Analysis of xx-mith-te3-00043861-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34.6..........2.7.8132............53.2.8.978.7..5..23...9.2.5..5...93.9......78 initial

Autosolve

position: ..34.6........9.237.8132.....9......53.2.8.978.79.53.23...9.2.5..5.2.93.9.2....78 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: 0:00:05.884076

The following important HDP chains were detected:

* DIS # B1: 1,2 # A4: 4,6 => CTR => A4: 1,2
* DIS # B1: 1,2 + A4: 1,2 # B4: 1,2 => CTR => B4: 4,6
* DIS # B1: 1,2 + A4: 1,2 + B4: 4,6 # C5: 4,6 => CTR => C5: 1
* PRF # B1: 1,2 + A4: 1,2 + B4: 4,6 + C5: 1 => SOL
* STA B1: 1,2
* CNT   4 HDP CHAINS /  23 HYP OPENED

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

Details

Positions

..34.6..........2.7.8132............53.2.8.978.7..5..23...9.2.5..5...93.9......78 initial
..34.6........9.237.8132.....9......53.2.8.978.79.53.23...9.2.5..5.2.93.9.2....78 autosolve
123456789456789123798132546269374851531268497847915362384697215675821934912543678 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
A1: 1,2
D2: 5,7
I1: 1,9
G4: 5,8
H4: 5,8
B7: 7,8
B8: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 2.. / A1 = 2  =>  6 pairs (_) / B1 = 2  => 13 pairs (_)
A4,B4: 2.. / A4 = 2  => 13 pairs (_) / B4 = 2  =>  6 pairs (_)
A1,A4: 2.. / A1 = 2  =>  6 pairs (_) / A4 = 2  => 13 pairs (_)
B1,B4: 2.. / B1 = 2  => 13 pairs (_) / B4 = 2  =>  6 pairs (_)
D4,F4: 3.. / D4 = 3  =>  8 pairs (_) / F4 = 3  => 13 pairs (_)
D9,F9: 3.. / D9 = 3  => 13 pairs (_) / F9 = 3  =>  8 pairs (_)
D4,D9: 3.. / D4 = 3  =>  8 pairs (_) / D9 = 3  => 13 pairs (_)
F4,F9: 3.. / F4 = 3  => 13 pairs (_) / F9 = 3  =>  8 pairs (_)
G4,H4: 5.. / G4 = 5  => 11 pairs (_) / H4 = 5  =>  7 pairs (_)
D9,E9: 5.. / D9 = 5  => 12 pairs (_) / E9 = 5  => 13 pairs (_)
D2,D9: 5.. / D2 = 5  => 13 pairs (_) / D9 = 5  => 12 pairs (_)
G1,G2: 7.. / G1 = 7  =>  8 pairs (_) / G2 = 7  => 10 pairs (_)
B7,B8: 7.. / B7 = 7  =>  7 pairs (_) / B8 = 7  =>  7 pairs (_)
E1,G1: 7.. / E1 = 7  => 10 pairs (_) / G1 = 7  =>  8 pairs (_)
E1,E2: 8.. / E1 = 8  =>  9 pairs (_) / E2 = 8  =>  8 pairs (_)
G4,H4: 8.. / G4 = 8  =>  7 pairs (_) / H4 = 8  => 11 pairs (_)
B7,B8: 8.. / B7 = 8  =>  7 pairs (_) / B8 = 8  =>  7 pairs (_)
D7,D8: 8.. / D7 = 8  =>  7 pairs (_) / D8 = 8  =>  7 pairs (_)
E2,G2: 8.. / E2 = 8  =>  8 pairs (_) / G2 = 8  =>  9 pairs (_)
B7,D7: 8.. / B7 = 8  =>  7 pairs (_) / D7 = 8  =>  7 pairs (_)
B8,D8: 8.. / B8 = 8  =>  7 pairs (_) / D8 = 8  =>  7 pairs (_)
H1,H4: 8.. / H1 = 8  =>  7 pairs (_) / H4 = 8  => 11 pairs (_)
B1,B3: 9.. / B1 = 9  =>  9 pairs (_) / B3 = 9  =>  8 pairs (_)
I1,I3: 9.. / I1 = 9  =>  8 pairs (_) / I3 = 9  =>  9 pairs (_)
B1,I1: 9.. / B1 = 9  =>  9 pairs (_) / I1 = 9  =>  8 pairs (_)
B3,I3: 9.. / B3 = 9  =>  8 pairs (_) / I3 = 9  =>  9 pairs (_)
* DURATION: 0:00:08.167897  START: 14:14:59.275492  END: 14:15:07.443389 2025-04-04
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:05.762772  START: 14:15:13.657588  END: 14:15:19.420360 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00043861-base-pr-002.dot
* REASONING
* DIS # B1: 1,2 # A4: 4,6 => CTR => A4: 1,2
* DIS # B1: 1,2 + A4: 1,2 # B4: 1,2 => CTR => B4: 4,6
* DIS # B1: 1,2 + A4: 1,2 + B4: 4,6 # C5: 4,6 => CTR => C5: 1
* PRF # B1: 1,2 + A4: 1,2 + B4: 4,6 + C5: 1 => SOL
* STA B1: 1,2
* CNT   4 HDP CHAINS /  23 HYP OPENED

Header Info

rating: 9081; r2: 345266; index: 43861

Solution

position: 123456789456789123798132546269374851531268497847915362384697215675821934912543678 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 # B1: 1,2 => UNS
* INC # B1: 5,9 => UNS
* INC # A4: 1,2 => UNS
* INC # A4: 4,6 => UNS
* INC # E1: 5,7 => UNS
* INC # E2: 5,7 => UNS
* INC # G2: 5,7 => UNS
* INC # G2: 1,4,6,8 => UNS
* INC # B1: 1,9 => UNS
* INC # B1: 2,5 => UNS
* INC # G1: 5,8 => UNS
* INC # G2: 5,8 => UNS
* INC # H1: 5,8 => UNS
* INC # H1: 1 => UNS
* INC # D7: 7,8 => UNS
* INC # D7: 6 => UNS
* INC # D8: 7,8 => UNS
* INC # D8: 6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 1,2 => UNS
* INC # B1: 5,9 => UNS
* INC # A4: 1,2 => UNS
* INC # A4: 4,6 => UNS
* INC # E1: 5,7 => UNS
* INC # E2: 5,7 => UNS
* INC # G2: 5,7 => UNS
* INC # G2: 1,4,6,8 => UNS
* INC # B1: 1,9 => UNS
* INC # B1: 2,5 => UNS
* INC # G1: 5,8 => UNS
* INC # G2: 5,8 => UNS
* INC # H1: 5,8 => UNS
* INC # H1: 1 => UNS
* INC # D7: 7,8 => UNS
* INC # D7: 6 => UNS
* INC # D8: 7,8 => UNS
* INC # D8: 6 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 1,2 => UNS
* INC # B1: 5,9 => UNS
* INC # A4: 1,2 => UNS
* INC # A4: 4,6 => UNS
* INC # E1: 5,7 => UNS
* INC # E2: 5,7 => UNS
* INC # G2: 5,7 => UNS
* INC # G2: 1,4,6,8 => UNS
* INC # B1: 1,9 => UNS
* INC # B1: 2,5 => UNS
* INC # G1: 5,8 => UNS
* INC # G2: 5,8 => UNS
* INC # H1: 5,8 => UNS
* INC # H1: 1 => UNS
* INC # D7: 7,8 => UNS
* INC # D7: 6 => UNS
* INC # D8: 7,8 => UNS
* INC # D8: 6 => UNS
* INC # B1: 1,2 # A4: 1,2 => UNS
* DIS # B1: 1,2 # A4: 4,6 => CTR => A4: 1,2
* DIS # B1: 1,2 + A4: 1,2 # B4: 1,2 => CTR => B4: 4,6
* DIS # B1: 1,2 + A4: 1,2 + B4: 4,6 # C5: 4,6 => CTR => C5: 1
* PRF # B1: 1,2 + A4: 1,2 + B4: 4,6 + C5: 1 => SOL
* STA B1: 1,2
* CNT  23 HDP CHAINS /  23 HYP OPENED