Analysis of xx-mith-te3-00075243-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2......9.5.18.2.3...2..5..2..39..51....129.89..5.832.39.8.1....7........64...1.2 initial

Autosolve

position: .2......9.5.18.2.3...2..5..2..39..51....129.89..5.832.39.8.1....7....8..864...1.2 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: 0:00:08.403071

The following important HDP chains were detected:

* PRF # C1: 3,6,7 # I6: 6,7 => SOL
* STA # C1: 3,6,7 + I6: 6,7
* CNT   1 HDP CHAINS /  38 HYP OPENED

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

Details

Positions

.2......9.5.18.2.3...2..5..2..39..51....129.89..5.832.39.8.1....7........64...1.2 initial
.2......9.5.18.2.3...2..5..2..39..51....129.89..5.832.39.8.1....7....8..864...1.2 autosolve
123456789457189263689273514248397651735612948916548327392861475571924836864735192 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
H1: 1,8
H3: 1,8
B4: 4,8
B5: 3,4
B6: 1,4
C7: 2,5
A8: 1,5
D9: 7,9
H8: 3,9
H9: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 10 pairs (_) / H3 = 1  =>  8 pairs (_)
B6,C6: 1.. / B6 = 1  => 10 pairs (_) / C6 = 1  => 11 pairs (_)
A8,C8: 1.. / A8 = 1  => 13 pairs (_) / C8 = 1  => 10 pairs (_)
B3,B6: 1.. / B3 = 1  => 11 pairs (_) / B6 = 1  => 10 pairs (_)
C7,C8: 2.. / C7 = 2  => 12 pairs (_) / C8 = 2  => 11 pairs (_)
E7,E8: 2.. / E7 = 2  => 11 pairs (_) / E8 = 2  => 12 pairs (_)
C7,E7: 2.. / C7 = 2  => 12 pairs (_) / E7 = 2  => 11 pairs (_)
C8,E8: 2.. / C8 = 2  => 11 pairs (_) / E8 = 2  => 12 pairs (_)
B5,C5: 3.. / B5 = 3  =>  9 pairs (_) / C5 = 3  => 15 pairs (_)
H8,H9: 3.. / H8 = 3  => 12 pairs (_) / H9 = 3  => 10 pairs (_)
B3,B5: 3.. / B3 = 3  => 15 pairs (_) / B5 = 3  =>  9 pairs (_)
E1,F1: 5.. / E1 = 5  => 11 pairs (_) / F1 = 5  => 11 pairs (_)
A5,C5: 5.. / A5 = 5  => 13 pairs (_) / C5 = 5  => 10 pairs (_)
E9,F9: 5.. / E9 = 5  => 11 pairs (_) / F9 = 5  => 11 pairs (_)
I7,I8: 5.. / I7 = 5  => 12 pairs (_) / I8 = 5  => 11 pairs (_)
C7,I7: 5.. / C7 = 5  => 11 pairs (_) / I7 = 5  => 12 pairs (_)
A5,A8: 5.. / A5 = 5  => 13 pairs (_) / A8 = 5  => 10 pairs (_)
E1,E9: 5.. / E1 = 5  => 11 pairs (_) / E9 = 5  => 11 pairs (_)
F1,F9: 5.. / F1 = 5  => 11 pairs (_) / F9 = 5  => 11 pairs (_)
H1,H3: 8.. / H1 = 8  =>  8 pairs (_) / H3 = 8  => 10 pairs (_)
B4,C4: 8.. / B4 = 8  => 10 pairs (_) / C4 = 8  =>  8 pairs (_)
C1,H1: 8.. / C1 = 8  => 10 pairs (_) / H1 = 8  =>  8 pairs (_)
B3,B4: 8.. / B3 = 8  =>  8 pairs (_) / B4 = 8  => 10 pairs (_)
C2,C3: 9.. / C2 = 9  => 10 pairs (_) / C3 = 9  => 10 pairs (_)
F2,F3: 9.. / F2 = 9  => 10 pairs (_) / F3 = 9  => 10 pairs (_)
D8,D9: 9.. / D8 = 9  => 12 pairs (_) / D9 = 9  => 10 pairs (_)
H8,H9: 9.. / H8 = 9  => 10 pairs (_) / H9 = 9  => 12 pairs (_)
C2,F2: 9.. / C2 = 9  => 10 pairs (_) / F2 = 9  => 10 pairs (_)
C3,F3: 9.. / C3 = 9  => 10 pairs (_) / F3 = 9  => 10 pairs (_)
D8,H8: 9.. / D8 = 9  => 12 pairs (_) / H8 = 9  => 10 pairs (_)
D9,H9: 9.. / D9 = 9  => 10 pairs (_) / H9 = 9  => 12 pairs (_)
* DURATION: 0:00:09.416695  START: 20:10:09.677149  END: 20:10:19.093844 2025-04-04
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:08.256531  START: 20:10:24.089431  END: 20:10:32.345962 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00075243-base-pr-002.dot
* REASONING
* PRF # C1: 3,6,7 # I6: 6,7 => SOL
* STA # C1: 3,6,7 + I6: 6,7
* CNT   1 HDP CHAINS /  38 HYP OPENED

Header Info

rating: 17240; r2: 413001; index: 75243

Solution

position: 123456789457189263689273514248397651735612948916548327392861475571924836864735192 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 # C1: 1,8 => UNS
* INC # C1: 3,6,7 => UNS
* INC # B3: 1,8 => UNS
* INC # C3: 1,8 => UNS
* INC # B3: 4,8 => UNS
* INC # B3: 1,3 => UNS
* INC # B3: 3,4 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 1,4 => UNS
* INC # B3: 3,8 => UNS
* INC # C8: 2,5 => UNS
* INC # C8: 1 => UNS
* INC # C8: 1,5 => UNS
* INC # C8: 2 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,8 => UNS
* INC # C1: 3,6,7 => UNS
* INC # B3: 1,8 => UNS
* INC # C3: 1,8 => UNS
* INC # B3: 4,8 => UNS
* INC # B3: 1,3 => UNS
* INC # B3: 3,4 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 1,4 => UNS
* INC # B3: 3,8 => UNS
* INC # C8: 2,5 => UNS
* INC # C8: 1 => UNS
* INC # C8: 1,5 => UNS
* INC # C8: 2 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 1,8 => UNS
* INC # C1: 3,6,7 => UNS
* INC # B3: 1,8 => UNS
* INC # C3: 1,8 => UNS
* INC # B3: 4,8 => UNS
* INC # B3: 1,3 => UNS
* INC # B3: 3,4 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 1,4 => UNS
* INC # B3: 3,8 => UNS
* INC # C8: 2,5 => UNS
* INC # C8: 1 => UNS
* INC # C8: 1,5 => UNS
* INC # C8: 2 => UNS
* INC # C1: 1,8 # B3: 1,8 => UNS
* INC # C1: 1,8 # C3: 1,8 => UNS
* INC # C1: 1,8 # E9: 3,5 => UNS
* INC # C1: 1,8 # E9: 7 => UNS
* INC # C1: 1,8 # F9: 3,5 => UNS
* INC # C1: 1,8 # F9: 7 => UNS
* INC # C1: 1,8 # B3: 1,8 => UNS
* INC # C1: 1,8 # C3: 1,8 => UNS
* INC # C1: 1,8 # B3: 4,8 => UNS
* INC # C1: 1,8 # B3: 1,3 => UNS
* INC # C1: 1,8 # B3: 3,4 => UNS
* INC # C1: 1,8 # B3: 1,8 => UNS
* INC # C1: 1,8 # B3: 1,4 => UNS
* INC # C1: 1,8 # B3: 3,8 => UNS
* INC # C1: 1,8 # C8: 2,5 => UNS
* INC # C1: 1,8 # C8: 1 => UNS
* INC # C1: 1,8 # C8: 1,5 => UNS
* INC # C1: 1,8 # C8: 2 => UNS
* INC # C1: 1,8 => UNS
* INC # C1: 3,6,7 # C4: 6,7 => UNS
* INC # C1: 3,6,7 # A5: 6,7 => UNS
* INC # C1: 3,6,7 # E6: 6,7 => UNS
* PRF # C1: 3,6,7 # I6: 6,7 => SOL
* STA # C1: 3,6,7 + I6: 6,7
* CNT  37 HDP CHAINS /  38 HYP OPENED