Analysis of xx-mith-te3-00130483-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...45.......1892.6....32........18.7.18....927.9..861..71......6.28.....98..1.... initial

Autosolve

position: .2.45.......1892.6.9..32...26...18.7.18....927.9..861..71.....86.28.....98..1.... 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: 0:00:32.151482

The following important HDP chains were detected:

* DIS # C1: 3 # F8: 4,7 => CTR => F8: 3,5
* DIS # C1: 3 + F8: 3,5 # G9: 4,5 => CTR => G9: 3,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 # H8: 5 => CTR => H8: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 # E5: 6 => CTR => E5: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 # F9: 3,5 => CTR => F9: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 + F9: 4,7 # G1: 1,9 => CTR => G1: 7
* PRF # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 + F9: 4,7 + G1: 7 => SOL
* STA C1: 3
* CNT   7 HDP CHAINS /  78 HYP OPENED

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

Details

Positions

...45.......1892.6....32........18.7.18....927.9..861..71......6.28.....98..1.... initial
.2.45.......1892.6.9..32...26...18.7.18....927.9..861..71.....86.28.....98..1.... autosolve
123456789457189236896732154265391847318674592749528613571963428632845971984217365 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A1: 1,8
A3: 1,8
F1: 6,7
D3: 6,7
E4: 4,9
E6: 2,4
H7: 2,6
H9: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  =>  7 pairs (_) / A3 = 1  => 12 pairs (_)
G8,I8: 1.. / G8 = 1  =>  8 pairs (_) / I8 = 1  =>  9 pairs (_)
D6,E6: 2.. / D6 = 2  =>  9 pairs (_) / E6 = 2  =>  8 pairs (_)
H7,H9: 2.. / H7 = 2  =>  6 pairs (_) / H9 = 2  => 10 pairs (_)
D9,H9: 2.. / D9 = 2  =>  6 pairs (_) / H9 = 2  => 10 pairs (_)
E6,E7: 2.. / E6 = 2  =>  8 pairs (_) / E7 = 2  =>  9 pairs (_)
C1,C3: 6.. / C1 = 6  =>  7 pairs (_) / C3 = 6  =>  9 pairs (_)
F1,D3: 6.. / F1 = 6  =>  9 pairs (_) / D3 = 6  =>  7 pairs (_)
H7,H9: 6.. / H7 = 6  => 10 pairs (_) / H9 = 6  =>  6 pairs (_)
C1,F1: 6.. / C1 = 6  =>  7 pairs (_) / F1 = 6  =>  9 pairs (_)
C3,D3: 6.. / C3 = 6  =>  9 pairs (_) / D3 = 6  =>  7 pairs (_)
E5,E7: 6.. / E5 = 6  => 10 pairs (_) / E7 = 6  =>  8 pairs (_)
F1,D3: 7.. / F1 = 7  =>  7 pairs (_) / D3 = 7  =>  9 pairs (_)
C2,H2: 7.. / C2 = 7  =>  9 pairs (_) / H2 = 7  => 11 pairs (_)
E5,E8: 7.. / E5 = 7  =>  7 pairs (_) / E8 = 7  => 11 pairs (_)
A1,A3: 8.. / A1 = 8  => 12 pairs (_) / A3 = 8  =>  7 pairs (_)
H1,H3: 8.. / H1 = 8  =>  7 pairs (_) / H3 = 8  => 12 pairs (_)
A1,H1: 8.. / A1 = 8  => 12 pairs (_) / H1 = 8  =>  7 pairs (_)
A3,H3: 8.. / A3 = 8  =>  7 pairs (_) / H3 = 8  => 12 pairs (_)
G1,I1: 9.. / G1 = 9  => 10 pairs (_) / I1 = 9  =>  8 pairs (_)
D4,E4: 9.. / D4 = 9  => 12 pairs (_) / E4 = 9  => 11 pairs (_)
D4,D7: 9.. / D4 = 9  => 12 pairs (_) / D7 = 9  => 11 pairs (_)
I1,I8: 9.. / I1 = 9  =>  8 pairs (_) / I8 = 9  => 10 pairs (_)
* DURATION: 0:00:08.141429  START: 19:56:47.939536  END: 19:56:56.080965 2025-04-06
* CP COUNT: (23)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:31.942719  START: 19:57:02.832835  END: 19:57:34.775554 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00130483-base-pr-002.dot
* REASONING
* DIS # C1: 3 # F8: 4,7 => CTR => F8: 3,5
* DIS # C1: 3 + F8: 3,5 # G9: 4,5 => CTR => G9: 3,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 # H8: 5 => CTR => H8: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 # E5: 6 => CTR => E5: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 # F9: 3,5 => CTR => F9: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 + F9: 4,7 # G1: 1,9 => CTR => G1: 7
* PRF # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 + F9: 4,7 + G1: 7 => SOL
* STA C1: 3
* CNT   7 HDP CHAINS /  78 HYP OPENED

Header Info

rating: 34350; r2: 653368; index: 130483

Solution

position: 123456789457189236896732154265391847318674592749528613571963428632845971984217365 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 # C1: 6,7 => UNS
* INC # C1: 3 => UNS
* INC # F5: 6,7 => UNS
* INC # F9: 6,7 => UNS
* INC # C3: 6,7 => UNS
* INC # C3: 4,5 => UNS
* INC # D5: 6,7 => UNS
* INC # D9: 6,7 => UNS
* INC # E7: 4,9 => UNS
* INC # E8: 4,9 => UNS
* INC # E7: 2,4 => UNS
* INC # E7: 6,9 => UNS
* INC # D7: 2,6 => UNS
* INC # E7: 2,6 => UNS
* INC # D9: 2,6 => UNS
* INC # D9: 3,5,7 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 6,7 => UNS
* INC # C1: 3 => UNS
* INC # F5: 6,7 => UNS
* INC # F9: 6,7 => UNS
* INC # C3: 6,7 => UNS
* INC # C3: 4,5 => UNS
* INC # D5: 6,7 => UNS
* INC # D9: 6,7 => UNS
* INC # E7: 4,9 => UNS
* INC # E8: 4,9 => UNS
* INC # E7: 2,4 => UNS
* INC # E7: 6,9 => UNS
* INC # D7: 2,6 => UNS
* INC # E7: 2,6 => UNS
* INC # D9: 2,6 => UNS
* INC # D9: 3,5,7 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 6,7 => UNS
* INC # C1: 3 => UNS
* INC # F5: 6,7 => UNS
* INC # F9: 6,7 => UNS
* INC # C3: 6,7 => UNS
* INC # C3: 4,5 => UNS
* INC # D5: 6,7 => UNS
* INC # D9: 6,7 => UNS
* INC # E7: 4,9 => UNS
* INC # E8: 4,9 => UNS
* INC # E7: 2,4 => UNS
* INC # E7: 6,9 => UNS
* INC # D7: 2,6 => UNS
* INC # E7: 2,6 => UNS
* INC # D9: 2,6 => UNS
* INC # D9: 3,5,7 => UNS
* INC # C1: 6,7 # C3: 6,7 => UNS
* INC # C1: 6,7 # C3: 4,5 => UNS
* INC # C1: 6,7 # F5: 6,7 => UNS
* INC # C1: 6,7 # F9: 6,7 => UNS
* INC # C1: 6,7 # C3: 6,7 => UNS
* INC # C1: 6,7 # C3: 4,5 => UNS
* INC # C1: 6,7 # D5: 6,7 => UNS
* INC # C1: 6,7 # D9: 6,7 => UNS
* INC # C1: 6,7 # E7: 4,9 => UNS
* INC # C1: 6,7 # E8: 4,9 => UNS
* INC # C1: 6,7 # E7: 2,4 => UNS
* INC # C1: 6,7 # E7: 6,9 => UNS
* INC # C1: 6,7 # D7: 2,6 => UNS
* INC # C1: 6,7 # E7: 2,6 => UNS
* INC # C1: 6,7 # D9: 2,6 => UNS
* INC # C1: 6,7 # D9: 3,5,7 => UNS
* INC # C1: 6,7 => UNS
* INC # C1: 3 # A5: 4,5 => UNS
* INC # C1: 3 # A7: 4,5 => UNS
* INC # C1: 3 # B6: 4,5 => UNS
* INC # C1: 3 # B8: 4,5 => UNS
* INC # C1: 3 # G1: 1,9 => UNS
* INC # C1: 3 # G1: 7 => UNS
* INC # C1: 3 # G3: 4,5 => UNS
* INC # C1: 3 # H3: 4,5 => UNS
* INC # C1: 3 # I6: 4,5 => UNS
* INC # C1: 3 # I9: 4,5 => UNS
* INC # C1: 3 # A5: 4,5 => UNS
* INC # C1: 3 # B6: 4,5 => UNS
* INC # C1: 3 # E5: 4,7 => UNS
* INC # C1: 3 # E5: 6 => UNS
* DIS # C1: 3 # F8: 4,7 => CTR => F8: 3,5
* INC # C1: 3 + F8: 3,5 # F9: 4,7 => UNS
* INC # C1: 3 + F8: 3,5 # F9: 4,7 => UNS
* INC # C1: 3 + F8: 3,5 # F9: 3,5 => UNS
* INC # C1: 3 + F8: 3,5 # E5: 4,7 => UNS
* INC # C1: 3 + F8: 3,5 # E5: 6 => UNS
* INC # C1: 3 + F8: 3,5 # F9: 4,7 => UNS
* INC # C1: 3 + F8: 3,5 # F9: 3,5 => UNS
* INC # C1: 3 + F8: 3,5 # G5: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 # I6: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 # H3: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 # H8: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 # A7: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 # B8: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 # F9: 4,5 => UNS
* DIS # C1: 3 + F8: 3,5 # G9: 4,5 => CTR => G9: 3,7
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # I9: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # A7: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # B8: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # F9: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # I9: 4,5 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # F9: 4,7 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # F9: 3,5 => UNS
* INC # C1: 3 + F8: 3,5 + G9: 3,7 # H8: 4,7 => UNS
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 # H8: 5 => CTR => H8: 4,7
* INC # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 # E5: 4,7 => UNS
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 # E5: 6 => CTR => E5: 4,7
* INC # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 # F9: 4,7 => UNS
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 # F9: 3,5 => CTR => F9: 4,7
* DIS # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 + F9: 4,7 # G1: 1,9 => CTR => G1: 7
* PRF # C1: 3 + F8: 3,5 + G9: 3,7 + H8: 4,7 + E5: 4,7 + F9: 4,7 + G1: 7 => SOL
* STA C1: 3
* CNT  78 HDP CHAINS /  78 HYP OPENED