Analysis of xx-mith-te3-00041809-base.sdk

Contents

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

Original Sudoku

level: hard

position: ....56..9..6...13.7.9...4..2.7.65.9..6.......9..87.62...562....6..5.8...8.2.97... initial

Autosolve

position: ....56..9..6...13.7.9...4..2.7.65.9..6.......9..87.62...562....6..5.8...8.2.97... 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: 0:00:05.617000

The following important HDP chains were detected:

* DIS # B2: 4,5 # A5: 1,3 => CTR => A5: 4,5
* DIS # B2: 4,5 + A5: 4,5 # C6: 1,3 => CTR => C6: 4
* PRF # B2: 4,5 + A5: 4,5 + C6: 4 => SOL
* STA B2: 4,5
* CNT   3 HDP CHAINS /  32 HYP OPENED

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

Details

Positions

`....56..9..6...13.7.9...4..2.7.65.9..6.......9..87.62...562....6..5.8...8.2.97...`	initial
`....56..9..6...13.7.9...4..2.7.65.9..6.......9..87.62...562....6..5.8...8.2.97...`	autosolve
`123456789456789132789213456217365894568942371934871625375624918691538247842197563`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A2: 4,5
E2: 4,8
H1: 7,8
D5: 2,9
F5: 2,9
G4: 3,8
B7: 7,9
B8: 7,9
G9: 3,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,F5: 2.. / D5 = 2  => 11 pairs (_) / F5 = 2  =>  8 pairs (_)
G8,I8: 2.. / G8 = 2  =>  9 pairs (_) / I8 = 2  =>  9 pairs (_)
G1,G8: 2.. / G1 = 2  =>  9 pairs (_) / G8 = 2  =>  9 pairs (_)
A5,B6: 5.. / A5 = 5  => 11 pairs (_) / B6 = 5  => 10 pairs (_)
B6,I6: 5.. / B6 = 5  => 10 pairs (_) / I6 = 5  => 11 pairs (_)
A2,A5: 5.. / A2 = 5  => 10 pairs (_) / A5 = 5  => 11 pairs (_)
G5,G9: 5.. / G5 = 5  => 14 pairs (_) / G9 = 5  =>  8 pairs (_)
H3,I3: 6.. / H3 = 6  =>  8 pairs (_) / I3 = 6  => 10 pairs (_)
H9,I9: 6.. / H9 = 6  => 10 pairs (_) / I9 = 6  =>  8 pairs (_)
H3,H9: 6.. / H3 = 6  =>  8 pairs (_) / H9 = 6  => 10 pairs (_)
I3,I9: 6.. / I3 = 6  => 10 pairs (_) / I9 = 6  =>  8 pairs (_)
D1,D2: 7.. / D1 = 7  => 11 pairs (_) / D2 = 7  =>  8 pairs (_)
B7,B8: 7.. / B7 = 7  =>  7 pairs (_) / B8 = 7  =>  8 pairs (_)
D2,I2: 7.. / D2 = 7  =>  8 pairs (_) / I2 = 7  => 11 pairs (_)
E2,E3: 8.. / E2 = 8  => 12 pairs (_) / E3 = 8  => 14 pairs (_)
B4,C5: 8.. / B4 = 8  => 11 pairs (_) / C5 = 8  =>  9 pairs (_)
C1,C5: 8.. / C1 = 8  => 11 pairs (_) / C5 = 8  =>  9 pairs (_)
D2,F2: 9.. / D2 = 9  => 11 pairs (_) / F2 = 9  =>  8 pairs (_)
D5,F5: 9.. / D5 = 9  =>  8 pairs (_) / F5 = 9  => 11 pairs (_)
B7,B8: 9.. / B7 = 9  =>  8 pairs (_) / B8 = 9  =>  7 pairs (_)
G7,G8: 9.. / G7 = 9  =>  7 pairs (_) / G8 = 9  =>  8 pairs (_)
B7,G7: 9.. / B7 = 9  =>  8 pairs (_) / G7 = 9  =>  7 pairs (_)
B8,G8: 9.. / B8 = 9  =>  7 pairs (_) / G8 = 9  =>  8 pairs (_)
D2,D5: 9.. / D2 = 9  => 11 pairs (_) / D5 = 9  =>  8 pairs (_)
F2,F5: 9.. / F2 = 9  =>  8 pairs (_) / F5 = 9  => 11 pairs (_)
* DURATION: 0:00:06.802950  START: 07:55:44.801740  END: 07:55:51.604690 2025-04-06
* CP COUNT: (25)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:05.471216  START: 07:55:59.908698  END: 07:56:05.379914 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00041809-base-pr-002.dot
* REASONING
* DIS # B2: 4,5 # A5: 1,3 => CTR => A5: 4,5
* DIS # B2: 4,5 + A5: 4,5 # C6: 1,3 => CTR => C6: 4
* PRF # B2: 4,5 + A5: 4,5 + C6: 4 => SOL
* STA B2: 4,5
* CNT   3 HDP CHAINS /  32 HYP OPENED

Header Info

rating: 8660; r2: 191037; index: 41809

Solution

position: 123456789456789132789213456217365894568942371934871625375624918691538247842197563 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: 2,8 => UNS
* INC # A5: 4,5 => UNS
* INC # A5: 1,3 => UNS
* INC # B2: 4,8 => UNS
* INC # B2: 2,5 => UNS
* INC # G1: 7,8 => UNS
* INC # I2: 7,8 => UNS
* INC # H5: 7,8 => UNS
* INC # H7: 7,8 => UNS
* INC # D2: 2,9 => UNS
* INC # D2: 4,7 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 4 => UNS
* INC # I4: 3,8 => UNS
* INC # G5: 3,8 => UNS
* INC # I5: 3,8 => UNS
* INC # B4: 3,8 => UNS
* INC # B4: 1,4 => UNS
* INC # G7: 3,8 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 3,8 => UNS
* INC # G8: 7,9 => UNS
* INC # G8: 2,3 => UNS
* INC # I9: 3,5 => UNS
* INC # I9: 1,4,6 => UNS
* INC # G5: 3,5 => UNS
* INC # G5: 7,8 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,5 => UNS
* INC # B2: 2,8 => UNS
* INC # A5: 4,5 => UNS
* INC # A5: 1,3 => UNS
* INC # B2: 4,8 => UNS
* INC # B2: 2,5 => UNS
* INC # G1: 7,8 => UNS
* INC # I2: 7,8 => UNS
* INC # H5: 7,8 => UNS
* INC # H7: 7,8 => UNS
* INC # D2: 2,9 => UNS
* INC # D2: 4,7 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 4 => UNS
* INC # I4: 3,8 => UNS
* INC # G5: 3,8 => UNS
* INC # I5: 3,8 => UNS
* INC # B4: 3,8 => UNS
* INC # B4: 1,4 => UNS
* INC # G7: 3,8 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 3,8 => UNS
* INC # G8: 7,9 => UNS
* INC # G8: 2,3 => UNS
* INC # I9: 3,5 => UNS
* INC # I9: 1,4,6 => UNS
* INC # G5: 3,5 => UNS
* INC # G5: 7,8 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 4,5 => UNS
* INC # B2: 2,8 => UNS
* INC # A5: 4,5 => UNS
* INC # A5: 1,3 => UNS
* INC # B2: 4,8 => UNS
* INC # B2: 2,5 => UNS
* INC # G1: 7,8 => UNS
* INC # I2: 7,8 => UNS
* INC # H5: 7,8 => UNS
* INC # H7: 7,8 => UNS
* INC # D2: 2,9 => UNS
* INC # D2: 4,7 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 4 => UNS
* INC # I4: 3,8 => UNS
* INC # G5: 3,8 => UNS
* INC # I5: 3,8 => UNS
* INC # B4: 3,8 => UNS
* INC # B4: 1,4 => UNS
* INC # G7: 3,8 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 3,8 => UNS
* INC # G8: 7,9 => UNS
* INC # G8: 2,3 => UNS
* INC # I9: 3,5 => UNS
* INC # I9: 1,4,6 => UNS
* INC # G5: 3,5 => UNS
* INC # G5: 7,8 => UNS
* DIS # B2: 4,5 # A5: 1,3 => CTR => A5: 4,5
* DIS # B2: 4,5 + A5: 4,5 # C6: 1,3 => CTR => C6: 4
* PRF # B2: 4,5 + A5: 4,5 + C6: 4 => SOL
* STA B2: 4,5
* CNT  32 HDP CHAINS /  32 HYP OPENED