Analysis of xx-mith-te3-00007337-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1.3.56.8..5718..3.8..7.3.1....57..615.....9..7.8...45.3...15...6..8.71........... initial

Autosolve

position: 1.3.56.8..5718..3.8..7.3.1....57..615.....9..7.8...45.3...15...6.58.71....1...... autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:05.519978

The following important HDP chains were detected:

* PRF # G9: 3,8 # B3: 4,9 => SOL
* STA # G9: 3,8 + B3: 4,9
* CNT   1 HDP CHAINS /  19 HYP OPENED

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

Details

Positions

1.3.56.8..5718..3.8..7.3.1....57..615.....9..7.8...45.3...15...6..8.71........... initial
1.3.56.8..5718..3.8..7.3.1....57..615.....9..7.8...45.3...15...6.58.71....1...... autosolve
123456789457189236896723514239574861514368927768291453372915648645837192981642375 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
G1: 2,7
G2: 2,6
G3: 2,5
G4: 3,8
H5: 2,7
I5: 7,8
I6: 2,3
B7: 7,8
B9: 7,8
I8: 2,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,B6: 1.. / B5 = 1  => 10 pairs (_) / B6 = 1  => 15 pairs (_)
F5,F6: 1.. / F5 = 1  => 15 pairs (_) / F6 = 1  => 10 pairs (_)
B5,F5: 1.. / B5 = 1  => 10 pairs (_) / F5 = 1  => 15 pairs (_)
B6,F6: 1.. / B6 = 1  => 15 pairs (_) / F6 = 1  => 10 pairs (_)
H5,I6: 2.. / H5 = 2  =>  9 pairs (_) / I6 = 2  => 12 pairs (_)
I6,I8: 2.. / I6 = 2  => 12 pairs (_) / I8 = 2  =>  9 pairs (_)
G4,I6: 3.. / G4 = 3  => 12 pairs (_) / I6 = 3  =>  9 pairs (_)
I8,G9: 3.. / I8 = 3  => 12 pairs (_) / G9 = 3  =>  9 pairs (_)
B4,G4: 3.. / B4 = 3  =>  9 pairs (_) / G4 = 3  => 12 pairs (_)
E8,I8: 3.. / E8 = 3  =>  9 pairs (_) / I8 = 3  => 12 pairs (_)
G4,G9: 3.. / G4 = 3  => 12 pairs (_) / G9 = 3  =>  9 pairs (_)
I6,I8: 3.. / I6 = 3  =>  9 pairs (_) / I8 = 3  => 12 pairs (_)
G3,I3: 5.. / G3 = 5  => 10 pairs (_) / I3 = 5  =>  9 pairs (_)
G9,I9: 5.. / G9 = 5  =>  9 pairs (_) / I9 = 5  => 10 pairs (_)
G3,G9: 5.. / G3 = 5  => 10 pairs (_) / G9 = 5  =>  9 pairs (_)
I3,I9: 5.. / I3 = 5  =>  9 pairs (_) / I9 = 5  => 10 pairs (_)
B3,C3: 6.. / B3 = 6  => 10 pairs (_) / C3 = 6  =>  0 pairs (*)
G2,I2: 6.. / G2 = 6  => 11 pairs (_) / I2 = 6  => 13 pairs (_)
D9,E9: 6.. / D9 = 6  => 10 pairs (_) / E9 = 6  => 10 pairs (_)
G7,I7: 6.. / G7 = 6  => 13 pairs (_) / I7 = 6  => 11 pairs (_)
C3,C5: 6.. / C3 = 6  =>  0 pairs (*) / C5 = 6  =>  0 pairs (X)
G2,G7: 6.. / G2 = 6  => 11 pairs (_) / G7 = 6  => 13 pairs (_)
I2,I7: 6.. / I2 = 6  => 13 pairs (_) / I7 = 6  => 11 pairs (_)
G1,I1: 7.. / G1 = 7  => 11 pairs (_) / I1 = 7  => 13 pairs (_)
H5,I5: 7.. / H5 = 7  => 12 pairs (_) / I5 = 7  =>  9 pairs (_)
B7,B9: 7.. / B7 = 7  => 11 pairs (_) / B9 = 7  => 10 pairs (_)
H5,H9: 7.. / H5 = 7  => 12 pairs (_) / H9 = 7  =>  9 pairs (_)
F4,F5: 8.. / F4 = 8  => 12 pairs (_) / F5 = 8  =>  9 pairs (_)
G4,I5: 8.. / G4 = 8  =>  9 pairs (_) / I5 = 8  => 12 pairs (_)
B7,B9: 8.. / B7 = 8  => 10 pairs (_) / B9 = 8  => 11 pairs (_)
F4,G4: 8.. / F4 = 8  => 12 pairs (_) / G4 = 8  =>  9 pairs (_)
F5,I5: 8.. / F5 = 8  =>  9 pairs (_) / I5 = 8  => 12 pairs (_)
* DURATION: 0:00:13.574595  START: 03:33:51.769376  END: 03:34:05.343971 2025-04-06
* CP COUNT: (32)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:05.396527  START: 03:34:12.091578  END: 03:34:17.488105 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00007337-base-pr-002.dot
* REASONING
* PRF # G9: 3,8 # B3: 4,9 => SOL
* STA # G9: 3,8 + B3: 4,9
* CNT   1 HDP CHAINS /  19 HYP OPENED

Header Info

rating: 1632; r2: 21629; index: 7337

Solution

position: 123456789457189236896723514239574861514368927768291453372915648645837192981642375 solved
Solution

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 # G9: 3,8 => UNS
* INC # G9: 5,7 => UNS
* INC # H9: 2,7 => UNS
* INC # H9: 4,9 => UNS
* INC # I7: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # B6: 2,3 => UNS
* INC # D6: 2,3 => UNS
* INC # E6: 2,3 => UNS
* INC # G7: 7,8 => UNS
* INC # I7: 7,8 => UNS
* INC # G9: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # E8: 2,3 => UNS
* INC # E8: 4,9 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G9: 3,8 => UNS
* INC # G9: 5,7 => UNS
* INC # H9: 2,7 => UNS
* INC # H9: 4,9 => UNS
* INC # I7: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # B6: 2,3 => UNS
* INC # D6: 2,3 => UNS
* INC # E6: 2,3 => UNS
* INC # G7: 7,8 => UNS
* INC # I7: 7,8 => UNS
* INC # G9: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # E8: 2,3 => UNS
* INC # E8: 4,9 => UNS
* CNT  15 HDP CHAINS /  15 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G9: 3,8 => UNS
* INC # G9: 5,7 => UNS
* INC # H9: 2,7 => UNS
* INC # H9: 4,9 => UNS
* INC # I7: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # B6: 2,3 => UNS
* INC # D6: 2,3 => UNS
* INC # E6: 2,3 => UNS
* INC # G7: 7,8 => UNS
* INC # I7: 7,8 => UNS
* INC # G9: 7,8 => UNS
* INC # I9: 7,8 => UNS
* INC # E8: 2,3 => UNS
* INC # E8: 4,9 => UNS
* INC # G9: 3,8 # I1: 4,9 => UNS
* INC # G9: 3,8 # I2: 4,9 => UNS
* PRF # G9: 3,8 # B3: 4,9 => SOL
* STA # G9: 3,8 + B3: 4,9
* CNT  18 HDP CHAINS /  19 HYP OPENED