Analysis of xx-mith-te3-00060533-base.sdk

Contents

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

Original Sudoku

level: hard

position: .23......4..78..3278..3.5.427.....485.....3.7.3...725..4.9..........8.25..261.... initial

Autosolve

position: .23......4..78..3278..3.5.427.....485.....3.7.3...725..4.9..........8.25..261.... 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: 0:00:05.399153

The following important HDP chains were detected:

* PRF # F3: 1,2 # C2: 6,9 => SOL
* STA # F3: 1,2 + C2: 6,9
* CNT   1 HDP CHAINS /  26 HYP OPENED

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

Details

Positions

`.23......4..78..3278..3.5.427.....485.....3.7.3...725..4.9..........8.25..261....`	initial
`.23......4..78..3278..3.5.427.....485.....3.7.3...725..4.9..........8.25..261....`	autosolve
`123456789456789132789231564271593648568124397934867251345972816617348925892615473`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (11)
D3: 1,2
G1: 7,8
H1: 7,8
C5: 4,8
C6: 4,8
C7: 5,7
B9: 5,9
F7: 2,5
D8: 3,4
E8: 4,7
I9: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D3,F3: 2.. / D3 = 2  => 10 pairs (_) / F3 = 2  => 11 pairs (_)
E7,F7: 2.. / E7 = 2  =>  8 pairs (_) / F7 = 2  => 10 pairs (_)
D3,D5: 2.. / D3 = 2  => 10 pairs (_) / D5 = 2  => 11 pairs (_)
E5,E7: 2.. / E5 = 2  => 10 pairs (_) / E7 = 2  =>  8 pairs (_)
D4,F4: 3.. / D4 = 3  => 11 pairs (_) / F4 = 3  => 15 pairs (_)
D8,F9: 3.. / D8 = 3  => 15 pairs (_) / F9 = 3  => 11 pairs (_)
I7,I9: 3.. / I7 = 3  => 14 pairs (_) / I9 = 3  => 14 pairs (_)
A7,I7: 3.. / A7 = 3  => 14 pairs (_) / I7 = 3  => 14 pairs (_)
A8,D8: 3.. / A8 = 3  => 11 pairs (_) / D8 = 3  => 15 pairs (_)
D4,D8: 3.. / D4 = 3  => 11 pairs (_) / D8 = 3  => 15 pairs (_)
F4,F9: 3.. / F4 = 3  => 15 pairs (_) / F9 = 3  => 11 pairs (_)
C5,C6: 4.. / C5 = 4  =>  9 pairs (_) / C6 = 4  => 10 pairs (_)
G8,G9: 4.. / G8 = 4  => 11 pairs (_) / G9 = 4  => 11 pairs (_)
F9,G9: 4.. / F9 = 4  => 11 pairs (_) / G9 = 4  => 11 pairs (_)
B2,C2: 5.. / B2 = 5  => 12 pairs (_) / C2 = 5  => 10 pairs (_)
C7,B9: 5.. / C7 = 5  => 12 pairs (_) / B9 = 5  => 10 pairs (_)
B9,F9: 5.. / B9 = 5  => 10 pairs (_) / F9 = 5  => 12 pairs (_)
B2,B9: 5.. / B2 = 5  => 12 pairs (_) / B9 = 5  => 10 pairs (_)
C2,C7: 5.. / C2 = 5  => 10 pairs (_) / C7 = 5  => 12 pairs (_)
D1,D4: 5.. / D1 = 5  => 12 pairs (_) / D4 = 5  => 16 pairs (_)
G1,H1: 7.. / G1 = 7  => 10 pairs (_) / H1 = 7  => 11 pairs (_)
C7,C8: 7.. / C7 = 7  => 10 pairs (_) / C8 = 7  => 12 pairs (_)
E7,E8: 7.. / E7 = 7  => 12 pairs (_) / E8 = 7  => 10 pairs (_)
G9,H9: 7.. / G9 = 7  => 11 pairs (_) / H9 = 7  => 10 pairs (_)
C7,E7: 7.. / C7 = 7  => 10 pairs (_) / E7 = 7  => 12 pairs (_)
C8,E8: 7.. / C8 = 7  => 12 pairs (_) / E8 = 7  => 10 pairs (_)
G1,G9: 7.. / G1 = 7  => 10 pairs (_) / G9 = 7  => 11 pairs (_)
H1,H9: 7.. / H1 = 7  => 11 pairs (_) / H9 = 7  => 10 pairs (_)
G1,H1: 8.. / G1 = 8  => 11 pairs (_) / H1 = 8  => 10 pairs (_)
C5,C6: 8.. / C5 = 8  => 10 pairs (_) / C6 = 8  =>  9 pairs (_)
D5,D6: 8.. / D5 = 8  =>  9 pairs (_) / D6 = 8  => 10 pairs (_)
A7,A9: 8.. / A7 = 8  => 14 pairs (_) / A9 = 8  => 12 pairs (_)
C5,D5: 8.. / C5 = 8  => 10 pairs (_) / D5 = 8  =>  9 pairs (_)
C6,D6: 8.. / C6 = 8  =>  9 pairs (_) / D6 = 8  => 10 pairs (_)
* DURATION: 0:00:10.499804  START: 17:36:15.428124  END: 17:36:25.927928 2025-04-04
* CP COUNT: (34)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:05.270077  START: 17:36:33.132523  END: 17:36:38.402600 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00060533-base-pr-002.dot
* REASONING
* PRF # F3: 1,2 # C2: 6,9 => SOL
* STA # F3: 1,2 + C2: 6,9
* CNT   1 HDP CHAINS /  26 HYP OPENED

Header Info

rating: 12922; r2: 332962; index: 60533

Solution

position: 123456789456789132789231564271593648568124397934867251345972816617348925892615473 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 # F3: 1,2 => UNS
* INC # F3: 6,9 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 4,8 => UNS
* INC # G9: 7,8 => UNS
* INC # G9: 4,9 => UNS
* INC # H9: 7,8 => UNS
* INC # H9: 9 => UNS
* INC # D5: 4,8 => UNS
* INC # D5: 1,2 => UNS
* INC # D6: 4,8 => UNS
* INC # D6: 1 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 2 => UNS
* INC # B2: 5,9 => UNS
* INC # B2: 1,6 => UNS
* INC # E7: 2,5 => UNS
* INC # E7: 7 => UNS
* INC # F9: 3,4 => UNS
* INC # F9: 5 => UNS
* INC # A9: 3,9 => UNS
* INC # A9: 8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F3: 1,2 => UNS
* INC # F3: 6,9 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 4,8 => UNS
* INC # G9: 7,8 => UNS
* INC # G9: 4,9 => UNS
* INC # H9: 7,8 => UNS
* INC # H9: 9 => UNS
* INC # D5: 4,8 => UNS
* INC # D5: 1,2 => UNS
* INC # D6: 4,8 => UNS
* INC # D6: 1 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 2 => UNS
* INC # B2: 5,9 => UNS
* INC # B2: 1,6 => UNS
* INC # E7: 2,5 => UNS
* INC # E7: 7 => UNS
* INC # F9: 3,4 => UNS
* INC # F9: 5 => UNS
* INC # A9: 3,9 => UNS
* INC # A9: 8 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F3: 1,2 => UNS
* INC # F3: 6,9 => UNS
* INC # D5: 1,2 => UNS
* INC # D5: 4,8 => UNS
* INC # G9: 7,8 => UNS
* INC # G9: 4,9 => UNS
* INC # H9: 7,8 => UNS
* INC # H9: 9 => UNS
* INC # D5: 4,8 => UNS
* INC # D5: 1,2 => UNS
* INC # D6: 4,8 => UNS
* INC # D6: 1 => UNS
* INC # E7: 5,7 => UNS
* INC # E7: 2 => UNS
* INC # B2: 5,9 => UNS
* INC # B2: 1,6 => UNS
* INC # E7: 2,5 => UNS
* INC # E7: 7 => UNS
* INC # F9: 3,4 => UNS
* INC # F9: 5 => UNS
* INC # A9: 3,9 => UNS
* INC # A9: 8 => UNS
* INC # F3: 1,2 # A1: 6,9 => UNS
* INC # F3: 1,2 # B2: 6,9 => UNS
* PRF # F3: 1,2 # C2: 6,9 => SOL
* STA # F3: 1,2 + C2: 6,9
* CNT  25 HDP CHAINS /  26 HYP OPENED