Analysis of xx-mith-te3-00072931-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .23..6..94.7..9..669.......27.36.49.3.92.46......97...73....96.....4..5.......8.2 initial

Autosolve

position: .23..6..94.7..9..669.......27.36.49.3.92.46......97...73....96.....4..5.....7.8.2 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: 0:00:07.834926

The following important HDP chains were detected:

* PRF # H1: 1,8 # H3: 1,8 => SOL
* STA # H1: 1,8 + H3: 1,8
* CNT   1 HDP CHAINS /  39 HYP OPENED

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

Details

Positions

.23..6..94.7..9..669.......27.36.49.3.92.46......97...73....96.....4..5.......8.2 initial
.23..6..94.7..9..669.......27.36.49.3.92.46......97...73....96.....4..5.....7.8.2 autosolve
123456789457189236698732514271365498389214675546897123734528961862941357915673842 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
D1: 4,7
D3: 4,7
B6: 4,6
C6: 4,6
D8: 6,9
D9: 6,9
I7: 1,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G6,H6: 2.. / G6 = 2  =>  7 pairs (_) / H6 = 2  =>  7 pairs (_)
C7,C8: 2.. / C7 = 2  => 12 pairs (_) / C8 = 2  =>  7 pairs (_)
C8,F8: 2.. / C8 = 2  =>  7 pairs (_) / F8 = 2  => 12 pairs (_)
E2,E3: 3.. / E2 = 3  =>  7 pairs (_) / E3 = 3  =>  7 pairs (_)
F8,F9: 3.. / F8 = 3  => 13 pairs (_) / F9 = 3  => 10 pairs (_)
F9,H9: 3.. / F9 = 3  => 10 pairs (_) / H9 = 3  => 13 pairs (_)
D1,D3: 4.. / D1 = 4  =>  5 pairs (_) / D3 = 4  =>  6 pairs (_)
B6,C6: 4.. / B6 = 4  =>  5 pairs (_) / C6 = 4  =>  6 pairs (_)
I7,H9: 4.. / I7 = 4  =>  7 pairs (_) / H9 = 4  => 17 pairs (_)
D1,H1: 4.. / D1 = 4  =>  5 pairs (_) / H1 = 4  =>  6 pairs (_)
C7,I7: 4.. / C7 = 4  => 17 pairs (_) / I7 = 4  =>  7 pairs (_)
B6,B9: 4.. / B6 = 4  =>  5 pairs (_) / B9 = 4  =>  6 pairs (_)
I3,I7: 4.. / I3 = 4  => 17 pairs (_) / I7 = 4  =>  7 pairs (_)
B6,C6: 6.. / B6 = 6  =>  6 pairs (_) / C6 = 6  =>  5 pairs (_)
D8,D9: 6.. / D8 = 6  =>  8 pairs (_) / D9 = 6  =>  6 pairs (_)
D1,D3: 7.. / D1 = 7  =>  6 pairs (_) / D3 = 7  =>  5 pairs (_)
H5,I5: 7.. / H5 = 7  =>  7 pairs (_) / I5 = 7  => 11 pairs (_)
G8,I8: 7.. / G8 = 7  => 10 pairs (_) / I8 = 7  =>  8 pairs (_)
A8,A9: 9.. / A8 = 9  =>  8 pairs (_) / A9 = 9  =>  6 pairs (_)
D8,D9: 9.. / D8 = 9  =>  6 pairs (_) / D9 = 9  =>  8 pairs (_)
A8,D8: 9.. / A8 = 9  =>  8 pairs (_) / D8 = 9  =>  6 pairs (_)
A9,D9: 9.. / A9 = 9  =>  6 pairs (_) / D9 = 9  =>  8 pairs (_)
* DURATION: 0:00:06.831872  START: 10:05:45.250418  END: 10:05:52.082290 2025-04-06
* CP COUNT: (22)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:07.690272  START: 10:05:57.107985  END: 10:06:04.798257 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00072931-base-pr-002.dot
* REASONING
* PRF # H1: 1,8 # H3: 1,8 => SOL
* STA # H1: 1,8 + H3: 1,8
* CNT   1 HDP CHAINS /  39 HYP OPENED

Header Info

rating: 16445; r2: 424592; index: 72931

Solution

position: 123456789457189236698732514271365498389214675546897123734528961862941357915673842 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 # H1: 4,7 => UNS
* INC # H1: 1,8 => UNS
* INC # H3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # B9: 4,6 => UNS
* INC # B9: 1,5 => UNS
* INC # C9: 4,6 => UNS
* INC # C9: 1,5 => UNS
* INC # H9: 1,4 => UNS
* INC # H9: 3 => UNS
* INC # C7: 1,4 => UNS
* INC # C7: 2,5,8 => UNS
* INC # I3: 1,4 => UNS
* INC # I3: 3,5,7,8 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 4,7 => UNS
* INC # H1: 1,8 => UNS
* INC # H3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # B9: 4,6 => UNS
* INC # B9: 1,5 => UNS
* INC # C9: 4,6 => UNS
* INC # C9: 1,5 => UNS
* INC # H9: 1,4 => UNS
* INC # H9: 3 => UNS
* INC # C7: 1,4 => UNS
* INC # C7: 2,5,8 => UNS
* INC # I3: 1,4 => UNS
* INC # I3: 3,5,7,8 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 4,7 => UNS
* INC # H1: 1,8 => UNS
* INC # H3: 4,7 => UNS
* INC # I3: 4,7 => UNS
* INC # B9: 4,6 => UNS
* INC # B9: 1,5 => UNS
* INC # C9: 4,6 => UNS
* INC # C9: 1,5 => UNS
* INC # H9: 1,4 => UNS
* INC # H9: 3 => UNS
* INC # C7: 1,4 => UNS
* INC # C7: 2,5,8 => UNS
* INC # I3: 1,4 => UNS
* INC # I3: 3,5,7,8 => UNS
* INC # H1: 4,7 # H3: 4,7 => UNS
* INC # H1: 4,7 # I3: 4,7 => UNS
* INC # H1: 4,7 # G2: 1,5 => UNS
* INC # H1: 4,7 # G3: 1,5 => UNS
* INC # H1: 4,7 # I3: 1,5 => UNS
* INC # H1: 4,7 # A1: 1,5 => UNS
* INC # H1: 4,7 # E1: 1,5 => UNS
* INC # H1: 4,7 # G6: 1,5 => UNS
* INC # H1: 4,7 # G6: 2,3 => UNS
* INC # H1: 4,7 # H3: 4,7 => UNS
* INC # H1: 4,7 # I3: 4,7 => UNS
* INC # H1: 4,7 # B9: 4,6 => UNS
* INC # H1: 4,7 # B9: 1,5 => UNS
* INC # H1: 4,7 # C9: 4,6 => UNS
* INC # H1: 4,7 # C9: 1,5 => UNS
* INC # H1: 4,7 # H9: 1,4 => UNS
* INC # H1: 4,7 # H9: 3 => UNS
* INC # H1: 4,7 # C7: 1,4 => UNS
* INC # H1: 4,7 # C7: 2,5,8 => UNS
* INC # H1: 4,7 # I3: 1,4 => UNS
* INC # H1: 4,7 # I3: 3,5,7,8 => UNS
* INC # H1: 4,7 => UNS
* INC # H1: 1,8 # H2: 1,8 => UNS
* PRF # H1: 1,8 # H3: 1,8 => SOL
* STA # H1: 1,8 + H3: 1,8
* CNT  38 HDP CHAINS /  39 HYP OPENED