Analysis of xx-mith-te3-00145582-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1.3...789....8.2........4..2.68.1...3...65.2...532....56..183.2.31......8.253.6.1 initial

Autosolve

position: 1.3...789....8.2........4..2.68.1...3...65.2...532....56..183.2.31......8.253.6.1 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: 0:00:07.873596

The following important HDP chains were detected:

* PRF # H4: 5,9 # B5: 4,7 => SOL
* STA # H4: 5,9 + B5: 4,7
* CNT   1 HDP CHAINS /  39 HYP OPENED

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

Details

Positions

`1.3...789....8.2........4..2.68.1...3...65.2...532....56..183.2.31......8.253.6.1`	initial
`1.3...789....8.2........4..2.68.1...3...65.2...532....56..183.2.31......8.253.6.1`	autosolve
`123456789457189236689273415276841953348965127915327864564718392731692548892534671`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
E1: 4,5
G4: 5,9
D8: 2,6
F8: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  4 pairs (_) / D3 = 1  =>  5 pairs (_)
H2,H3: 1.. / H2 = 1  =>  5 pairs (_) / H3 = 1  =>  4 pairs (_)
B5,B6: 1.. / B5 = 1  =>  5 pairs (_) / B6 = 1  =>  6 pairs (_)
G5,G6: 1.. / G5 = 1  =>  6 pairs (_) / G6 = 1  =>  5 pairs (_)
D2,H2: 1.. / D2 = 1  =>  4 pairs (_) / H2 = 1  =>  5 pairs (_)
D3,H3: 1.. / D3 = 1  =>  5 pairs (_) / H3 = 1  =>  4 pairs (_)
B5,G5: 1.. / B5 = 1  =>  5 pairs (_) / G5 = 1  =>  6 pairs (_)
B6,G6: 1.. / B6 = 1  =>  6 pairs (_) / G6 = 1  =>  5 pairs (_)
B1,B3: 2.. / B1 = 2  =>  6 pairs (_) / B3 = 2  =>  9 pairs (_)
D8,F8: 2.. / D8 = 2  =>  3 pairs (_) / F8 = 2  =>  3 pairs (_)
F2,F3: 3.. / F2 = 3  =>  5 pairs (_) / F3 = 3  =>  6 pairs (_)
H4,I4: 3.. / H4 = 3  =>  4 pairs (_) / I4 = 3  =>  8 pairs (_)
E1,E3: 5.. / E1 = 5  =>  5 pairs (_) / E3 = 5  => 10 pairs (_)
B1,E1: 5.. / B1 = 5  => 10 pairs (_) / E1 = 5  =>  5 pairs (_)
G4,G8: 5.. / G4 = 5  =>  4 pairs (_) / G8 = 5  => 12 pairs (_)
A2,A3: 6.. / A2 = 6  =>  6 pairs (_) / A3 = 6  =>  5 pairs (_)
D1,F1: 6.. / D1 = 6  =>  3 pairs (_) / F1 = 6  =>  3 pairs (_)
H6,I6: 6.. / H6 = 6  =>  4 pairs (_) / I6 = 6  => 11 pairs (_)
D8,F8: 6.. / D8 = 6  =>  3 pairs (_) / F8 = 6  =>  3 pairs (_)
D1,D8: 6.. / D1 = 6  =>  3 pairs (_) / D8 = 6  =>  3 pairs (_)
F1,F8: 6.. / F1 = 6  =>  3 pairs (_) / F8 = 6  =>  3 pairs (_)
B3,C3: 8.. / B3 = 8  => 13 pairs (_) / C3 = 8  =>  6 pairs (_)
G8,I8: 8.. / G8 = 8  =>  5 pairs (_) / I8 = 8  => 10 pairs (_)
C3,C5: 8.. / C3 = 8  =>  6 pairs (_) / C5 = 8  => 13 pairs (_)
* DURATION: 0:00:06.226843  START: 22:04:01.272113  END: 22:04:07.498956 2025-04-06
* CP COUNT: (24)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:07.700886  START: 22:04:10.643077  END: 22:04:18.343963 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00145582-base-pr-002.dot
* REASONING
* PRF # H4: 5,9 # B5: 4,7 => SOL
* STA # H4: 5,9 + B5: 4,7
* CNT   1 HDP CHAINS /  39 HYP OPENED

Header Info

rating: 38885; r2: 689274; index: 145582

Solution

position: 123456789457189236689273415276841953348965127915327864564718392731692548892534671 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 # B1: 4,5 => UNS
* INC # B1: 2 => UNS
* INC # H4: 5,9 => UNS
* INC # H4: 3,4,7 => UNS
* INC # G8: 5,9 => UNS
* INC # G8: 8 => UNS
* INC # D1: 2,6 => UNS
* INC # D1: 4 => UNS
* INC # F1: 2,6 => UNS
* INC # F1: 4 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 4,5 => UNS
* INC # B1: 2 => UNS
* INC # H4: 5,9 => UNS
* INC # H4: 3,4,7 => UNS
* INC # G8: 5,9 => UNS
* INC # G8: 8 => UNS
* INC # D1: 2,6 => UNS
* INC # D1: 4 => UNS
* INC # F1: 2,6 => UNS
* INC # F1: 4 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 4,5 => UNS
* INC # B1: 2 => UNS
* INC # H4: 5,9 => UNS
* INC # H4: 3,4,7 => UNS
* INC # G8: 5,9 => UNS
* INC # G8: 8 => UNS
* INC # D1: 2,6 => UNS
* INC # D1: 4 => UNS
* INC # F1: 2,6 => UNS
* INC # F1: 4 => UNS
* INC # B1: 4,5 # B2: 4,5 => UNS
* INC # B1: 4,5 # B2: 7,9 => UNS
* INC # B1: 4,5 # G5: 1,8 => UNS
* INC # B1: 4,5 # G5: 9 => UNS
* INC # B1: 4,5 # G6: 1,8 => UNS
* INC # B1: 4,5 # G6: 9 => UNS
* INC # B1: 4,5 # H4: 5,9 => UNS
* INC # B1: 4,5 # H4: 3,4,7 => UNS
* INC # B1: 4,5 # G8: 5,9 => UNS
* INC # B1: 4,5 # G8: 8 => UNS
* INC # B1: 4,5 => UNS
* INC # B1: 2 # D2: 7,9 => UNS
* INC # B1: 2 # F2: 7,9 => UNS
* INC # B1: 2 # D3: 7,9 => UNS
* INC # B1: 2 # F3: 7,9 => UNS
* INC # B1: 2 # A3: 7,9 => UNS
* INC # B1: 2 # B3: 7,9 => UNS
* INC # B1: 2 # C3: 7,9 => UNS
* INC # B1: 2 # E4: 7,9 => UNS
* INC # B1: 2 # E8: 7,9 => UNS
* INC # B1: 2 # H4: 5,9 => UNS
* INC # B1: 2 # H4: 3,4,7 => UNS
* INC # B1: 2 # G8: 5,9 => UNS
* INC # B1: 2 # G8: 8 => UNS
* INC # B1: 2 => UNS
* INC # H4: 5,9 # B1: 4,5 => UNS
* INC # H4: 5,9 # B1: 2 => UNS
* PRF # H4: 5,9 # B5: 4,7 => SOL
* STA # H4: 5,9 + B5: 4,7
* CNT  38 HDP CHAINS /  39 HYP OPENED