Analysis of xx-mith-te3-00091516-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1.3...789.56...1.27.9..1......19.8.....8.79.49...24.17..4.1827.......4....2....9. initial

Autosolve

position: 1.3...789.56...1.27.9..1......19.8.....8.79.49...24.17..4.1827.......4....2....9. 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: 0:00:09.439032

The following important HDP chains were detected:

* DIS # B3: 8 # F4: 5,6 => CTR => F4: 3
* PRF # B3: 8 + F4: 3 => SOL
* STA B3: 8
* CNT   2 HDP CHAINS /  49 HYP OPENED

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

Details

Positions

`1.3...789.56...1.27.9..1......19.8.....8.79.49...24.17..4.1827.......4....2....9.`	initial
`1.3...789.56...1.27.9..1......19.8.....8.79.49...24.17..4.1827.......4....2....9.`	autosolve
`123456789456789132789231546247193865315867924968524317594618273631972458872345691`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B1: 2,4
A2: 4,8
F2: 3,9
H2: 3,4
C4: 5,7
C5: 1,5
C6: 5,8
I8: 1,8
I9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C5: 1.. / B5 = 1  =>  6 pairs (_) / C5 = 1  =>  9 pairs (_)
I8,I9: 1.. / I8 = 1  =>  9 pairs (_) / I9 = 1  =>  7 pairs (_)
B9,I9: 1.. / B9 = 1  =>  9 pairs (_) / I9 = 1  =>  7 pairs (_)
C5,C8: 1.. / C5 = 1  =>  9 pairs (_) / C8 = 1  =>  6 pairs (_)
B1,B3: 2.. / B1 = 2  => 11 pairs (_) / B3 = 2  => 15 pairs (_)
A4,A5: 2.. / A4 = 2  => 17 pairs (_) / A5 = 2  =>  9 pairs (_)
H4,H5: 2.. / H4 = 2  =>  9 pairs (_) / H5 = 2  => 17 pairs (_)
D8,F8: 2.. / D8 = 2  => 10 pairs (_) / F8 = 2  =>  9 pairs (_)
B3,D3: 2.. / B3 = 2  => 15 pairs (_) / D3 = 2  => 11 pairs (_)
A4,H4: 2.. / A4 = 2  => 17 pairs (_) / H4 = 2  =>  9 pairs (_)
A5,H5: 2.. / A5 = 2  =>  9 pairs (_) / H5 = 2  => 17 pairs (_)
F1,F8: 2.. / F1 = 2  => 10 pairs (_) / F8 = 2  =>  9 pairs (_)
H2,H3: 4.. / H2 = 4  => 15 pairs (_) / H3 = 4  => 14 pairs (_)
A4,B4: 4.. / A4 = 4  => 14 pairs (_) / B4 = 4  => 14 pairs (_)
D9,E9: 4.. / D9 = 4  => 10 pairs (_) / E9 = 4  => 11 pairs (_)
A2,A4: 4.. / A2 = 4  => 14 pairs (_) / A4 = 4  => 14 pairs (_)
D2,E2: 7.. / D2 = 7  =>  8 pairs (_) / E2 = 7  => 13 pairs (_)
B4,C4: 7.. / B4 = 7  => 16 pairs (_) / C4 = 7  =>  8 pairs (_)
C4,C8: 7.. / C4 = 7  =>  8 pairs (_) / C8 = 7  => 16 pairs (_)
A2,B3: 8.. / A2 = 8  => 14 pairs (_) / B3 = 8  => 14 pairs (_)
E2,E3: 8.. / E2 = 8  => 14 pairs (_) / E3 = 8  => 14 pairs (_)
B6,C6: 8.. / B6 = 8  => 12 pairs (_) / C6 = 8  =>  9 pairs (_)
I8,I9: 8.. / I8 = 8  =>  7 pairs (_) / I9 = 8  =>  9 pairs (_)
A2,E2: 8.. / A2 = 8  => 14 pairs (_) / E2 = 8  => 14 pairs (_)
B3,E3: 8.. / B3 = 8  => 14 pairs (_) / E3 = 8  => 14 pairs (_)
C6,C8: 8.. / C6 = 8  =>  9 pairs (_) / C8 = 8  => 12 pairs (_)
D2,F2: 9.. / D2 = 9  => 10 pairs (_) / F2 = 9  =>  8 pairs (_)
B7,B8: 9.. / B7 = 9  => 11 pairs (_) / B8 = 9  =>  0 pairs (X)
B7,D7: 9.. / B7 = 9  => 11 pairs (_) / D7 = 9  =>  0 pairs (X)
F2,F8: 9.. / F2 = 9  =>  8 pairs (_) / F8 = 9  => 10 pairs (_)
* DURATION: 0:00:08.619688  START: 23:30:05.511683  END: 23:30:14.131371 2025-04-04
* CP COUNT: (30)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:09.276679  START: 23:30:22.189997  END: 23:30:31.466676 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00091516-base-pr-002.dot
* REASONING
* DIS # B3: 8 # F4: 5,6 => CTR => F4: 3
* PRF # B3: 8 + F4: 3 => SOL
* STA B3: 8
* CNT   2 HDP CHAINS /  49 HYP OPENED

Header Info

rating: 23013; r2: 462079; index: 91516

Solution

position: 123456789456789132789231546247193865315867924968524317594618273631972458872345691 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 # B3: 2,4 => UNS
* INC # B3: 8 => UNS
* INC # D1: 2,4 => UNS
* INC # D1: 5,6 => UNS
* INC # B3: 4,8 => UNS
* INC # B3: 2 => UNS
* INC # E2: 4,8 => UNS
* INC # E2: 3,7 => UNS
* INC # D2: 3,9 => UNS
* INC # D2: 4,7 => UNS
* INC # F8: 3,9 => UNS
* INC # F8: 2,5,6 => UNS
* INC # H3: 3,4 => UNS
* INC # H3: 5,6 => UNS
* INC # D2: 3,4 => UNS
* INC # E2: 3,4 => UNS
* INC # C8: 5,7 => UNS
* INC # C8: 1,8 => UNS
* INC # C8: 1,5 => UNS
* INC # C8: 7,8 => UNS
* INC # C8: 5,8 => UNS
* INC # C8: 1,7 => UNS
* INC # B8: 1,8 => UNS
* INC # C8: 1,8 => UNS
* INC # B9: 1,8 => UNS
* INC # B9: 3,6,7 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B3: 2,4 => UNS
* INC # B3: 8 => UNS
* INC # D1: 2,4 => UNS
* INC # D1: 5,6 => UNS
* INC # B3: 4,8 => UNS
* INC # B3: 2 => UNS
* INC # E2: 4,8 => UNS
* INC # E2: 3,7 => UNS
* INC # D2: 3,9 => UNS
* INC # D2: 4,7 => UNS
* INC # F8: 3,9 => UNS
* INC # F8: 2,5,6 => UNS
* INC # H3: 3,4 => UNS
* INC # H3: 5,6 => UNS
* INC # D2: 3,4 => UNS
* INC # E2: 3,4 => UNS
* INC # C8: 5,7 => UNS
* INC # C8: 1,8 => UNS
* INC # C8: 1,5 => UNS
* INC # C8: 7,8 => UNS
* INC # C8: 5,8 => UNS
* INC # C8: 1,7 => UNS
* INC # B8: 1,8 => UNS
* INC # C8: 1,8 => UNS
* INC # B9: 1,8 => UNS
* INC # B9: 3,6,7 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B3: 2,4 => UNS
* INC # B3: 8 => UNS
* INC # D1: 2,4 => UNS
* INC # D1: 5,6 => UNS
* INC # B3: 4,8 => UNS
* INC # B3: 2 => UNS
* INC # E2: 4,8 => UNS
* INC # E2: 3,7 => UNS
* INC # D2: 3,9 => UNS
* INC # D2: 4,7 => UNS
* INC # F8: 3,9 => UNS
* INC # F8: 2,5,6 => UNS
* INC # H3: 3,4 => UNS
* INC # H3: 5,6 => UNS
* INC # D2: 3,4 => UNS
* INC # E2: 3,4 => UNS
* INC # C8: 5,7 => UNS
* INC # C8: 1,8 => UNS
* INC # C8: 1,5 => UNS
* INC # C8: 7,8 => UNS
* INC # C8: 5,8 => UNS
* INC # C8: 1,7 => UNS
* INC # B8: 1,8 => UNS
* INC # C8: 1,8 => UNS
* INC # B9: 1,8 => UNS
* INC # B9: 3,6,7 => UNS
* INC # B3: 2,4 # D1: 2,4 => UNS
* INC # B3: 2,4 # D1: 5,6 => UNS
* INC # B3: 2,4 # D3: 2,4 => UNS
* INC # B3: 2,4 # D3: 3 => UNS
* INC # B3: 2,4 # D2: 3,9 => UNS
* INC # B3: 2,4 # D2: 4,7 => UNS
* INC # B3: 2,4 # H3: 3,4 => UNS
* INC # B3: 2,4 # H3: 5,6 => UNS
* INC # B3: 2,4 # D2: 3,4 => UNS
* INC # B3: 2,4 # E2: 3,4 => UNS
* INC # B3: 2,4 # B8: 1,8 => UNS
* INC # B3: 2,4 # C8: 1,8 => UNS
* INC # B3: 2,4 # D2: 4,7 => UNS
* INC # B3: 2,4 # D2: 3,9 => UNS
* INC # B3: 2,4 # E2: 4,7 => UNS
* INC # B3: 2,4 # E2: 3 => UNS
* INC # B3: 2,4 # B8: 1,8 => UNS
* INC # B3: 2,4 # C8: 1,8 => UNS
* INC # B3: 2,4 => UNS
* INC # B3: 8 # D1: 5,6 => UNS
* INC # B3: 8 # E1: 5,6 => UNS
* DIS # B3: 8 # F4: 5,6 => CTR => F4: 3
* PRF # B3: 8 + F4: 3 => SOL
* STA B3: 8
* CNT  49 HDP CHAINS /  49 HYP OPENED