Analysis of xx-mith-te3-00083836-base.sdk

Contents

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

Original Sudoku

level: hard

position: 123....89.......23......56.24.8.....3.9....1..8....24...492....8..3.1...9...48... initial

Autosolve

position: 123....89.......23......56.24.81....3.9....1..81...24...492....8..3.1...9...48... 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: 0:00:10.090277

The following important HDP chains were detected:

* PRF # A2: 4,7 # C8: 5,6 => SOL
* STA # A2: 4,7 + C8: 5,6
* CNT   1 HDP CHAINS /  36 HYP OPENED

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

Details

Positions

`123....89.......23......56.24.8.....3.9....1..8....24...492....8..3.1...9...48...`	initial
`123....89.......23......56.24.81....3.9....1..81...24...492....8..3.1...9...48...`	autosolve
`123456789456789123798132564247815936369274815581693247614927358875361492932548671`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A3: 4,7
B3: 7,9
C3: 7,8
E2: 8,9
G1: 4,7
D5: 2,4
F5: 2,4
E6: 3,9
F6: 3,9
G4: 3,9
H4: 3,9
B7: 1,3
B9: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  => 17 pairs (_) / D3 = 1  =>  9 pairs (_)
G2,I3: 1.. / G2 = 1  =>  9 pairs (_) / I3 = 1  => 17 pairs (_)
B7,B9: 1.. / B7 = 1  => 18 pairs (_) / B9 = 1  => 16 pairs (_)
D2,G2: 1.. / D2 = 1  => 17 pairs (_) / G2 = 1  =>  9 pairs (_)
D3,I3: 1.. / D3 = 1  =>  9 pairs (_) / I3 = 1  => 17 pairs (_)
D3,F3: 2.. / D3 = 2  => 15 pairs (_) / F3 = 2  =>  6 pairs (_)
D5,F5: 2.. / D5 = 2  =>  6 pairs (_) / F5 = 2  => 15 pairs (_)
C8,C9: 2.. / C8 = 2  => 14 pairs (_) / C9 = 2  =>  0 pairs (*)
I8,I9: 2.. / I8 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
C8,I8: 2.. / C8 = 2  => 14 pairs (_) / I8 = 2  =>  0 pairs (*)
C9,I9: 2.. / C9 = 2  =>  0 pairs (*) / I9 = 2  =>  0 pairs (X)
D3,D5: 2.. / D3 = 2  => 15 pairs (_) / D5 = 2  =>  6 pairs (_)
F3,F5: 2.. / F3 = 2  =>  6 pairs (_) / F5 = 2  => 15 pairs (_)
E3,F3: 3.. / E3 = 3  =>  9 pairs (_) / F3 = 3  => 15 pairs (_)
E6,F6: 3.. / E6 = 3  => 15 pairs (_) / F6 = 3  =>  9 pairs (_)
G4,H4: 3.. / G4 = 3  => 14 pairs (_) / H4 = 3  => 15 pairs (_)
B7,B9: 3.. / B7 = 3  => 16 pairs (_) / B9 = 3  => 18 pairs (_)
E3,E6: 3.. / E3 = 3  =>  9 pairs (_) / E6 = 3  => 15 pairs (_)
F3,F6: 3.. / F3 = 3  => 15 pairs (_) / F6 = 3  =>  9 pairs (_)
A2,A3: 4.. / A2 = 4  => 16 pairs (_) / A3 = 4  => 14 pairs (_)
D5,F5: 4.. / D5 = 4  => 15 pairs (_) / F5 = 4  =>  6 pairs (_)
G8,I8: 4.. / G8 = 4  => 18 pairs (_) / I8 = 4  => 15 pairs (_)
I3,I8: 4.. / I3 = 4  => 18 pairs (_) / I8 = 4  => 15 pairs (_)
C2,C3: 8.. / C2 = 8  => 14 pairs (_) / C3 = 8  => 12 pairs (_)
E2,E3: 8.. / E2 = 8  => 12 pairs (_) / E3 = 8  => 14 pairs (_)
G5,I5: 8.. / G5 = 8  => 16 pairs (_) / I5 = 8  => 15 pairs (_)
G7,I7: 8.. / G7 = 8  => 15 pairs (_) / I7 = 8  => 16 pairs (_)
C2,E2: 8.. / C2 = 8  => 14 pairs (_) / E2 = 8  => 12 pairs (_)
C3,E3: 8.. / C3 = 8  => 12 pairs (_) / E3 = 8  => 14 pairs (_)
G5,G7: 8.. / G5 = 8  => 16 pairs (_) / G7 = 8  => 15 pairs (_)
I5,I7: 8.. / I5 = 8  => 15 pairs (_) / I7 = 8  => 16 pairs (_)
B2,B3: 9.. / B2 = 9  => 18 pairs (_) / B3 = 9  => 13 pairs (_)
E6,F6: 9.. / E6 = 9  =>  9 pairs (_) / F6 = 9  => 15 pairs (_)
G4,H4: 9.. / G4 = 9  => 15 pairs (_) / H4 = 9  => 14 pairs (_)
G8,H8: 9.. / G8 = 9  => 14 pairs (_) / H8 = 9  => 15 pairs (_)
G4,G8: 9.. / G4 = 9  => 15 pairs (_) / G8 = 9  => 14 pairs (_)
H4,H8: 9.. / H4 = 9  => 14 pairs (_) / H8 = 9  => 15 pairs (_)
* DURATION: 0:00:15.201557  START: 21:59:39.459097  END: 21:59:54.660654 2025-04-04
* CP COUNT: (37)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:09.949771  START: 22:00:07.418408  END: 22:00:17.368179 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00083836-base-pr-002.dot
* REASONING
* PRF # A2: 4,7 # C8: 5,6 => SOL
* STA # A2: 4,7 + C8: 5,6
* CNT   1 HDP CHAINS /  36 HYP OPENED

Header Info

rating: 20874; r2: 506371; index: 83836

Solution

position: 123456789456789123798132564247815936369274815581693247614927358875361492932548671 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 # A2: 4,7 => UNS
* INC # A2: 5,6 => UNS
* INC # D3: 4,7 => UNS
* INC # F3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # B2: 7,9 => UNS
* INC # B2: 5,6 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2,3,4 => UNS
* INC # C2: 7,8 => UNS
* INC # C2: 5,6 => UNS
* INC # E3: 8,9 => UNS
* INC # E3: 3 => UNS
* INC # G2: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # D1: 4,7 => UNS
* INC # F1: 4,7 => UNS
* INC # D3: 2,4 => UNS
* INC # D3: 1,7 => UNS
* INC # F3: 2,4 => UNS
* INC # F3: 3,7,9 => UNS
* INC # E3: 3,9 => UNS
* INC # E3: 8 => UNS
* INC # F3: 3,9 => UNS
* INC # F3: 2,4,7 => UNS
* INC # G7: 1,3 => UNS
* INC # G7: 6,8 => UNS
* INC # G9: 1,3 => UNS
* INC # G9: 6 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 4,7 => UNS
* INC # A2: 5,6 => UNS
* INC # D3: 4,7 => UNS
* INC # F3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # B2: 7,9 => UNS
* INC # B2: 5,6 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2,3,4 => UNS
* INC # C2: 7,8 => UNS
* INC # C2: 5,6 => UNS
* INC # E3: 8,9 => UNS
* INC # E3: 3 => UNS
* INC # G2: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # D1: 4,7 => UNS
* INC # F1: 4,7 => UNS
* INC # D3: 2,4 => UNS
* INC # D3: 1,7 => UNS
* INC # F3: 2,4 => UNS
* INC # F3: 3,7,9 => UNS
* INC # E3: 3,9 => UNS
* INC # E3: 8 => UNS
* INC # F3: 3,9 => UNS
* INC # F3: 2,4,7 => UNS
* INC # G7: 1,3 => UNS
* INC # G7: 6,8 => UNS
* INC # G9: 1,3 => UNS
* INC # G9: 6 => UNS
* CNT  29 HDP CHAINS /  29 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 4,7 => UNS
* INC # A2: 5,6 => UNS
* INC # D3: 4,7 => UNS
* INC # F3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # B2: 7,9 => UNS
* INC # B2: 5,6 => UNS
* INC # F3: 7,9 => UNS
* INC # F3: 2,3,4 => UNS
* INC # C2: 7,8 => UNS
* INC # C2: 5,6 => UNS
* INC # E3: 8,9 => UNS
* INC # E3: 3 => UNS
* INC # G2: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # D1: 4,7 => UNS
* INC # F1: 4,7 => UNS
* INC # D3: 2,4 => UNS
* INC # D3: 1,7 => UNS
* INC # F3: 2,4 => UNS
* INC # F3: 3,7,9 => UNS
* INC # E3: 3,9 => UNS
* INC # E3: 8 => UNS
* INC # F3: 3,9 => UNS
* INC # F3: 2,4,7 => UNS
* INC # G7: 1,3 => UNS
* INC # G7: 6,8 => UNS
* INC # G9: 1,3 => UNS
* INC # G9: 6 => UNS
* INC # A2: 4,7 # D2: 4,7 => UNS
* INC # A2: 4,7 # G2: 4,7 => UNS
* INC # A2: 4,7 # B5: 5,6 => UNS
* INC # A2: 4,7 # B8: 5,6 => UNS
* INC # A2: 4,7 # C4: 5,6 => UNS
* PRF # A2: 4,7 # C8: 5,6 => SOL
* STA # A2: 4,7 + C8: 5,6
* CNT  35 HDP CHAINS /  36 HYP OPENED