Analysis of xx-mith-te3-00130900-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12.45.7..4.71.9....9..27..121....65....5..9........3.85..79.....7..45...94.2.1... initial

Autosolve

position: 12.45.7..4.71.9....9..27..121....65....5..9........3.85..79.....7..45...94.2.1... 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: 0:00:20.086697

The following important HDP chains were detected:

* PRF # C6: 5,6 # C3: 3,8 => SOL
* STA # C6: 5,6 + C3: 3,8
* CNT   1 HDP CHAINS / 122 HYP OPENED

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

Details

Positions

12.45.7..4.71.9....9..27..121....65....5..9........3.85..79.....7..45...94.2.1... initial
12.45.7..4.71.9....9..27..121....65....5..9........3.85..79.....7..45...94.2.1... autosolve
123456789457189236698327541219873654384562917765914328531798462872645193946231875 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A6: 6,7
B6: 5,6
D6: 6,9
I4: 4,7
C7: 1,2
C8: 1,2
G9: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E5,E6: 1.. / E5 = 1  =>  9 pairs (_) / E6 = 1  =>  7 pairs (_)
H5,H6: 1.. / H5 = 1  =>  7 pairs (_) / H6 = 1  =>  9 pairs (_)
C7,C8: 1.. / C7 = 1  =>  5 pairs (_) / C8 = 1  =>  5 pairs (_)
G7,G8: 1.. / G7 = 1  =>  5 pairs (_) / G8 = 1  =>  5 pairs (_)
E5,H5: 1.. / E5 = 1  =>  9 pairs (_) / H5 = 1  =>  7 pairs (_)
E6,H6: 1.. / E6 = 1  =>  7 pairs (_) / H6 = 1  =>  9 pairs (_)
C7,G7: 1.. / C7 = 1  =>  5 pairs (_) / G7 = 1  =>  5 pairs (_)
C8,G8: 1.. / C8 = 1  =>  5 pairs (_) / G8 = 1  =>  5 pairs (_)
F5,F6: 2.. / F5 = 2  =>  8 pairs (_) / F6 = 2  =>  7 pairs (_)
C7,C8: 2.. / C7 = 2  =>  5 pairs (_) / C8 = 2  =>  5 pairs (_)
F6,H6: 2.. / F6 = 2  =>  7 pairs (_) / H6 = 2  =>  8 pairs (_)
G3,H3: 4.. / G3 = 4  =>  6 pairs (_) / H3 = 4  =>  6 pairs (_)
G3,G7: 4.. / G3 = 4  =>  6 pairs (_) / G7 = 4  =>  6 pairs (_)
B2,C3: 5.. / B2 = 5  =>  0 pairs (*) / C3 = 5  =>  0 pairs (X)
B6,C6: 5.. / B6 = 5  =>  7 pairs (_) / C6 = 5  =>  0 pairs (*)
G9,I9: 5.. / G9 = 5  =>  7 pairs (_) / I9 = 5  => 11 pairs (_)
C3,G3: 5.. / C3 = 5  =>  7 pairs (_) / G3 = 5  =>  0 pairs (*)
B2,B6: 5.. / B2 = 5  =>  0 pairs (*) / B6 = 5  =>  0 pairs (X)
C3,C6: 5.. / C3 = 5  =>  7 pairs (_) / C6 = 5  =>  0 pairs (*)
I2,I9: 5.. / I2 = 5  =>  7 pairs (_) / I9 = 5  => 11 pairs (_)
A5,A6: 7.. / A5 = 7  => 15 pairs (_) / A6 = 7  =>  7 pairs (_)
H9,I9: 7.. / H9 = 7  =>  7 pairs (_) / I9 = 7  => 15 pairs (_)
E4,I4: 7.. / E4 = 7  => 11 pairs (_) / I4 = 7  => 10 pairs (_)
H1,I1: 9.. / H1 = 9  =>  8 pairs (_) / I1 = 9  =>  7 pairs (_)
C4,C6: 9.. / C4 = 9  =>  7 pairs (_) / C6 = 9  =>  9 pairs (_)
D4,D6: 9.. / D4 = 9  =>  9 pairs (_) / D6 = 9  =>  7 pairs (_)
H8,I8: 9.. / H8 = 9  =>  7 pairs (_) / I8 = 9  =>  8 pairs (_)
C4,D4: 9.. / C4 = 9  =>  7 pairs (_) / D4 = 9  =>  9 pairs (_)
C6,D6: 9.. / C6 = 9  =>  9 pairs (_) / D6 = 9  =>  7 pairs (_)
H1,H8: 9.. / H1 = 9  =>  8 pairs (_) / H8 = 9  =>  7 pairs (_)
I1,I8: 9.. / I1 = 9  =>  7 pairs (_) / I8 = 9  =>  8 pairs (_)
* DURATION: 0:00:07.797658  START: 10:16:23.627952  END: 10:16:31.425610 2025-04-05
* CP COUNT: (31)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:19.826295  START: 10:16:36.660643  END: 10:16:56.486938 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00130900-base-pr-002.dot
* REASONING
* PRF # C6: 5,6 # C3: 3,8 => SOL
* STA # C6: 5,6 + C3: 3,8
* CNT   1 HDP CHAINS / 122 HYP OPENED

Header Info

rating: 34499; r2: 643383; index: 130900

Solution

position: 123456789457189236698327541219873654384562917765914328531798462872645193946231875 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 # A5: 6,7 => UNS
* INC # A5: 3,8 => UNS
* INC # E6: 6,7 => UNS
* INC # E6: 1 => UNS
* INC # C6: 5,6 => UNS
* INC # C6: 4,9 => UNS
* INC # B2: 5,6 => UNS
* INC # B2: 3,8 => UNS
* INC # C6: 6,9 => UNS
* INC # C6: 4,5 => UNS
* INC # H5: 4,7 => UNS
* INC # I5: 4,7 => UNS
* INC # H6: 4,7 => UNS
* INC # G7: 1,2 => UNS
* INC # G7: 4,8 => UNS
* INC # G8: 1,2 => UNS
* INC # G8: 8 => UNS
* INC # G2: 5,8 => UNS
* INC # G3: 5,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 6,7 => UNS
* INC # A5: 3,8 => UNS
* INC # E6: 6,7 => UNS
* INC # E6: 1 => UNS
* INC # C6: 5,6 => UNS
* INC # C6: 4,9 => UNS
* INC # B2: 5,6 => UNS
* INC # B2: 3,8 => UNS
* INC # C6: 6,9 => UNS
* INC # C6: 4,5 => UNS
* INC # H5: 4,7 => UNS
* INC # I5: 4,7 => UNS
* INC # H6: 4,7 => UNS
* INC # G7: 1,2 => UNS
* INC # G7: 4,8 => UNS
* INC # G8: 1,2 => UNS
* INC # G8: 8 => UNS
* INC # G2: 5,8 => UNS
* INC # G3: 5,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 6,7 => UNS
* INC # A5: 3,8 => UNS
* INC # E6: 6,7 => UNS
* INC # E6: 1 => UNS
* INC # C6: 5,6 => UNS
* INC # C6: 4,9 => UNS
* INC # B2: 5,6 => UNS
* INC # B2: 3,8 => UNS
* INC # C6: 6,9 => UNS
* INC # C6: 4,5 => UNS
* INC # H5: 4,7 => UNS
* INC # I5: 4,7 => UNS
* INC # H6: 4,7 => UNS
* INC # G7: 1,2 => UNS
* INC # G7: 4,8 => UNS
* INC # G8: 1,2 => UNS
* INC # G8: 8 => UNS
* INC # G2: 5,8 => UNS
* INC # G3: 5,8 => UNS
* INC # A5: 6,7 # C1: 3,8 => UNS
* INC # A5: 6,7 # B2: 3,8 => UNS
* INC # A5: 6,7 # D3: 3,8 => UNS
* INC # A5: 6,7 # H3: 3,8 => UNS
* INC # A5: 6,7 # H3: 4,8 => UNS
* INC # A5: 6,7 # H3: 3,6 => UNS
* INC # A5: 6,7 # G7: 4,8 => UNS
* INC # A5: 6,7 # G7: 1,2 => UNS
* INC # A5: 6,7 # E5: 6,7 => UNS
* INC # A5: 6,7 # E5: 1,3,8 => UNS
* INC # A5: 6,7 # C4: 3,8 => UNS
* INC # A5: 6,7 # C5: 3,8 => UNS
* INC # A5: 6,7 # E5: 3,8 => UNS
* INC # A5: 6,7 # F5: 3,8 => UNS
* INC # A5: 6,7 # B2: 3,8 => UNS
* INC # A5: 6,7 # B7: 3,8 => UNS
* INC # A5: 6,7 # E6: 6,7 => UNS
* INC # A5: 6,7 # E6: 1 => UNS
* INC # A5: 6,7 # C4: 4,9 => UNS
* INC # A5: 6,7 # C4: 3,8 => UNS
* INC # A5: 6,7 # H5: 4,7 => UNS
* INC # A5: 6,7 # I5: 4,7 => UNS
* INC # A5: 6,7 # H6: 4,7 => UNS
* INC # A5: 6,7 # G7: 1,2 => UNS
* INC # A5: 6,7 # G7: 4,8 => UNS
* INC # A5: 6,7 # B7: 3,8 => UNS
* INC # A5: 6,7 # C9: 3,8 => UNS
* INC # A5: 6,7 # D8: 3,8 => UNS
* INC # A5: 6,7 # H8: 3,8 => UNS
* INC # A5: 6,7 # G8: 1,2 => UNS
* INC # A5: 6,7 # G8: 8 => UNS
* INC # A5: 6,7 # G2: 5,8 => UNS
* INC # A5: 6,7 # G2: 2 => UNS
* INC # A5: 6,7 => UNS
* INC # A5: 3,8 # C4: 3,8 => UNS
* INC # A5: 3,8 # B5: 3,8 => UNS
* INC # A5: 3,8 # C5: 3,8 => UNS
* INC # A5: 3,8 # E5: 3,8 => UNS
* INC # A5: 3,8 # F5: 3,8 => UNS
* INC # A5: 3,8 # A3: 3,8 => UNS
* INC # A5: 3,8 # A8: 3,8 => UNS
* INC # A5: 3,8 # C6: 5,6 => UNS
* INC # A5: 3,8 # C6: 4,9 => UNS
* INC # A5: 3,8 # B2: 5,6 => UNS
* INC # A5: 3,8 # B2: 3,8 => UNS
* INC # A5: 3,8 # C6: 6,9 => UNS
* INC # A5: 3,8 # C6: 4,5 => UNS
* INC # A5: 3,8 # E5: 1,6 => UNS
* INC # A5: 3,8 # E5: 3,7,8 => UNS
* INC # A5: 3,8 # H5: 4,7 => UNS
* INC # A5: 3,8 # I5: 4,7 => UNS
* INC # A5: 3,8 # G7: 1,2 => UNS
* INC # A5: 3,8 # G7: 4,8 => UNS
* INC # A5: 3,8 # G8: 1,2 => UNS
* INC # A5: 3,8 # G8: 8 => UNS
* INC # A5: 3,8 # G2: 5,8 => UNS
* INC # A5: 3,8 # G3: 5,8 => UNS
* INC # A5: 3,8 => UNS
* INC # E6: 6,7 # H3: 4,8 => UNS
* INC # E6: 6,7 # H3: 3,6 => UNS
* INC # E6: 6,7 # G7: 4,8 => UNS
* INC # E6: 6,7 # G7: 1,2 => UNS
* INC # E6: 6,7 # A5: 6,7 => UNS
* INC # E6: 6,7 # A5: 3,8 => UNS
* INC # E6: 6,7 # E4: 3,8 => UNS
* INC # E6: 6,7 # F4: 3,8 => UNS
* INC # E6: 6,7 # D3: 3,8 => UNS
* INC # E6: 6,7 # D8: 3,8 => UNS
* INC # E6: 6,7 # H5: 4,7 => UNS
* INC # E6: 6,7 # I5: 4,7 => UNS
* INC # E6: 6,7 # G7: 1,2 => UNS
* INC # E6: 6,7 # G7: 4,8 => UNS
* INC # E6: 6,7 # G8: 1,2 => UNS
* INC # E6: 6,7 # G8: 8 => UNS
* INC # E6: 6,7 # G2: 5,8 => UNS
* INC # E6: 6,7 # G2: 2 => UNS
* INC # E6: 6,7 => UNS
* INC # E6: 1 # A5: 6,7 => UNS
* INC # E6: 1 # A5: 3,8 => UNS
* INC # E6: 1 # C6: 5,6 => UNS
* INC # E6: 1 # C6: 4,9 => UNS
* INC # E6: 1 # B2: 5,6 => UNS
* INC # E6: 1 # B2: 3,8 => UNS
* INC # E6: 1 # C6: 6,9 => UNS
* INC # E6: 1 # C6: 4,5 => UNS
* INC # E6: 1 # I5: 4,7 => UNS
* INC # E6: 1 # H6: 4,7 => UNS
* INC # E6: 1 # G7: 1,2 => UNS
* INC # E6: 1 # G7: 4,8 => UNS
* INC # E6: 1 # G8: 1,2 => UNS
* INC # E6: 1 # G8: 8 => UNS
* INC # E6: 1 # G2: 5,8 => UNS
* INC # E6: 1 # G3: 5,8 => UNS
* INC # E6: 1 => UNS
* INC # C6: 5,6 # A3: 3,8 => UNS
* INC # C6: 5,6 # A8: 3,8 => UNS
* INC # C6: 5,6 # B2: 3,8 => UNS
* INC # C6: 5,6 # B7: 3,8 => UNS
* INC # C6: 5,6 # B2: 5,6 => UNS
* INC # C6: 5,6 # B2: 3,8 => UNS
* INC # C6: 5,6 # C3: 5,6 => UNS
* PRF # C6: 5,6 # C3: 3,8 => SOL
* STA # C6: 5,6 + C3: 3,8
* CNT 121 HDP CHAINS / 122 HYP OPENED