Analysis of xx-mith-te3-00029518-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ......78.4.....2.689....15..........5..9.43..7..53....3..8.5.4..4879....9.5.43.7. initial

Autosolve

position: ......78.4.....2.689....15..3.......5..9.43..7..53....3..8.5.4..4879....9.5.43.7. 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: 0:00:34.446063

The following important HDP chains were detected:

* PRF # I1: 9 # F3: 2,6 => SOL
* STA # I1: 9 + F3: 2,6
* CNT   1 HDP CHAINS / 180 HYP OPENED

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

Details

Positions

......78.4.....2.689....15..........5..9.43..7..53....3..8.5.4..4879....9.5.43.7. initial
......78.4.....2.689....15..3.......5..9.43..7..53....3..8.5.4..4879....9.5.43.7. autosolve
123456789457189236896372154234617895581924367769538412372865941648791523915243678 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
D2: 1,3
H2: 3,9
I3: 3,4
C4: 4,9
C6: 4,9
G7: 6,9
G8: 5,6
G9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H8,I8: 3.. / H8 = 3  => 12 pairs (_) / I8 = 3  =>  8 pairs (_)
H2,H8: 3.. / H2 = 3  =>  8 pairs (_) / H8 = 3  => 12 pairs (_)
D1,D3: 4.. / D1 = 4  =>  8 pairs (_) / D3 = 4  => 10 pairs (_)
I1,I3: 4.. / I1 = 4  => 10 pairs (_) / I3 = 4  =>  8 pairs (_)
C4,C6: 4.. / C4 = 4  =>  6 pairs (_) / C6 = 4  =>  7 pairs (_)
G4,G6: 4.. / G4 = 4  =>  7 pairs (_) / G6 = 4  =>  6 pairs (_)
D1,I1: 4.. / D1 = 4  =>  8 pairs (_) / I1 = 4  => 10 pairs (_)
D3,I3: 4.. / D3 = 4  => 10 pairs (_) / I3 = 4  =>  8 pairs (_)
C4,G4: 4.. / C4 = 4  =>  6 pairs (_) / G4 = 4  =>  7 pairs (_)
C6,G6: 4.. / C6 = 4  =>  7 pairs (_) / G6 = 4  =>  6 pairs (_)
B1,B2: 5.. / B1 = 5  => 12 pairs (_) / B2 = 5  =>  8 pairs (_)
E1,E2: 5.. / E1 = 5  =>  8 pairs (_) / E2 = 5  => 12 pairs (_)
G4,I4: 5.. / G4 = 5  =>  9 pairs (_) / I4 = 5  =>  7 pairs (_)
G8,I8: 5.. / G8 = 5  =>  7 pairs (_) / I8 = 5  =>  9 pairs (_)
B1,E1: 5.. / B1 = 5  => 12 pairs (_) / E1 = 5  =>  8 pairs (_)
B2,E2: 5.. / B2 = 5  =>  8 pairs (_) / E2 = 5  => 12 pairs (_)
G4,G8: 5.. / G4 = 5  =>  9 pairs (_) / G8 = 5  =>  7 pairs (_)
I4,I8: 5.. / I4 = 5  =>  7 pairs (_) / I8 = 5  =>  9 pairs (_)
I4,I5: 7.. / I4 = 7  =>  0 pairs (X) / I5 = 7  =>  8 pairs (_)
B7,C7: 7.. / B7 = 7  =>  9 pairs (_) / C7 = 7  => 12 pairs (_)
E5,I5: 7.. / E5 = 7  =>  0 pairs (X) / I5 = 7  =>  8 pairs (_)
B2,B7: 7.. / B2 = 7  => 12 pairs (_) / B7 = 7  =>  9 pairs (_)
E2,F2: 8.. / E2 = 8  =>  8 pairs (_) / F2 = 8  => 11 pairs (_)
B5,B6: 8.. / B5 = 8  =>  8 pairs (_) / B6 = 8  =>  0 pairs (X)
G9,I9: 8.. / G9 = 8  =>  8 pairs (_) / I9 = 8  => 10 pairs (_)
F1,F2: 9.. / F1 = 9  => 12 pairs (_) / F2 = 9  =>  8 pairs (_)
I1,H2: 9.. / I1 = 9  =>  8 pairs (_) / H2 = 9  => 12 pairs (_)
C4,C6: 9.. / C4 = 9  =>  7 pairs (_) / C6 = 9  =>  6 pairs (_)
G7,I7: 9.. / G7 = 9  =>  8 pairs (_) / I7 = 9  => 12 pairs (_)
F1,I1: 9.. / F1 = 9  => 12 pairs (_) / I1 = 9  =>  8 pairs (_)
F2,H2: 9.. / F2 = 9  =>  8 pairs (_) / H2 = 9  => 12 pairs (_)
* DURATION: 0:00:08.393448  START: 11:25:59.335689  END: 11:26:07.729137 2025-04-04
* CP COUNT: (31)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:33.983496  START: 11:26:14.051308  END: 11:26:48.034804 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00029518-base-pr-002.dot
* REASONING
* PRF # I1: 9 # F3: 2,6 => SOL
* STA # I1: 9 + F3: 2,6
* CNT   1 HDP CHAINS / 180 HYP OPENED

Header Info

rating: 6003; r2: 152797; index: 29518

Solution

position: 123456789457189236896372154234617895581924367769538412372865941648791523915243678 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 # D1: 1,3 => UNS
* INC # D1: 2,4,6 => UNS
* INC # C2: 1,3 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 9 => UNS
* INC # D3: 3,4 => UNS
* INC # D3: 2,6 => UNS
* INC # G4: 4,9 => UNS
* INC # G4: 5,6,8 => UNS
* INC # G6: 4,9 => UNS
* INC # G6: 6,8 => UNS
* INC # G4: 6,9 => UNS
* INC # G6: 6,9 => UNS
* INC # G4: 5,6 => UNS
* INC # G4: 4,8,9 => UNS
* INC # G4: 6,8 => UNS
* INC # G6: 6,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 1,3 => UNS
* INC # D1: 2,4,6 => UNS
* INC # C2: 1,3 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 9 => UNS
* INC # D3: 3,4 => UNS
* INC # D3: 2,6 => UNS
* INC # G4: 4,9 => UNS
* INC # G4: 5,6,8 => UNS
* INC # G6: 4,9 => UNS
* INC # G6: 6,8 => UNS
* INC # G4: 6,9 => UNS
* INC # G6: 6,9 => UNS
* INC # G4: 5,6 => UNS
* INC # G4: 4,8,9 => UNS
* INC # G4: 6,8 => UNS
* INC # G6: 6,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 1,3 => UNS
* INC # D1: 2,4,6 => UNS
* INC # C2: 1,3 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 9 => UNS
* INC # D3: 3,4 => UNS
* INC # D3: 2,6 => UNS
* INC # G4: 4,9 => UNS
* INC # G4: 5,6,8 => UNS
* INC # G6: 4,9 => UNS
* INC # G6: 6,8 => UNS
* INC # G4: 6,9 => UNS
* INC # G6: 6,9 => UNS
* INC # G4: 5,6 => UNS
* INC # G4: 4,8,9 => UNS
* INC # G4: 6,8 => UNS
* INC # G6: 6,8 => UNS
* INC # D1: 1,3 # C1: 1,3 => UNS
* INC # D1: 1,3 # C1: 2,6 => UNS
* INC # D1: 1,3 # C2: 1,3 => UNS
* INC # D1: 1,3 # C2: 7 => UNS
* INC # D1: 1,3 # E2: 7,8 => UNS
* INC # D1: 1,3 # E2: 5 => UNS
* INC # D1: 1,3 # E1: 2,6 => UNS
* INC # D1: 1,3 # E3: 2,6 => UNS
* INC # D1: 1,3 # C3: 2,6 => UNS
* INC # D1: 1,3 # C3: 7 => UNS
* INC # D1: 1,3 # F6: 2,6 => UNS
* INC # D1: 1,3 # F8: 2,6 => UNS
* INC # D1: 1,3 # G4: 4,9 => UNS
* INC # D1: 1,3 # G4: 5 => UNS
* INC # D1: 1,3 # G6: 4,9 => UNS
* INC # D1: 1,3 # G6: 8 => UNS
* INC # D1: 1,3 # E5: 2,6 => UNS
* INC # D1: 1,3 # F6: 2,6 => UNS
* INC # D1: 1,3 # A4: 2,6 => UNS
* INC # D1: 1,3 # H4: 2,6 => UNS
* INC # D1: 1,3 # E2: 7,8 => UNS
* INC # D1: 1,3 # E2: 5 => UNS
* INC # D1: 1,3 # G4: 5,9 => UNS
* INC # D1: 1,3 # G4: 4 => UNS
* INC # D1: 1,3 # G6: 8,9 => UNS
* INC # D1: 1,3 # G6: 4 => UNS
* INC # D1: 1,3 # E7: 2,6 => UNS
* INC # D1: 1,3 # F8: 2,6 => UNS
* INC # D1: 1,3 # B9: 2,6 => UNS
* INC # D1: 1,3 # B9: 1 => UNS
* INC # D1: 1,3 => UNS
* INC # D1: 2,4,6 # C2: 1,3 => UNS
* INC # D1: 2,4,6 # C2: 7 => UNS
* INC # D1: 2,4,6 # I1: 3,9 => UNS
* INC # D1: 2,4,6 # I1: 4 => UNS
* INC # D1: 2,4,6 # I1: 3,4 => UNS
* INC # D1: 2,4,6 # I1: 9 => UNS
* INC # D1: 2,4,6 # D3: 3,4 => UNS
* INC # D1: 2,4,6 # D3: 2,6 => UNS
* INC # D1: 2,4,6 # G4: 4,9 => UNS
* INC # D1: 2,4,6 # G4: 5,6,8 => UNS
* INC # D1: 2,4,6 # G6: 4,9 => UNS
* INC # D1: 2,4,6 # G6: 6,8 => UNS
* INC # D1: 2,4,6 # G4: 6,9 => UNS
* INC # D1: 2,4,6 # G6: 6,9 => UNS
* INC # D1: 2,4,6 # G4: 5,6 => UNS
* INC # D1: 2,4,6 # G4: 4,8,9 => UNS
* INC # D1: 2,4,6 # G4: 6,8 => UNS
* INC # D1: 2,4,6 # G6: 6,8 => UNS
* INC # D1: 2,4,6 => UNS
* INC # C2: 1,3 # E2: 5,7 => UNS
* INC # C2: 1,3 # E2: 8 => UNS
* INC # C2: 1,3 # C1: 1,3 => UNS
* INC # C2: 1,3 # C1: 2,6 => UNS
* INC # C2: 1,3 # D1: 1,3 => UNS
* INC # C2: 1,3 # D1: 2,4,6 => UNS
* INC # C2: 1,3 # E2: 7,8 => UNS
* INC # C2: 1,3 # E2: 5 => UNS
* INC # C2: 1,3 # D1: 2,6 => UNS
* INC # C2: 1,3 # E1: 2,6 => UNS
* INC # C2: 1,3 # D3: 2,6 => UNS
* INC # C2: 1,3 # E3: 2,6 => UNS
* INC # C2: 1,3 # C3: 2,6 => UNS
* INC # C2: 1,3 # C3: 3,7 => UNS
* INC # C2: 1,3 # F6: 2,6 => UNS
* INC # C2: 1,3 # F8: 2,6 => UNS
* INC # C2: 1,3 # D1: 3,4 => UNS
* INC # C2: 1,3 # D1: 1,2,6 => UNS
* INC # C2: 1,3 # D3: 3,4 => UNS
* INC # C2: 1,3 # D3: 2,6 => UNS
* INC # C2: 1,3 # G4: 4,9 => UNS
* INC # C2: 1,3 # G4: 5 => UNS
* INC # C2: 1,3 # G6: 4,9 => UNS
* INC # C2: 1,3 # G6: 8 => UNS
* INC # C2: 1,3 # E2: 7,8 => UNS
* INC # C2: 1,3 # E2: 5 => UNS
* INC # C2: 1,3 # G4: 5,9 => UNS
* INC # C2: 1,3 # G4: 4 => UNS
* INC # C2: 1,3 # G6: 8,9 => UNS
* INC # C2: 1,3 # G6: 4 => UNS
* INC # C2: 1,3 => UNS
* INC # C2: 7 # B1: 1,5 => UNS
* INC # C2: 7 # B1: 2,6 => UNS
* INC # C2: 7 # E2: 1,5 => UNS
* INC # C2: 7 # E2: 8 => UNS
* INC # C2: 7 # D1: 1,3 => UNS
* INC # C2: 7 # D1: 2,4,6 => UNS
* INC # C2: 7 # I1: 3,9 => UNS
* INC # C2: 7 # I1: 4 => UNS
* INC # C2: 7 # I1: 3,4 => UNS
* INC # C2: 7 # I1: 9 => UNS
* INC # C2: 7 # D3: 3,4 => UNS
* INC # C2: 7 # D3: 2,6 => UNS
* INC # C2: 7 # G4: 4,9 => UNS
* INC # C2: 7 # G4: 5,6,8 => UNS
* INC # C2: 7 # G6: 4,9 => UNS
* INC # C2: 7 # G6: 6,8 => UNS
* INC # C2: 7 # G4: 6,9 => UNS
* INC # C2: 7 # G6: 6,9 => UNS
* INC # C2: 7 # G4: 5,6 => UNS
* INC # C2: 7 # G4: 4,8,9 => UNS
* INC # C2: 7 # G4: 6,8 => UNS
* INC # C2: 7 # G6: 6,8 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 # C2: 1,3 => UNS
* INC # I1: 3,9 # C2: 7 => UNS
* INC # I1: 3,9 # G4: 4,9 => UNS
* INC # I1: 3,9 # G4: 5,6,8 => UNS
* INC # I1: 3,9 # G6: 4,9 => UNS
* INC # I1: 3,9 # G6: 6,8 => UNS
* INC # I1: 3,9 # G4: 6,9 => UNS
* INC # I1: 3,9 # G6: 6,9 => UNS
* INC # I1: 3,9 # G4: 5,6 => UNS
* INC # I1: 3,9 # G4: 4,8,9 => UNS
* INC # I1: 3,9 # G4: 6,8 => UNS
* INC # I1: 3,9 # G6: 6,8 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 4 # D1: 1,3 => UNS
* INC # I1: 4 # D1: 2,6 => UNS
* INC # I1: 4 # C2: 1,3 => UNS
* INC # I1: 4 # C2: 7 => UNS
* INC # I1: 4 # G4: 4,9 => UNS
* INC # I1: 4 # G4: 5 => UNS
* INC # I1: 4 # G6: 4,9 => UNS
* INC # I1: 4 # G6: 8 => UNS
* INC # I1: 4 # E2: 7,8 => UNS
* INC # I1: 4 # E2: 1,5 => UNS
* INC # I1: 4 # F2: 7,8 => UNS
* INC # I1: 4 # F2: 1 => UNS
* INC # I1: 4 # G4: 5,9 => UNS
* INC # I1: 4 # G4: 4 => UNS
* INC # I1: 4 # G6: 8,9 => UNS
* INC # I1: 4 # G6: 4 => UNS
* INC # I1: 4 => UNS
* INC # I1: 3,4 # D1: 1,3 => UNS
* INC # I1: 3,4 # D1: 2,4,6 => UNS
* INC # I1: 3,4 # C2: 1,3 => UNS
* INC # I1: 3,4 # C2: 7 => UNS
* INC # I1: 3,4 # D1: 3,4 => UNS
* INC # I1: 3,4 # D1: 1,2,6 => UNS
* INC # I1: 3,4 # D3: 3,4 => UNS
* INC # I1: 3,4 # D3: 2,6 => UNS
* INC # I1: 3,4 # G4: 4,9 => UNS
* INC # I1: 3,4 # G4: 5 => UNS
* INC # I1: 3,4 # G6: 4,9 => UNS
* INC # I1: 3,4 # G6: 8 => UNS
* INC # I1: 3,4 # E2: 7,8 => UNS
* INC # I1: 3,4 # E2: 1,5 => UNS
* INC # I1: 3,4 # F2: 7,8 => UNS
* INC # I1: 3,4 # F2: 1 => UNS
* INC # I1: 3,4 # G4: 5,9 => UNS
* INC # I1: 3,4 # G4: 4 => UNS
* INC # I1: 3,4 # G6: 8,9 => UNS
* INC # I1: 3,4 # G6: 4 => UNS
* INC # I1: 3,4 => UNS
* INC # I1: 9 # A1: 2,6 => UNS
* INC # I1: 9 # B1: 2,6 => UNS
* INC # I1: 9 # E3: 2,6 => UNS
* PRF # I1: 9 # F3: 2,6 => SOL
* STA # I1: 9 + F3: 2,6
* CNT 179 HDP CHAINS / 180 HYP OPENED