Analysis of xx-mith-te3-00004195-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...4.678.4........78..234...3...8..664.2.7..88..63....37....65.......91.....628.7 initial

Autosolve

position: ...4.678.4........78..234...3...8..664.2.7..88..63....37....65.......91.....628.7 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # H2: 6,9 => CTR => H2: 2,3
* DIS # B8: 2,5 => CTR => B8: 6
* DIS # C8: 2,5 => CTR => C8: 4,6,8
* CNT   3 HDP CHAINS /  28 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # H2: 6,9 => CTR => H2: 2,3
* DIS H2: 2,3 # B8: 2,5 => CTR => B8: 6
* DIS H2: 2,3 + B8: 6 # C8: 2,5 => CTR => C8: 4,8
* STA H2: 2,3 + B8: 6 + C8: 4,8
* CNT   3 HDP CHAINS /  41 HYP OPENED

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

Pair Reduction Position

position: ..34.678.4.6......78..2346..3...8..664.2.7..88..63....37....65..6....91.....628.7 pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:22.882666

The following important HDP chains were detected:

* PRF # G2: 1,5 # C4: 1,5 => SOL
* STA # G2: 1,5 + C4: 1,5
* CNT   1 HDP CHAINS / 104 HYP OPENED

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

Details

Positions

...4.678.4........78..234...3...8..664.2.7..88..63....37....65.......91.....628.7 initial
...4.678.4........78..234...3...8..664.2.7..88..63....37....65.......91.....628.7 autosolve
..34.678.4.6......78..2346..3...8..664.2.7..88..63....37....65..6....91.....628.7 pair_reduction
123456789456789123789123465231948576645217398897635241372891654568374912914562837 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
D2: 7,8
E2: 7,8
H3: 6,9
H5: 3,9
A8: 2,5
F8: 4,5
I7: 2,4
H9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,H2: 2.. / G2 = 2  => 13 pairs (_) / H2 = 2  =>  7 pairs (_)
I7,I8: 2.. / I7 = 2  =>  8 pairs (_) / I8 = 2  => 10 pairs (_)
C7,I7: 2.. / C7 = 2  => 10 pairs (_) / I7 = 2  =>  8 pairs (_)
C1,C2: 3.. / C1 = 3  =>  8 pairs (_) / C2 = 3  =>  0 pairs (X)
G5,H5: 3.. / G5 = 3  =>  9 pairs (_) / H5 = 3  => 10 pairs (_)
D8,D9: 3.. / D8 = 3  => 10 pairs (_) / D9 = 3  => 10 pairs (_)
I8,H9: 3.. / I8 = 3  => 10 pairs (_) / H9 = 3  => 10 pairs (_)
C1,I1: 3.. / C1 = 3  =>  8 pairs (_) / I1 = 3  =>  0 pairs (X)
D8,I8: 3.. / D8 = 3  => 10 pairs (_) / I8 = 3  => 10 pairs (_)
D9,H9: 3.. / D9 = 3  => 10 pairs (_) / H9 = 3  => 10 pairs (_)
G2,G5: 3.. / G2 = 3  => 10 pairs (_) / G5 = 3  =>  9 pairs (_)
E4,F6: 4.. / E4 = 4  =>  8 pairs (_) / F6 = 4  => 14 pairs (_)
E4,H4: 4.. / E4 = 4  =>  8 pairs (_) / H4 = 4  => 14 pairs (_)
C9,H9: 4.. / C9 = 4  => 10 pairs (_) / H9 = 4  => 10 pairs (_)
H2,H3: 6.. / H2 = 6  =>  0 pairs (X) / H3 = 6  =>  7 pairs (_)
B8,C8: 6.. / B8 = 6  =>  8 pairs (_) / C8 = 6  =>  0 pairs (X)
C3,H3: 6.. / C3 = 6  =>  0 pairs (X) / H3 = 6  =>  7 pairs (_)
B2,B8: 6.. / B2 = 6  =>  0 pairs (X) / B8 = 6  =>  8 pairs (_)
D2,E2: 7.. / D2 = 7  =>  6 pairs (_) / E2 = 7  => 10 pairs (_)
C4,C6: 7.. / C4 = 7  =>  8 pairs (_) / C6 = 7  =>  8 pairs (_)
H4,H6: 7.. / H4 = 7  =>  8 pairs (_) / H6 = 7  =>  8 pairs (_)
D8,E8: 7.. / D8 = 7  => 10 pairs (_) / E8 = 7  =>  6 pairs (_)
C4,H4: 7.. / C4 = 7  =>  8 pairs (_) / H4 = 7  =>  8 pairs (_)
C6,H6: 7.. / C6 = 7  =>  8 pairs (_) / H6 = 7  =>  8 pairs (_)
D2,D8: 7.. / D2 = 7  =>  6 pairs (_) / D8 = 7  => 10 pairs (_)
E2,E8: 7.. / E2 = 7  => 10 pairs (_) / E8 = 7  =>  6 pairs (_)
D2,E2: 8.. / D2 = 8  => 10 pairs (_) / E2 = 8  =>  6 pairs (_)
C7,C8: 8.. / C7 = 8  => 13 pairs (_) / C8 = 8  =>  8 pairs (_)
* DURATION: 0:00:08.033395  START: 03:13:02.700428  END: 03:13:10.733823 2025-04-06
* CP COUNT: (28)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:22.638143  START: 03:13:22.761007  END: 03:13:45.399150 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00004195-base-pr-002.dot
* REASONING
* PRF # G2: 1,5 # C4: 1,5 => SOL
* STA # G2: 1,5 + C4: 1,5
* CNT   1 HDP CHAINS / 104 HYP OPENED

Header Info

rating: 735; r2: 136588; index: 4195

Solution

position: 123456789456789123789123465231948576645217398897635241372891654568374912914562837 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 # D8: 7,8 => UNS
* INC # D8: 3,5 => UNS
* INC # E8: 7,8 => UNS
* INC # E8: 4,5 => UNS
* DIS # H2: 6,9 => CTR => H2: 2,3
* INC # H2: 2,3 => UNS
* INC # C3: 6,9 => UNS
* INC # C3: 1,5 => UNS
* INC # H2: 3,9 => UNS
* INC # H2: 2,6 => UNS
* DIS # B8: 2,5 => CTR => B8: 6
* INC # B8: 6 => UNS
* DIS # C8: 2,5 => CTR => C8: 4,6,8
* INC # C8: 4,6,8 => UNS
* INC # A1: 2,5 => UNS
* INC # A4: 2,5 => UNS
* INC # E8: 4,5 => UNS
* INC # E8: 7,8 => UNS
* INC # C8: 4,5 => UNS
* INC # C8: 2,6,8 => UNS
* INC # F6: 4,5 => UNS
* INC # F6: 1,9 => UNS
* INC # I8: 2,4 => UNS
* INC # I8: 3 => UNS
* INC # C7: 2,4 => UNS
* INC # C7: 1,8,9 => UNS
* INC # I8: 3,4 => UNS
* INC # I8: 2 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D8: 7,8 => UNS
* INC # D8: 3,5 => UNS
* INC # E8: 7,8 => UNS
* INC # E8: 4,5 => UNS
* DIS # H2: 6,9 => CTR => H2: 2,3
* DIS H2: 2,3 # B8: 2,5 => CTR => B8: 6
* DIS H2: 2,3 + B8: 6 # C8: 2,5 => CTR => C8: 4,8
* INC H2: 2,3 + B8: 6 + C8: 4,8 # A1: 2,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # A4: 2,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 4,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 7,8 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # F6: 4,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # F6: 1,9 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 2,4 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 3 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # C7: 2,4 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # C7: 1,8,9 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 3,4 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 2 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # D8: 7,8 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # D8: 3,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 7,8 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 4,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # G2: 2,3 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # G2: 1,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # A1: 2,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # A4: 2,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # C7: 4,8 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # C7: 1,2,9 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 4,8 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 5,7 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 4,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # E8: 7,8 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # F6: 4,5 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # F6: 1,9 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 2,4 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 3 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # C7: 2,4 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # C7: 1,8,9 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 3,4 => UNS
* INC H2: 2,3 + B8: 6 + C8: 4,8 # I8: 2 => UNS
* STA H2: 2,3 + B8: 6 + C8: 4,8
* CNT  41 HDP CHAINS /  41 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D8: 7,8 => UNS
* INC # D8: 3,5 => UNS
* INC # E8: 7,8 => UNS
* INC # E8: 4,5 => UNS
* INC # G2: 2,3 => UNS
* INC # G2: 1,5 => UNS
* INC # A1: 2,5 => UNS
* INC # A4: 2,5 => UNS
* INC # C7: 4,8 => UNS
* INC # C7: 1,2,9 => UNS
* INC # E8: 4,8 => UNS
* INC # E8: 5,7 => UNS
* INC # E8: 4,5 => UNS
* INC # E8: 7,8 => UNS
* INC # F6: 4,5 => UNS
* INC # F6: 1,9 => UNS
* INC # I8: 2,4 => UNS
* INC # I8: 3 => UNS
* INC # C7: 2,4 => UNS
* INC # C7: 1,8,9 => UNS
* INC # I8: 3,4 => UNS
* INC # I8: 2 => UNS
* INC # D8: 7,8 # E8: 7,8 => UNS
* INC # D8: 7,8 # E8: 5 => UNS
* INC # D8: 7,8 # H4: 2,7 => UNS
* INC # D8: 7,8 # H4: 9 => UNS
* INC # D8: 7,8 # H6: 2,7 => UNS
* INC # D8: 7,8 # H6: 9 => UNS
* INC # D8: 7,8 # E7: 1,9 => UNS
* INC # D8: 7,8 # F7: 1,9 => UNS
* INC # D8: 7,8 # D3: 1,9 => UNS
* INC # D8: 7,8 # D4: 1,9 => UNS
* INC # D8: 7,8 # E8: 7,8 => UNS
* INC # D8: 7,8 # E8: 5 => UNS
* INC # D8: 7,8 => UNS
* INC # D8: 3,5 # G2: 2,3 => UNS
* INC # D8: 3,5 # G2: 1,5 => UNS
* INC # D8: 3,5 # A1: 2,5 => UNS
* INC # D8: 3,5 # A4: 2,5 => UNS
* INC # D8: 3,5 # D9: 3,5 => UNS
* INC # D8: 3,5 # D9: 1,9 => UNS
* INC # D8: 3,5 # F6: 4,5 => UNS
* INC # D8: 3,5 # F6: 1,9 => UNS
* INC # D8: 3,5 # I8: 2,4 => UNS
* INC # D8: 3,5 # I8: 3 => UNS
* INC # D8: 3,5 # C7: 2,4 => UNS
* INC # D8: 3,5 # C7: 1,9 => UNS
* INC # D8: 3,5 # I8: 3,4 => UNS
* INC # D8: 3,5 # I8: 2 => UNS
* INC # D8: 3,5 => UNS
* INC # E8: 7,8 # D8: 7,8 => UNS
* INC # E8: 7,8 # D8: 3,5 => UNS
* INC # E8: 7,8 # G2: 2,3 => UNS
* INC # E8: 7,8 # G2: 1,5 => UNS
* INC # E8: 7,8 # A1: 2,5 => UNS
* INC # E8: 7,8 # A4: 2,5 => UNS
* INC # E8: 7,8 # C7: 4,8 => UNS
* INC # E8: 7,8 # C7: 1,2,9 => UNS
* INC # E8: 7,8 # D8: 7,8 => UNS
* INC # E8: 7,8 # D8: 3,5 => UNS
* INC # E8: 7,8 # F6: 4,5 => UNS
* INC # E8: 7,8 # F6: 1,9 => UNS
* INC # E8: 7,8 # I8: 2,4 => UNS
* INC # E8: 7,8 # I8: 3 => UNS
* INC # E8: 7,8 # C7: 2,4 => UNS
* INC # E8: 7,8 # C7: 1,8,9 => UNS
* INC # E8: 7,8 # I8: 3,4 => UNS
* INC # E8: 7,8 # I8: 2 => UNS
* INC # E8: 7,8 => UNS
* INC # E8: 4,5 # F2: 1,9 => UNS
* INC # E8: 4,5 # D3: 1,9 => UNS
* INC # E8: 4,5 # A1: 1,9 => UNS
* INC # E8: 4,5 # I1: 1,9 => UNS
* INC # E8: 4,5 # H4: 2,7 => UNS
* INC # E8: 4,5 # H4: 9 => UNS
* INC # E8: 4,5 # H6: 2,7 => UNS
* INC # E8: 4,5 # H6: 9 => UNS
* INC # E8: 4,5 # D4: 1,9 => UNS
* INC # E8: 4,5 # F6: 1,9 => UNS
* INC # E8: 4,5 # C5: 1,9 => UNS
* INC # E8: 4,5 # C5: 5 => UNS
* INC # E8: 4,5 # D3: 1,9 => UNS
* INC # E8: 4,5 # D4: 1,9 => UNS
* INC # E8: 4,5 # F2: 1,9 => UNS
* INC # E8: 4,5 # F6: 1,9 => UNS
* INC # E8: 4,5 => UNS
* INC # G2: 2,3 # D8: 7,8 => UNS
* INC # G2: 2,3 # D8: 5 => UNS
* INC # G2: 2,3 # E8: 7,8 => UNS
* INC # G2: 2,3 # E8: 5 => UNS
* INC # G2: 2,3 # H4: 2,7 => UNS
* INC # G2: 2,3 # H4: 9 => UNS
* INC # G2: 2,3 # H6: 2,7 => UNS
* INC # G2: 2,3 # H6: 9 => UNS
* INC # G2: 2,3 => UNS
* INC # G2: 1,5 # I1: 1,5 => UNS
* INC # G2: 1,5 # I3: 1,5 => UNS
* INC # G2: 1,5 # B2: 1,5 => UNS
* INC # G2: 1,5 # F2: 1,5 => UNS
* INC # G2: 1,5 # G4: 1,5 => UNS
* INC # G2: 1,5 # G6: 1,5 => UNS
* INC # G2: 1,5 # A4: 1,5 => UNS
* PRF # G2: 1,5 # C4: 1,5 => SOL
* STA # G2: 1,5 + C4: 1,5
* CNT 103 HDP CHAINS / 104 HYP OPENED