
B9: 7,8
I8: 1,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,E5: 2.. / D5 = 2  => 14 pairs (_) / E5 = 2  =>  7 pairs (_)
G7,H7: 2.. / G7 = 2  =>  9 pairs (_) / H7 = 2  => 10 pairs (_)
B4,A5: 5.. / B4 = 5  =>  9 pairs (_) / A5 = 5  => 13 pairs (_)
G8,I8: 5.. / G8 = 5  => 11 pairs (_) / I8 = 5  =>  9 pairs (_)
B4,H4: 5.. / B4 = 5  =>  9 pairs (_) / H4 = 5  => 13 pairs (_)
A2,A5: 5.. / A2 = 5  =>  9 pairs (_) / A5 = 5  => 13 pairs (_)
I5,I8: 5.. / I5 = 5  => 11 pairs (_) / I8 = 5  =>  9 pairs (_)
G3,H3: 6.. / G3 = 6  =>  7 pairs (_) / H3 = 6  =>  9 pairs (_)
G9,H9: 6.. / G9 = 6  =>  9 pairs (_) / H9 = 6  =>  7 pairs (_)
G3,G9: 6.. / G3 = 6  =>  7 pairs (_) / G9 = 6  =>  9 pairs (_)
H3,H9: 6.. / H3 = 6  =>  9 pairs (_) / H9 = 6  =>  7 pairs (_)
D1,D2: 7.. / D1 = 7  => 10 pairs (_) / D2 = 7  =>  8 pairs (_)
B7,B9: 7.. / B7 = 7  =>  7 pairs (_) / B9 = 7  =>  7 pairs (_)
D2,H2: 7.. / D2 = 7  =>  8 pairs (_) / H2 = 7  => 10 pairs (_)
H1,H2: 8.. / H1 = 8  =>  8 pairs (_) / H2 = 8  => 12 pairs (_)
D5,E5: 8.. / D5 = 8  =>  7 pairs (_) / E5 = 8  => 14 pairs (_)
B7,B9: 8.. / B7 = 8  =>  7 pairs (_) / B9 = 8  =>  7 pairs (_)
I7,I9: 8.. / I7 = 8  =>  7 pairs (_) / I9 = 8  =>  7 pairs (_)
D1,H1: 8.. / D1 = 8  => 12 pairs (_) / H1 = 8  =>  8 pairs (_)
B7,I7: 8.. / B7 = 8  =>  7 pairs (_) / I7 = 8  =>  7 pairs (_)
B9,I9: 8.. / B9 = 8  =>  7 pairs (_) / I9 = 8  =>  7 pairs (_)
E2,E5: 8.. / E2 = 8  =>  7 pairs (_) / E5 = 8  => 14 pairs (_)
B2,B3: 9.. / B2 = 9  => 12 pairs (_) / B3 = 9  => 11 pairs (_)
F2,F3: 9.. / F2 = 9  => 11 pairs (_) / F3 = 9  => 12 pairs (_)
B2,F2: 9.. / B2 = 9  => 12 pairs (_) / F2 = 9  => 11 pairs (_)
B3,F3: 9.. / B3 = 9  => 11 pairs (_) / F3 = 9  => 12 pairs (_)
* DURATION: 0:00:08.095896  START: 03:31:45.728002  END: 03:31:53.823898 2025-04-06
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:07.707933  START: 03:32:01.336939  END: 03:32:09.044872 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00006468-base-pr-002.dot
* REASONING
* PRF # B2: 4,5 # B4: 1,3 => SOL
* STA # B2: 4,5 + B4: 1,3
* CNT   1 HDP CHAINS /  31 HYP OPENED

Header Info

rating: 1343; r2: 343840; index: 6468

Solution

position: 123456789456789123798213564214397856569821437837645912385964271642178395971532648 solved

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 # B2: 4,5 => UNS
* INC # B2: 2,9 => UNS
* INC # A5: 4,5 => UNS
* INC # A5: 1,3 => UNS
* INC # B2: 4,9 => UNS
* INC # B2: 2,5 => UNS
* INC # H1: 2,7 => UNS
* INC # H2: 2,7 => UNS
* INC # D1: 2,7 => UNS
* INC # D1: 1,3,4,8 => UNS
* INC # G7: 2,7 => UNS
* INC # G7: 3,4 => UNS
* INC # D1: 2,8 => UNS
* INC # D2: 2,8 => UNS
* INC # E2: 2,8 => UNS
* INC # E2: 4 => UNS
* INC # I7: 7,8 => UNS
* INC # I7: 1 => UNS
* INC # I9: 7,8 => UNS
* INC # I9: 1 => UNS
* INC # I5: 1,5 => UNS
* INC # I5: 7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,5 => UNS
* INC # B2: 2,9 => UNS
* INC # A5: 4,5 => UNS
* INC # A5: 1,3 => UNS
* INC # B2: 4,9 => UNS
* INC # B2: 2,5 => UNS
* INC # H1: 2,7 => UNS
* INC # H2: 2,7 => UNS
* INC # D1: 2,7 => UNS
* INC # D1: 1,3,4,8 => UNS
* INC # G7: 2,7 => UNS
* INC # G7: 3,4 => UNS
* INC # D1: 2,8 => UNS
* INC # D2: 2,8 => UNS
* INC # E2: 2,8 => UNS
* INC # E2: 4 => UNS
* INC # I7: 7,8 => UNS
* INC # I7: 1 => UNS
* INC # I9: 7,8 => UNS
* INC # I9: 1 => UNS
* INC # I5: 1,5 => UNS
* INC # I5: 7 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,5 => UNS
* INC # B2: 2,9 => UNS
* INC # A5: 4,5 => UNS
* INC # A5: 1,3 => UNS
* INC # B2: 4,9 => UNS
* INC # B2: 2,5 => UNS
* INC # H1: 2,7 => UNS
* INC # H2: 2,7 => UNS
* INC # D1: 2,7 => UNS
* INC # D1: 1,3,4,8 => UNS
* INC # G7: 2,7 => UNS
* INC # G7: 3,4 => UNS
* INC # D1: 2,8 => UNS
* INC # D2: 2,8 => UNS
* INC # E2: 2,8 => UNS
* INC # E2: 4 => UNS
* INC # I7: 7,8 => UNS
* INC # I7: 1 => UNS
* INC # I9: 7,8 => UNS
* INC # I9: 1 => UNS
* INC # I5: 1,5 => UNS
* INC # I5: 7 => UNS
* INC # B2: 4,5 # A5: 1,3 => UNS
* INC # B2: 4,5 # A7: 1,3 => UNS
* INC # B2: 4,5 # C4: 1,3 => UNS
* INC # B2: 4,5 # C9: 1,3 => UNS
* INC # B2: 4,5 # A5: 4,5 => UNS
* INC # B2: 4,5 # A5: 1,3 => UNS
* INC # B2: 4,5 # B4: 4,5 => UNS
* PRF # B2: 4,5 # B4: 1,3 => SOL
* STA # B2: 4,5 + B4: 1,3
* CNT  30 HDP CHAINS /  31 HYP OPENED