Analysis of xx-mith-te3-00026919-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1..4.678.4..18.........3......6.134......8.17.1.73.6.8.95......7.1....6...23..... initial

Autosolve

position: 1..4.678.4..18...6....73......6.134......8.17.1.73.6.8.95......7.1....6...23..... 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: 0:00:16.903659

The following important HDP chains were detected:

* PRF # I1: 3,9 # E5: 2,5 => SOL
* STA # I1: 3,9 + E5: 2,5
* CNT   1 HDP CHAINS /  82 HYP OPENED

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

Details

Positions

`1..4.678.4..18.........3......6.134......8.17.1.73.6.8.95......7.1....6...23.....`	initial
`1..4.678.4..18...6....73......6.134......8.17.1.73.6.8.95......7.1....6...23.....`	autosolve
`123456789457189236986273154278691345364528917519734628695812473731945862842367591`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C1: 3,9
G3: 1,4
I3: 1,4
C6: 4,9
A9: 6,8
D7: 2,8
E7: 1,6
E9: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  6 pairs (_) / I3 = 1  =>  6 pairs (_)
E7,E9: 1.. / E7 = 1  => 10 pairs (_) / E9 = 1  =>  7 pairs (_)
I1,H2: 3.. / I1 = 3  => 12 pairs (_) / H2 = 3  => 10 pairs (_)
A7,B8: 3.. / A7 = 3  =>  9 pairs (_) / B8 = 3  => 14 pairs (_)
B8,I8: 3.. / B8 = 3  => 14 pairs (_) / I8 = 3  =>  9 pairs (_)
A5,A7: 3.. / A5 = 3  => 14 pairs (_) / A7 = 3  =>  9 pairs (_)
H2,H7: 3.. / H2 = 3  => 10 pairs (_) / H7 = 3  => 12 pairs (_)
G3,I3: 4.. / G3 = 4  =>  6 pairs (_) / I3 = 4  =>  6 pairs (_)
C5,C6: 4.. / C5 = 4  => 15 pairs (_) / C6 = 4  =>  7 pairs (_)
E5,F6: 4.. / E5 = 4  =>  7 pairs (_) / F6 = 4  => 15 pairs (_)
B8,B9: 4.. / B8 = 4  => 11 pairs (_) / B9 = 4  =>  9 pairs (_)
C5,E5: 4.. / C5 = 4  => 15 pairs (_) / E5 = 4  =>  7 pairs (_)
C6,F6: 4.. / C6 = 4  =>  7 pairs (_) / F6 = 4  => 15 pairs (_)
E5,E8: 4.. / E5 = 4  =>  7 pairs (_) / E8 = 4  => 15 pairs (_)
E7,E9: 6.. / E7 = 6  =>  7 pairs (_) / E9 = 6  => 10 pairs (_)
A7,E7: 6.. / A7 = 6  => 10 pairs (_) / E7 = 6  =>  7 pairs (_)
C3,C5: 6.. / C3 = 6  =>  8 pairs (_) / C5 = 6  =>  9 pairs (_)
B2,C2: 7.. / B2 = 7  =>  9 pairs (_) / C2 = 7  =>  9 pairs (_)
B4,C4: 7.. / B4 = 7  =>  9 pairs (_) / C4 = 7  =>  9 pairs (_)
F7,F9: 7.. / F7 = 7  =>  9 pairs (_) / F9 = 7  => 11 pairs (_)
H7,H9: 7.. / H7 = 7  => 11 pairs (_) / H9 = 7  =>  9 pairs (_)
F7,H7: 7.. / F7 = 7  =>  9 pairs (_) / H7 = 7  => 11 pairs (_)
F9,H9: 7.. / F9 = 7  => 11 pairs (_) / H9 = 7  =>  9 pairs (_)
B2,B4: 7.. / B2 = 7  =>  9 pairs (_) / B4 = 7  =>  9 pairs (_)
C2,C4: 7.. / C2 = 7  =>  9 pairs (_) / C4 = 7  =>  9 pairs (_)
D7,D8: 8.. / D7 = 8  =>  8 pairs (_) / D8 = 8  => 12 pairs (_)
C3,C4: 8.. / C3 = 8  =>  9 pairs (_) / C4 = 8  =>  9 pairs (_)
* DURATION: 0:00:08.239333  START: 06:39:26.149374  END: 06:39:34.388707 2025-04-06
* CP COUNT: (27)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:16.552077  START: 06:39:41.343690  END: 06:39:57.895767 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00026919-base-pr-002.dot
* REASONING
* PRF # I1: 3,9 # E5: 2,5 => SOL
* STA # I1: 3,9 + E5: 2,5
* CNT   1 HDP CHAINS /  82 HYP OPENED

Header Info

rating: 5570; r2: 297962; index: 26919

Solution

position: 123456789457189236986273154278691345364528917519734628695812473731945862842367591 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 # C2: 3,9 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 2,5 => UNS
* INC # C5: 3,9 => UNS
* INC # C5: 4,6 => UNS
* INC # G7: 1,4 => UNS
* INC # G9: 1,4 => UNS
* INC # I7: 1,4 => UNS
* INC # I9: 1,4 => UNS
* INC # C5: 4,9 => UNS
* INC # C5: 3,6 => UNS
* INC # F6: 4,9 => UNS
* INC # F6: 2,5 => UNS
* INC # A7: 6,8 => UNS
* INC # B9: 6,8 => UNS
* INC # A3: 6,8 => UNS
* INC # A3: 2,5,9 => UNS
* INC # D8: 2,8 => UNS
* INC # D8: 5,9 => UNS
* INC # G7: 2,8 => UNS
* INC # G7: 1,4 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 3,9 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 2,5 => UNS
* INC # C5: 3,9 => UNS
* INC # C5: 4,6 => UNS
* INC # G7: 1,4 => UNS
* INC # G9: 1,4 => UNS
* INC # I7: 1,4 => UNS
* INC # I9: 1,4 => UNS
* INC # C5: 4,9 => UNS
* INC # C5: 3,6 => UNS
* INC # F6: 4,9 => UNS
* INC # F6: 2,5 => UNS
* INC # A7: 6,8 => UNS
* INC # B9: 6,8 => UNS
* INC # A3: 6,8 => UNS
* INC # A3: 2,5,9 => UNS
* INC # D8: 2,8 => UNS
* INC # D8: 5,9 => UNS
* INC # G7: 2,8 => UNS
* INC # G7: 1,4 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C2: 3,9 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 => UNS
* INC # I1: 2,5 => UNS
* INC # C5: 3,9 => UNS
* INC # C5: 4,6 => UNS
* INC # G7: 1,4 => UNS
* INC # G9: 1,4 => UNS
* INC # I7: 1,4 => UNS
* INC # I9: 1,4 => UNS
* INC # C5: 4,9 => UNS
* INC # C5: 3,6 => UNS
* INC # F6: 4,9 => UNS
* INC # F6: 2,5 => UNS
* INC # A7: 6,8 => UNS
* INC # B9: 6,8 => UNS
* INC # A3: 6,8 => UNS
* INC # A3: 2,5,9 => UNS
* INC # D8: 2,8 => UNS
* INC # D8: 5,9 => UNS
* INC # G7: 2,8 => UNS
* INC # G7: 1,4 => UNS
* INC # C2: 3,9 # A3: 2,5 => UNS
* INC # C2: 3,9 # B3: 2,5 => UNS
* INC # C2: 3,9 # E1: 2,5 => UNS
* INC # C2: 3,9 # I1: 2,5 => UNS
* INC # C2: 3,9 # B4: 2,5 => UNS
* INC # C2: 3,9 # B5: 2,5 => UNS
* INC # C2: 3,9 # I1: 3,9 => UNS
* INC # C2: 3,9 # I1: 2,5 => UNS
* INC # C2: 3,9 # H2: 3,9 => UNS
* INC # C2: 3,9 # H2: 2,5 => UNS
* INC # C2: 3,9 # G7: 1,4 => UNS
* INC # C2: 3,9 # G9: 1,4 => UNS
* INC # C2: 3,9 # I7: 1,4 => UNS
* INC # C2: 3,9 # I9: 1,4 => UNS
* INC # C2: 3,9 # A7: 6,8 => UNS
* INC # C2: 3,9 # B9: 6,8 => UNS
* INC # C2: 3,9 # D8: 2,8 => UNS
* INC # C2: 3,9 # D8: 5,9 => UNS
* INC # C2: 3,9 # G7: 2,8 => UNS
* INC # C2: 3,9 # G7: 1,4 => UNS
* INC # C2: 3,9 => UNS
* INC # C2: 7 # I1: 3,9 => UNS
* INC # C2: 7 # I1: 2,5 => UNS
* INC # C2: 7 # C5: 3,9 => UNS
* INC # C2: 7 # C5: 4,6 => UNS
* INC # C2: 7 # G7: 1,4 => UNS
* INC # C2: 7 # G9: 1,4 => UNS
* INC # C2: 7 # I7: 1,4 => UNS
* INC # C2: 7 # I9: 1,4 => UNS
* INC # C2: 7 # A4: 8,9 => UNS
* INC # C2: 7 # A4: 2,5 => UNS
* INC # C2: 7 # C3: 8,9 => UNS
* INC # C2: 7 # C3: 6 => UNS
* INC # C2: 7 # C5: 4,9 => UNS
* INC # C2: 7 # C5: 3,6 => UNS
* INC # C2: 7 # F6: 4,9 => UNS
* INC # C2: 7 # F6: 2,5 => UNS
* INC # C2: 7 # A7: 6,8 => UNS
* INC # C2: 7 # B9: 6,8 => UNS
* INC # C2: 7 # A3: 6,8 => UNS
* INC # C2: 7 # A3: 2,5,9 => UNS
* INC # C2: 7 # D8: 2,8 => UNS
* INC # C2: 7 # D8: 5,9 => UNS
* INC # C2: 7 # G7: 2,8 => UNS
* INC # C2: 7 # G7: 1,4 => UNS
* INC # C2: 7 => UNS
* INC # I1: 3,9 # B2: 2,5 => UNS
* INC # I1: 3,9 # A3: 2,5 => UNS
* INC # I1: 3,9 # B3: 2,5 => UNS
* INC # I1: 3,9 # B4: 2,5 => UNS
* INC # I1: 3,9 # B5: 2,5 => UNS
* INC # I1: 3,9 # C2: 3,9 => UNS
* INC # I1: 3,9 # C2: 7 => UNS
* INC # I1: 3,9 # C5: 3,9 => UNS
* INC # I1: 3,9 # C5: 4,6 => UNS
* INC # I1: 3,9 # F2: 2,5 => UNS
* INC # I1: 3,9 # D3: 2,5 => UNS
* INC # I1: 3,9 # E4: 2,5 => UNS
* PRF # I1: 3,9 # E5: 2,5 => SOL
* STA # I1: 3,9 + E5: 2,5
* CNT  81 HDP CHAINS /  82 HYP OPENED