Analysis of xx-mith-te3-00157188-base.sdk

Contents

Original Sudoku
Autosolve
Pair Reduction Variants
Details
Solution
Appendix: Full HDP Chains

Original Sudoku

level: hard

position: 1.3.56.8...7.8...6.....7....36..5...51.67....7.8.136..3.1...5.8.....1394....3.1.2 initial

Autosolve

position: 1.3.56.8..57.8...6.....7....36..5...51.67....7.8.136..3.1...5.8.....1394....3.1.2 autosolve

Pair Reduction Variants

Pair Reduction Analysis

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

Pair Reduction

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

Deep Pair Reduction

Time used: 0:00:14.121197

The following important HDP chains were detected:

* PRF # A8: 6,8 # F9: 4,9 => SOL
* STA # A8: 6,8 + F9: 4,9
* CNT   1 HDP CHAINS /  50 HYP OPENED

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

Details

Positions

`1.3.56.8...7.8...6.....7....36..5...51.67....7.8.136..3.1...5.8.....1394....3.1.2`	initial
`1.3.56.8..57.8...6.....7....36..5...51.67....7.8.136..3.1...5.8.....1394....3.1.2`	autosolve
`123456789457189236689327451236945817514678923798213645341792568872561394965834172`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (13)
A3: 6,8
B3: 6,8
D2: 1,3
D3: 1,3
I1: 7,9
H2: 1,3
G5: 8,9
I5: 3,9
I6: 5,9
C8: 2,5
E8: 2,6
H7: 6,7
H9: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  => 12 pairs (_) / D3 = 1  => 11 pairs (_)
H4,I4: 1.. / H4 = 1  => 11 pairs (_) / I4 = 1  => 13 pairs (_)
D2,H2: 1.. / D2 = 1  => 12 pairs (_) / H2 = 1  => 11 pairs (_)
I3,I4: 1.. / I3 = 1  => 11 pairs (_) / I4 = 1  => 13 pairs (_)
D2,D3: 3.. / D2 = 3  => 11 pairs (_) / D3 = 3  => 12 pairs (_)
H5,I5: 3.. / H5 = 3  => 10 pairs (_) / I5 = 3  => 14 pairs (_)
D2,H2: 3.. / D2 = 3  => 11 pairs (_) / H2 = 3  => 12 pairs (_)
I3,I5: 3.. / I3 = 3  => 10 pairs (_) / I5 = 3  => 14 pairs (_)
H3,I3: 5.. / H3 = 5  => 14 pairs (_) / I3 = 5  => 14 pairs (_)
H6,I6: 5.. / H6 = 5  => 14 pairs (_) / I6 = 5  => 14 pairs (_)
C8,C9: 5.. / C8 = 5  => 13 pairs (_) / C9 = 5  => 12 pairs (_)
D8,D9: 5.. / D8 = 5  => 12 pairs (_) / D9 = 5  => 13 pairs (_)
C8,D8: 5.. / C8 = 5  => 13 pairs (_) / D8 = 5  => 12 pairs (_)
C9,D9: 5.. / C9 = 5  => 12 pairs (_) / D9 = 5  => 13 pairs (_)
H3,H6: 5.. / H3 = 5  => 14 pairs (_) / H6 = 5  => 14 pairs (_)
I3,I6: 5.. / I3 = 5  => 14 pairs (_) / I6 = 5  => 14 pairs (_)
A3,B3: 6.. / A3 = 6  => 12 pairs (_) / B3 = 6  => 14 pairs (_)
E7,E8: 6.. / E7 = 6  => 19 pairs (_) / E8 = 6  => 13 pairs (_)
H7,H9: 6.. / H7 = 6  => 11 pairs (_) / H9 = 6  => 16 pairs (_)
G1,I1: 7.. / G1 = 7  => 14 pairs (_) / I1 = 7  => 12 pairs (_)
G4,I4: 7.. / G4 = 7  => 12 pairs (_) / I4 = 7  => 14 pairs (_)
H7,H9: 7.. / H7 = 7  => 16 pairs (_) / H9 = 7  => 11 pairs (_)
B8,D8: 7.. / B8 = 7  => 13 pairs (_) / D8 = 7  => 13 pairs (_)
G1,G4: 7.. / G1 = 7  => 14 pairs (_) / G4 = 7  => 12 pairs (_)
I1,I4: 7.. / I1 = 7  => 12 pairs (_) / I4 = 7  => 14 pairs (_)
A3,B3: 8.. / A3 = 8  => 14 pairs (_) / B3 = 8  => 12 pairs (_)
D4,F5: 8.. / D4 = 8  => 13 pairs (_) / F5 = 8  => 17 pairs (_)
G4,G5: 8.. / G4 = 8  => 17 pairs (_) / G5 = 8  => 13 pairs (_)
D4,G4: 8.. / D4 = 8  => 13 pairs (_) / G4 = 8  => 17 pairs (_)
F5,G5: 8.. / F5 = 8  => 17 pairs (_) / G5 = 8  => 13 pairs (_)
F5,F9: 8.. / F5 = 8  => 17 pairs (_) / F9 = 8  => 13 pairs (_)
* DURATION: 0:00:10.829207  START: 15:47:53.234126  END: 15:48:04.063333 2025-04-05
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:13.969725  START: 15:48:13.600170  END: 15:48:27.569895 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00157188-base-pr-002.dot
* REASONING
* PRF # A8: 6,8 # F9: 4,9 => SOL
* STA # A8: 6,8 + F9: 4,9
* CNT   1 HDP CHAINS /  50 HYP OPENED

Header Info

rating: 43747; r2: 827853; index: 157188

Solution

position: 123456789457189236689327451236945817514678923798213645341792568872561394965834172 solved

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 # A8: 6,8 => UNS
* INC # A9: 6,8 => UNS
* INC # B8: 6,8 => UNS
* INC # B9: 6,8 => UNS
* INC # H3: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 2,4 => UNS
* INC # I4: 7,9 => UNS
* INC # I4: 1 => UNS
* INC # H3: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # G4: 8,9 => UNS
* INC # G4: 7 => UNS
* INC # F5: 8,9 => UNS
* INC # F5: 2,4 => UNS
* INC # D8: 2,5 => UNS
* INC # D8: 7,8 => UNS
* INC # E7: 2,6 => UNS
* INC # E7: 4,9 => UNS
* INC # A8: 2,6 => UNS
* INC # B8: 2,6 => UNS
* INC # B7: 6,7 => UNS
* INC # B7: 2,4,9 => UNS
* INC # B9: 6,7 => UNS
* INC # B9: 4,8,9 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 6,8 => UNS
* INC # A9: 6,8 => UNS
* INC # B8: 6,8 => UNS
* INC # B9: 6,8 => UNS
* INC # H3: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 2,4 => UNS
* INC # I4: 7,9 => UNS
* INC # I4: 1 => UNS
* INC # H3: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # G4: 8,9 => UNS
* INC # G4: 7 => UNS
* INC # F5: 8,9 => UNS
* INC # F5: 2,4 => UNS
* INC # D8: 2,5 => UNS
* INC # D8: 7,8 => UNS
* INC # E7: 2,6 => UNS
* INC # E7: 4,9 => UNS
* INC # A8: 2,6 => UNS
* INC # B8: 2,6 => UNS
* INC # B7: 6,7 => UNS
* INC # B7: 2,4,9 => UNS
* INC # B9: 6,7 => UNS
* INC # B9: 4,8,9 => UNS
* CNT  26 HDP CHAINS /  26 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A8: 6,8 => UNS
* INC # A9: 6,8 => UNS
* INC # B8: 6,8 => UNS
* INC # B9: 6,8 => UNS
* INC # H3: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 2,4 => UNS
* INC # I4: 7,9 => UNS
* INC # I4: 1 => UNS
* INC # H3: 1,3 => UNS
* INC # I3: 1,3 => UNS
* INC # G4: 8,9 => UNS
* INC # G4: 7 => UNS
* INC # F5: 8,9 => UNS
* INC # F5: 2,4 => UNS
* INC # D8: 2,5 => UNS
* INC # D8: 7,8 => UNS
* INC # E7: 2,6 => UNS
* INC # E7: 4,9 => UNS
* INC # A8: 2,6 => UNS
* INC # B8: 2,6 => UNS
* INC # B7: 6,7 => UNS
* INC # B7: 2,4,9 => UNS
* INC # B9: 6,7 => UNS
* INC # B9: 4,8,9 => UNS
* INC # A8: 6,8 # B8: 6,8 => UNS
* INC # A8: 6,8 # B9: 6,8 => UNS
* INC # A8: 6,8 # H3: 1,3 => UNS
* INC # A8: 6,8 # I3: 1,3 => UNS
* INC # A8: 6,8 # G1: 7,9 => UNS
* INC # A8: 6,8 # G1: 2,4 => UNS
* INC # A8: 6,8 # I4: 7,9 => UNS
* INC # A8: 6,8 # I4: 1 => UNS
* INC # A8: 6,8 # H3: 1,3 => UNS
* INC # A8: 6,8 # I3: 1,3 => UNS
* INC # A8: 6,8 # G4: 8,9 => UNS
* INC # A8: 6,8 # G4: 7 => UNS
* INC # A8: 6,8 # F5: 8,9 => UNS
* INC # A8: 6,8 # F5: 2,4 => UNS
* INC # A8: 6,8 # B8: 6,8 => UNS
* INC # A8: 6,8 # B9: 6,8 => UNS
* INC # A8: 6,8 # D8: 2,5 => UNS
* INC # A8: 6,8 # D8: 7,8 => UNS
* INC # A8: 6,8 # B7: 4,9 => UNS
* INC # A8: 6,8 # B9: 4,9 => UNS
* INC # A8: 6,8 # C9: 4,9 => UNS
* INC # A8: 6,8 # D9: 4,9 => UNS
* PRF # A8: 6,8 # F9: 4,9 => SOL
* STA # A8: 6,8 + F9: 4,9
* CNT  49 HDP CHAINS /  50 HYP OPENED