Analysis of xx-mith-te3-00126366-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1.3......4.6..9...78....54.2...7589....9........8.2.5..4.2...78.....79.5.7...842. initial

Autosolve

position: 1.3......4.6..9...78....54.2.4.7589....9.......78.2.54.4.2...78.....79.5.7...842. 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: 0:00:12.033229

The following important HDP chains were detected:

* PRF # B1: 2,5 # D8: 3,6 => SOL
* STA # B1: 2,5 + D8: 3,6
* CNT   1 HDP CHAINS /  44 HYP OPENED

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

Details

Positions

`1.3......4.6..9...78....54.2...7589....9........8.2.5..4.2...78.....79.5.7...842.`	initial
`1.3......4.6..9...78....54.2.4.7589....9.......78.2.54.4.2...78.....79.5.7...842.`	autosolve
`123456789456789132789123546234675891518934267697812354345291678862347915971568423`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
B2: 2,5
C3: 2,9
F1: 4,6
H1: 6,8
A5: 5,8
C5: 5,8
G5: 2,7
I5: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G5,I5: 2.. / G5 = 2  =>  7 pairs (_) / I5 = 2  =>  7 pairs (_)
B8,C8: 2.. / B8 = 2  => 10 pairs (_) / C8 = 2  => 10 pairs (_)
C3,C8: 2.. / C3 = 2  => 10 pairs (_) / C8 = 2  => 10 pairs (_)
E5,F5: 4.. / E5 = 4  =>  7 pairs (_) / F5 = 4  => 19 pairs (_)
D8,E8: 4.. / D8 = 4  =>  8 pairs (_) / E8 = 4  => 16 pairs (_)
D1,D8: 4.. / D1 = 4  => 16 pairs (_) / D8 = 4  =>  8 pairs (_)
F1,F5: 4.. / F1 = 4  =>  7 pairs (_) / F5 = 4  => 19 pairs (_)
B1,B2: 5.. / B1 = 5  =>  8 pairs (_) / B2 = 5  =>  8 pairs (_)
A5,C5: 5.. / A5 = 5  =>  7 pairs (_) / C5 = 5  => 10 pairs (_)
D1,D2: 7.. / D1 = 7  =>  9 pairs (_) / D2 = 7  =>  8 pairs (_)
G5,I5: 7.. / G5 = 7  =>  7 pairs (_) / I5 = 7  =>  7 pairs (_)
E1,E2: 8.. / E1 = 8  => 11 pairs (_) / E2 = 8  =>  8 pairs (_)
H1,H2: 8.. / H1 = 8  =>  8 pairs (_) / H2 = 8  => 11 pairs (_)
A5,C5: 8.. / A5 = 8  => 10 pairs (_) / C5 = 8  =>  7 pairs (_)
A8,C8: 8.. / A8 = 8  =>  7 pairs (_) / C8 = 8  => 10 pairs (_)
E1,H1: 8.. / E1 = 8  => 11 pairs (_) / H1 = 8  =>  8 pairs (_)
E2,H2: 8.. / E2 = 8  =>  8 pairs (_) / H2 = 8  => 11 pairs (_)
A5,A8: 8.. / A5 = 8  => 10 pairs (_) / A8 = 8  =>  7 pairs (_)
C5,C8: 8.. / C5 = 8  =>  7 pairs (_) / C8 = 8  => 10 pairs (_)
B1,C3: 9.. / B1 = 9  => 10 pairs (_) / C3 = 9  => 10 pairs (_)
I1,I3: 9.. / I1 = 9  => 10 pairs (_) / I3 = 9  => 10 pairs (_)
A6,B6: 9.. / A6 = 9  => 10 pairs (_) / B6 = 9  => 10 pairs (_)
E7,E9: 9.. / E7 = 9  => 10 pairs (_) / E9 = 9  =>  9 pairs (_)
B1,I1: 9.. / B1 = 9  => 10 pairs (_) / I1 = 9  => 10 pairs (_)
C3,I3: 9.. / C3 = 9  => 10 pairs (_) / I3 = 9  => 10 pairs (_)
B1,B6: 9.. / B1 = 9  => 10 pairs (_) / B6 = 9  => 10 pairs (_)
* DURATION: 0:00:07.838453  START: 09:01:45.375992  END: 09:01:53.214445 2025-04-05
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:11.884475  START: 09:01:59.309106  END: 09:02:11.193581 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00126366-base-pr-002.dot
* REASONING
* PRF # B1: 2,5 # D8: 3,6 => SOL
* STA # B1: 2,5 + D8: 3,6
* CNT   1 HDP CHAINS /  44 HYP OPENED

Header Info

rating: 33095; r2: 759504; index: 126366

Solution

position: 123456789456789132789123546234675891518934267697812354345291678862347915971568423 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: 2,5 => UNS
* INC # B1: 9 => UNS
* INC # E2: 2,5 => UNS
* INC # E2: 1,3,8 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 5 => UNS
* INC # I3: 2,9 => UNS
* INC # I3: 1,3,6 => UNS
* INC # D1: 4,6 => UNS
* INC # E1: 4,6 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 1,3 => UNS
* INC # E1: 6,8 => UNS
* INC # E1: 2,4,5 => UNS
* INC # G1: 2,7 => UNS
* INC # G2: 2,7 => UNS
* INC # I1: 2,7 => UNS
* INC # I2: 2,7 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # B1: 9 => UNS
* INC # E2: 2,5 => UNS
* INC # E2: 1,3,8 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 5 => UNS
* INC # I3: 2,9 => UNS
* INC # I3: 1,3,6 => UNS
* INC # D1: 4,6 => UNS
* INC # E1: 4,6 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 1,3 => UNS
* INC # E1: 6,8 => UNS
* INC # E1: 2,4,5 => UNS
* INC # G1: 2,7 => UNS
* INC # G2: 2,7 => UNS
* INC # I1: 2,7 => UNS
* INC # I2: 2,7 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,5 => UNS
* INC # B1: 9 => UNS
* INC # E2: 2,5 => UNS
* INC # E2: 1,3,8 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 5 => UNS
* INC # I3: 2,9 => UNS
* INC # I3: 1,3,6 => UNS
* INC # D1: 4,6 => UNS
* INC # E1: 4,6 => UNS
* INC # F5: 4,6 => UNS
* INC # F5: 1,3 => UNS
* INC # E1: 6,8 => UNS
* INC # E1: 2,4,5 => UNS
* INC # G1: 2,7 => UNS
* INC # G2: 2,7 => UNS
* INC # I1: 2,7 => UNS
* INC # I2: 2,7 => UNS
* INC # B1: 2,5 # E1: 2,5 => UNS
* INC # B1: 2,5 # E1: 4,6,8 => UNS
* INC # B1: 2,5 # E2: 2,5 => UNS
* INC # B1: 2,5 # E2: 1,3,8 => UNS
* INC # B1: 2,5 # D1: 4,6 => UNS
* INC # B1: 2,5 # E1: 4,6 => UNS
* INC # B1: 2,5 # F5: 4,6 => UNS
* INC # B1: 2,5 # F5: 1,3 => UNS
* INC # B1: 2,5 # E1: 6,8 => UNS
* INC # B1: 2,5 # E1: 2,4,5 => UNS
* INC # B1: 2,5 # B4: 3,6 => UNS
* INC # B1: 2,5 # B5: 3,6 => UNS
* INC # B1: 2,5 # E6: 3,6 => UNS
* INC # B1: 2,5 # G6: 3,6 => UNS
* INC # B1: 2,5 # A7: 3,6 => UNS
* INC # B1: 2,5 # A9: 3,6 => UNS
* INC # B1: 2,5 # G1: 2,7 => UNS
* INC # B1: 2,5 # G2: 2,7 => UNS
* INC # B1: 2,5 # I2: 2,7 => UNS
* INC # B1: 2,5 # I2: 1,3 => UNS
* INC # B1: 2,5 # E7: 1,5 => UNS
* INC # B1: 2,5 # E7: 3,6,9 => UNS
* INC # B1: 2,5 # A7: 3,6 => UNS
* INC # B1: 2,5 # A9: 3,6 => UNS
* PRF # B1: 2,5 # D8: 3,6 => SOL
* STA # B1: 2,5 + D8: 3,6
* CNT  43 HDP CHAINS /  44 HYP OPENED