Analysis of xx-mith-te3-00037913-base.sdk

Contents

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

Original Sudoku

level: hard

position: .23......4..7......89....46.15.68.74......8.5.48...61....8.5.6....61...88...47.51 initial

Autosolve

position: .23......4..7......89....46.15.68.74......8.5.4857.61....8.5.6....61...88...47.51 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: 0:00:10.333106

The following important HDP chains were detected:

* DIS # A1: 5,6 # G1: 7,9 => CTR => G1: 1,5
* DIS # A1: 1,7 # A3: 5 => CTR => A3: 1,7
* PRF # A1: 1,7 + A3: 1,7 # G1: 1,7 => SOL
* STA # A1: 1,7 + A3: 1,7 + G1: 1,7
* CNT   3 HDP CHAINS /  52 HYP OPENED

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

Details

Positions

`.23......4..7......89....46.15.68.74......8.5.48...61....8.5.6....61...88...47.51`	initial
`.23......4..7......89....46.15.68.74......8.5.4857.61....8.5.6....61...88...47.51`	autosolve
`123456789456789132789231546215368974637194825948572613391825467574613298862947351`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
B2: 5,6
C2: 1,6
H1: 8,9
I1: 7,9
D5: 1,4
F5: 1,4
C9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,F5: 1.. / D5 = 1  =>  6 pairs (_) / F5 = 1  => 11 pairs (_)
A7,C7: 1.. / A7 = 1  =>  7 pairs (_) / C7 = 1  =>  9 pairs (_)
C2,C7: 1.. / C2 = 1  =>  7 pairs (_) / C7 = 1  =>  9 pairs (_)
D1,F1: 4.. / D1 = 4  =>  6 pairs (_) / F1 = 4  => 11 pairs (_)
D5,F5: 4.. / D5 = 4  => 11 pairs (_) / F5 = 4  =>  6 pairs (_)
C7,C8: 4.. / C7 = 4  =>  9 pairs (_) / C8 = 4  =>  7 pairs (_)
G7,G8: 4.. / G7 = 4  =>  7 pairs (_) / G8 = 4  =>  9 pairs (_)
C7,G7: 4.. / C7 = 4  =>  9 pairs (_) / G7 = 4  =>  7 pairs (_)
C8,G8: 4.. / C8 = 4  =>  7 pairs (_) / G8 = 4  =>  9 pairs (_)
D1,D5: 4.. / D1 = 4  =>  6 pairs (_) / D5 = 4  => 11 pairs (_)
F1,F5: 4.. / F1 = 4  => 11 pairs (_) / F5 = 4  =>  6 pairs (_)
A8,B8: 5.. / A8 = 5  =>  7 pairs (_) / B8 = 5  =>  9 pairs (_)
B2,B8: 5.. / B2 = 5  =>  7 pairs (_) / B8 = 5  =>  9 pairs (_)
F1,F2: 6.. / F1 = 6  =>  7 pairs (_) / F2 = 6  => 11 pairs (_)
B9,C9: 6.. / B9 = 6  => 10 pairs (_) / C9 = 6  =>  8 pairs (_)
A1,F1: 6.. / A1 = 6  => 11 pairs (_) / F1 = 6  =>  7 pairs (_)
A1,A5: 6.. / A1 = 6  => 11 pairs (_) / A5 = 6  =>  7 pairs (_)
A1,A3: 7.. / A1 = 7  =>  0 pairs (X) / A3 = 7  =>  7 pairs (_)
B5,C5: 7.. / B5 = 7  => 13 pairs (_) / C5 = 7  =>  8 pairs (_)
A3,G3: 7.. / A3 = 7  =>  7 pairs (_) / G3 = 7  =>  0 pairs (X)
I1,I7: 7.. / I1 = 7  =>  8 pairs (_) / I7 = 7  => 19 pairs (_)
E1,E2: 8.. / E1 = 8  => 13 pairs (_) / E2 = 8  =>  7 pairs (_)
H1,H2: 8.. / H1 = 8  =>  7 pairs (_) / H2 = 8  => 13 pairs (_)
E1,H1: 8.. / E1 = 8  => 13 pairs (_) / H1 = 8  =>  7 pairs (_)
E2,H2: 8.. / E2 = 8  =>  7 pairs (_) / H2 = 8  => 13 pairs (_)
* DURATION: 0:00:07.203831  START: 07:32:19.861896  END: 07:32:27.065727 2025-04-06
* CP COUNT: (25)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.156793  START: 07:32:33.623386  END: 07:32:43.780179 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00037913-base-pr-002.dot
* REASONING
* DIS # A1: 5,6 # G1: 7,9 => CTR => G1: 1,5
* DIS # A1: 1,7 # A3: 5 => CTR => A3: 1,7
* PRF # A1: 1,7 + A3: 1,7 # G1: 1,7 => SOL
* STA # A1: 1,7 + A3: 1,7 + G1: 1,7
* CNT   3 HDP CHAINS /  52 HYP OPENED

Header Info

rating: 7906; r2: 264582; index: 37913

Solution

position: 123456789456789132789231546215368974637194825948572613391825467574613298862947351 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 # A1: 5,6 => UNS
* INC # A1: 1,7 => UNS
* INC # A1: 1,6 => UNS
* INC # A1: 5,7 => UNS
* INC # F2: 1,6 => UNS
* INC # F2: 2,3,9 => UNS
* INC # H2: 8,9 => UNS
* INC # H2: 2,3 => UNS
* INC # E1: 8,9 => UNS
* INC # E1: 5 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 1,5 => UNS
* INC # I7: 7,9 => UNS
* INC # I7: 2,3 => UNS
* INC # D1: 1,4 => UNS
* INC # D1: 9 => UNS
* INC # F1: 1,4 => UNS
* INC # F1: 6,9 => UNS
* INC # C5: 2,6 => UNS
* INC # C5: 7 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,6 => UNS
* INC # A1: 1,7 => UNS
* INC # A1: 1,6 => UNS
* INC # A1: 5,7 => UNS
* INC # F2: 1,6 => UNS
* INC # F2: 2,3,9 => UNS
* INC # H2: 8,9 => UNS
* INC # H2: 2,3 => UNS
* INC # E1: 8,9 => UNS
* INC # E1: 5 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 1,5 => UNS
* INC # I7: 7,9 => UNS
* INC # I7: 2,3 => UNS
* INC # D1: 1,4 => UNS
* INC # D1: 9 => UNS
* INC # F1: 1,4 => UNS
* INC # F1: 6,9 => UNS
* INC # C5: 2,6 => UNS
* INC # C5: 7 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A1: 5,6 => UNS
* INC # A1: 1,7 => UNS
* INC # A1: 1,6 => UNS
* INC # A1: 5,7 => UNS
* INC # F2: 1,6 => UNS
* INC # F2: 2,3,9 => UNS
* INC # H2: 8,9 => UNS
* INC # H2: 2,3 => UNS
* INC # E1: 8,9 => UNS
* INC # E1: 5 => UNS
* INC # G1: 7,9 => UNS
* INC # G1: 1,5 => UNS
* INC # I7: 7,9 => UNS
* INC # I7: 2,3 => UNS
* INC # D1: 1,4 => UNS
* INC # D1: 9 => UNS
* INC # F1: 1,4 => UNS
* INC # F1: 6,9 => UNS
* INC # C5: 2,6 => UNS
* INC # C5: 7 => UNS
* INC # A1: 5,6 # H2: 8,9 => UNS
* INC # A1: 5,6 # H2: 2,3 => UNS
* INC # A1: 5,6 # E1: 8,9 => UNS
* INC # A1: 5,6 # E1: 5 => UNS
* DIS # A1: 5,6 # G1: 7,9 => CTR => G1: 1,5
* INC # A1: 5,6 + G1: 1,5 # D1: 1,4 => UNS
* INC # A1: 5,6 + G1: 1,5 # D1: 9 => UNS
* INC # A1: 5,6 + G1: 1,5 # F1: 1,4 => UNS
* INC # A1: 5,6 + G1: 1,5 # F1: 6,9 => UNS
* INC # A1: 5,6 + G1: 1,5 # C5: 2,6 => UNS
* INC # A1: 5,6 + G1: 1,5 # C5: 7 => UNS
* INC # A1: 5,6 + G1: 1,5 # G3: 1,5 => UNS
* INC # A1: 5,6 + G1: 1,5 # G3: 2,3 => UNS
* INC # A1: 5,6 + G1: 1,5 # H2: 8,9 => UNS
* INC # A1: 5,6 + G1: 1,5 # H2: 2,3 => UNS
* INC # A1: 5,6 + G1: 1,5 # E1: 8,9 => UNS
* INC # A1: 5,6 + G1: 1,5 # E1: 5 => UNS
* INC # A1: 5,6 + G1: 1,5 # D1: 1,4 => UNS
* INC # A1: 5,6 + G1: 1,5 # D1: 9 => UNS
* INC # A1: 5,6 + G1: 1,5 # F1: 1,4 => UNS
* INC # A1: 5,6 + G1: 1,5 # F1: 6,9 => UNS
* INC # A1: 5,6 + G1: 1,5 # C5: 2,6 => UNS
* INC # A1: 5,6 + G1: 1,5 # C5: 7 => UNS
* INC # A1: 5,6 + G1: 1,5 # C7: 4,7 => UNS
* INC # A1: 5,6 + G1: 1,5 # C7: 2 => UNS
* INC # A1: 5,6 + G1: 1,5 # C8: 4,7 => UNS
* INC # A1: 5,6 + G1: 1,5 # C8: 2 => UNS
* INC # A1: 5,6 + G1: 1,5 => UNS
* INC # A1: 1,7 # A3: 1,7 => UNS
* DIS # A1: 1,7 # A3: 5 => CTR => A3: 1,7
* PRF # A1: 1,7 + A3: 1,7 # G1: 1,7 => SOL
* STA # A1: 1,7 + A3: 1,7 + G1: 1,7
* CNT  51 HDP CHAINS /  52 HYP OPENED