Analysis of xx-mith-te3-00012238-base.sdk

Contents

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

Original Sudoku

level: hard

position: ...4.678.......2...8.27....2.836....37..42....468.7..2...6.4..3.34...9...6.....14 initial

Autosolve

position: ...4.678...7...2...8.27....2.836....37..42..8.468.7..2...6.4..3.34...9...6.....14 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: 0:00:16.167365

The following important HDP chains were detected:

* PRF # H2: 3,5,9 # F9: 5,8 => SOL
* STA # H2: 3,5,9 + F9: 5,8
* CNT   1 HDP CHAINS /  63 HYP OPENED

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

Details

Positions

`...4.678.......2...8.27....2.836....37..42....468.7..2...6.4..3.34...9...6.....14`	initial
`...4.678...7...2...8.27....2.836....37..42..8.468.7..2...6.4..3.34...9...6.....14`	autosolve
`123456789457189236689273145298365471371942658546817392715694823834521967962738514`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A2: 4,6
A3: 4,6
G4: 1,4
G5: 1,6
G6: 1,3
G7: 5,8
H7: 2,7
I8: 6,7
G9: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B1,C1: 2.. / B1 = 2  =>  9 pairs (_) / C1 = 2  =>  0 pairs (X)
H7,H8: 2.. / H7 = 2  => 10 pairs (_) / H8 = 2  => 10 pairs (_)
E8,H8: 2.. / E8 = 2  => 10 pairs (_) / H8 = 2  => 10 pairs (_)
C9,E9: 2.. / C9 = 2  =>  9 pairs (_) / E9 = 2  => 10 pairs (_)
B1,B7: 2.. / B1 = 2  =>  9 pairs (_) / B7 = 2  =>  0 pairs (X)
C1,C3: 3.. / C1 = 3  =>  9 pairs (_) / C3 = 3  => 16 pairs (_)
G6,H6: 3.. / G6 = 3  =>  9 pairs (_) / H6 = 3  => 11 pairs (_)
E9,F9: 3.. / E9 = 3  =>  9 pairs (_) / F9 = 3  =>  9 pairs (_)
C1,E1: 3.. / C1 = 3  =>  9 pairs (_) / E1 = 3  => 16 pairs (_)
G3,G6: 3.. / G3 = 3  => 11 pairs (_) / G6 = 3  =>  9 pairs (_)
A2,A3: 4.. / A2 = 4  =>  7 pairs (_) / A3 = 4  =>  8 pairs (_)
G4,H4: 4.. / G4 = 4  =>  8 pairs (_) / H4 = 4  => 10 pairs (_)
A2,H2: 4.. / A2 = 4  =>  7 pairs (_) / H2 = 4  =>  8 pairs (_)
G3,G4: 4.. / G3 = 4  => 10 pairs (_) / G4 = 4  =>  8 pairs (_)
G7,G9: 5.. / G7 = 5  =>  7 pairs (_) / G9 = 5  =>  9 pairs (_)
A2,A3: 6.. / A2 = 6  =>  8 pairs (_) / A3 = 6  =>  7 pairs (_)
G5,H5: 6.. / G5 = 6  =>  9 pairs (_) / H5 = 6  => 10 pairs (_)
H8,I8: 6.. / H8 = 6  =>  8 pairs (_) / I8 = 6  => 12 pairs (_)
G3,G5: 6.. / G3 = 6  => 10 pairs (_) / G5 = 6  =>  9 pairs (_)
H4,I4: 7.. / H4 = 7  =>  8 pairs (_) / I4 = 7  => 12 pairs (_)
D8,D9: 7.. / D8 = 7  => 11 pairs (_) / D9 = 7  => 10 pairs (_)
A7,H7: 7.. / A7 = 7  => 10 pairs (_) / H7 = 7  => 10 pairs (_)
A9,D9: 7.. / A9 = 7  => 11 pairs (_) / D9 = 7  => 10 pairs (_)
I4,I8: 7.. / I4 = 7  => 12 pairs (_) / I8 = 7  =>  8 pairs (_)
E2,F2: 8.. / E2 = 8  =>  9 pairs (_) / F2 = 8  => 10 pairs (_)
G7,G9: 8.. / G7 = 8  =>  9 pairs (_) / G9 = 8  =>  7 pairs (_)
* DURATION: 0:00:07.836837  START: 04:19:29.954765  END: 04:19:37.791602 2025-04-06
* CP COUNT: (26)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:15.951080  START: 04:19:44.215868  END: 04:20:00.166948 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00012238-base-pr-002.dot
* REASONING
* PRF # H2: 3,5,9 # F9: 5,8 => SOL
* STA # H2: 3,5,9 + F9: 5,8
* CNT   1 HDP CHAINS /  63 HYP OPENED

Header Info

rating: 2791; r2: 147175; index: 12238

Solution

position: 123456789457189236689273145298365471371942658546817392715694823834521967962738514 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 # H2: 4,6 => UNS
* INC # H2: 3,5,9 => UNS
* INC # G3: 4,6 => UNS
* INC # H3: 4,6 => UNS
* INC # G3: 1,4 => UNS
* INC # G3: 3,6 => UNS
* INC # G3: 1,6 => UNS
* INC # G3: 3,4 => UNS
* INC # G3: 1,3 => UNS
* INC # G3: 4,6 => UNS
* INC # A7: 5,8 => UNS
* INC # E7: 5,8 => UNS
* INC # H8: 2,7 => UNS
* INC # H8: 6 => UNS
* INC # H8: 6,7 => UNS
* INC # H8: 2 => UNS
* INC # A9: 5,8 => UNS
* INC # E9: 5,8 => UNS
* INC # F9: 5,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 4,6 => UNS
* INC # H2: 3,5,9 => UNS
* INC # G3: 4,6 => UNS
* INC # H3: 4,6 => UNS
* INC # G3: 1,4 => UNS
* INC # G3: 3,6 => UNS
* INC # G3: 1,6 => UNS
* INC # G3: 3,4 => UNS
* INC # G3: 1,3 => UNS
* INC # G3: 4,6 => UNS
* INC # A7: 5,8 => UNS
* INC # E7: 5,8 => UNS
* INC # H8: 2,7 => UNS
* INC # H8: 6 => UNS
* INC # H8: 6,7 => UNS
* INC # H8: 2 => UNS
* INC # A9: 5,8 => UNS
* INC # E9: 5,8 => UNS
* INC # F9: 5,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 4,6 => UNS
* INC # H2: 3,5,9 => UNS
* INC # G3: 4,6 => UNS
* INC # H3: 4,6 => UNS
* INC # G3: 1,4 => UNS
* INC # G3: 3,6 => UNS
* INC # G3: 1,6 => UNS
* INC # G3: 3,4 => UNS
* INC # G3: 1,3 => UNS
* INC # G3: 4,6 => UNS
* INC # A7: 5,8 => UNS
* INC # E7: 5,8 => UNS
* INC # H8: 2,7 => UNS
* INC # H8: 6 => UNS
* INC # H8: 6,7 => UNS
* INC # H8: 2 => UNS
* INC # A9: 5,8 => UNS
* INC # E9: 5,8 => UNS
* INC # F9: 5,8 => UNS
* INC # H2: 4,6 # G3: 4,6 => UNS
* INC # H2: 4,6 # H3: 4,6 => UNS
* INC # H2: 4,6 # E9: 3,8 => UNS
* INC # H2: 4,6 # E9: 2,5,9 => UNS
* INC # H2: 4,6 # F9: 3,8 => UNS
* INC # H2: 4,6 # F9: 5,9 => UNS
* INC # H2: 4,6 # G3: 4,6 => UNS
* INC # H2: 4,6 # H3: 4,6 => UNS
* INC # H2: 4,6 # G3: 1,4 => UNS
* INC # H2: 4,6 # G3: 3,6 => UNS
* INC # H2: 4,6 # G3: 1,6 => UNS
* INC # H2: 4,6 # G3: 3,4 => UNS
* INC # H2: 4,6 # G3: 1,3 => UNS
* INC # H2: 4,6 # G3: 4,6 => UNS
* INC # H2: 4,6 # A7: 5,8 => UNS
* INC # H2: 4,6 # E7: 5,8 => UNS
* INC # H2: 4,6 # H8: 2,7 => UNS
* INC # H2: 4,6 # H8: 6 => UNS
* INC # H2: 4,6 # H8: 6,7 => UNS
* INC # H2: 4,6 # H8: 2 => UNS
* INC # H2: 4,6 # A9: 5,8 => UNS
* INC # H2: 4,6 # E9: 5,8 => UNS
* INC # H2: 4,6 # F9: 5,8 => UNS
* INC # H2: 4,6 => UNS
* INC # H2: 3,5,9 # C3: 1,3 => UNS
* INC # H2: 3,5,9 # F3: 1,3 => UNS
* INC # H2: 3,5,9 # I4: 5,9 => UNS
* INC # H2: 3,5,9 # H6: 5,9 => UNS
* INC # H2: 3,5,9 # C5: 5,9 => UNS
* INC # H2: 3,5,9 # D5: 5,9 => UNS
* INC # H2: 3,5,9 # H2: 5,9 => UNS
* INC # H2: 3,5,9 # H2: 3 => UNS
* INC # H2: 3,5,9 # E7: 1,5 => UNS
* INC # H2: 3,5,9 # F8: 1,5 => UNS
* INC # H2: 3,5,9 # A8: 1,5 => UNS
* INC # H2: 3,5,9 # A8: 8 => UNS
* INC # H2: 3,5,9 # D2: 1,5 => UNS
* INC # H2: 3,5,9 # D5: 1,5 => UNS
* INC # H2: 3,5,9 # E7: 5,8 => UNS
* INC # H2: 3,5,9 # E7: 1,9 => UNS
* INC # H2: 3,5,9 # A9: 5,8 => UNS
* INC # H2: 3,5,9 # E9: 5,8 => UNS
* PRF # H2: 3,5,9 # F9: 5,8 => SOL
* STA # H2: 3,5,9 + F9: 5,8
* CNT  62 HDP CHAINS /  63 HYP OPENED