Analysis of xx-mith-te3-00104860-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 12.45..89.....9......2.1.4...1..8..5...9.4.18..851..2..14895...6.....85.875....9. initial

Autosolve

position: 12.45..89....89....8.2.154...1..8..5...9.4.18..851..2..14895...6.....85.875....9. 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: 0:00:08.545703

The following important HDP chains were detected:

* DIS # G9: 3,4 # G1: 3,6 => CTR => G1: 7
* PRF # G9: 3,4 + G1: 7 # E4: 3,6 => SOL
* STA # G9: 3,4 + G1: 7 + E4: 3,6
* CNT   2 HDP CHAINS /  37 HYP OPENED

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

Details

Positions

12.45..89.....9......2.1.4...1..8..5...9.4.18..851..2..14895...6.....85.875....9. initial
12.45..89....89....8.2.154...1..8..5...9.4.18..851..2..14895...6.....85.875....9. autosolve
123456789456789132789231546241368975537924618968517423314895267692173854875642391 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
A2: 4,5
B2: 4,5
G2: 1,2
I2: 1,2
A7: 2,3
B8: 3,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,I2: 1.. / G2 = 1  =>  4 pairs (_) / I2 = 1  =>  7 pairs (_)
D8,D9: 1.. / D8 = 1  =>  7 pairs (_) / D9 = 1  =>  7 pairs (_)
D8,I8: 1.. / D8 = 1  =>  7 pairs (_) / I8 = 1  =>  7 pairs (_)
G2,G9: 1.. / G2 = 1  =>  4 pairs (_) / G9 = 1  =>  7 pairs (_)
G2,I2: 2.. / G2 = 2  =>  7 pairs (_) / I2 = 2  =>  4 pairs (_)
E4,E5: 2.. / E4 = 2  =>  6 pairs (_) / E5 = 2  => 11 pairs (_)
A7,C8: 2.. / A7 = 2  => 13 pairs (_) / C8 = 2  => 13 pairs (_)
F8,F9: 2.. / F8 = 2  => 14 pairs (_) / F9 = 2  =>  7 pairs (_)
A4,E4: 2.. / A4 = 2  => 11 pairs (_) / E4 = 2  =>  6 pairs (_)
C5,C8: 2.. / C5 = 2  => 13 pairs (_) / C8 = 2  => 13 pairs (_)
A2,B2: 4.. / A2 = 4  =>  5 pairs (_) / B2 = 4  =>  4 pairs (_)
E8,E9: 4.. / E8 = 4  =>  7 pairs (_) / E9 = 4  => 10 pairs (_)
E8,I8: 4.. / E8 = 4  =>  7 pairs (_) / I8 = 4  => 10 pairs (_)
A2,B2: 5.. / A2 = 5  =>  4 pairs (_) / B2 = 5  =>  5 pairs (_)
A5,B5: 5.. / A5 = 5  =>  5 pairs (_) / B5 = 5  =>  4 pairs (_)
A2,A5: 5.. / A2 = 5  =>  4 pairs (_) / A5 = 5  =>  5 pairs (_)
B2,B5: 5.. / B2 = 5  =>  5 pairs (_) / B5 = 5  =>  4 pairs (_)
A3,C3: 9.. / A3 = 9  => 11 pairs (_) / C3 = 9  =>  8 pairs (_)
G4,G6: 9.. / G4 = 9  =>  6 pairs (_) / G6 = 9  =>  6 pairs (_)
B8,C8: 9.. / B8 = 9  =>  8 pairs (_) / C8 = 9  => 11 pairs (_)
C3,C8: 9.. / C3 = 9  =>  8 pairs (_) / C8 = 9  => 11 pairs (_)
* DURATION: 0:00:06.900551  START: 01:49:42.936289  END: 01:49:49.836840 2025-04-05
* CP COUNT: (21)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:08.369379  START: 01:49:55.128259  END: 01:50:03.497638 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00104860-base-pr-002.dot
* REASONING
* DIS # G9: 3,4 # G1: 3,6 => CTR => G1: 7
* PRF # G9: 3,4 + G1: 7 # E4: 3,6 => SOL
* STA # G9: 3,4 + G1: 7 + E4: 3,6
* CNT   2 HDP CHAINS /  37 HYP OPENED

Header Info

rating: 26297; r2: 516746; index: 104860

Solution

position: 123456789456789132789231546241368975537924618968517423314895267692173854875642391 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 # G9: 1,2 => UNS
* INC # G9: 3,4 => UNS
* INC # I8: 1,2 => UNS
* INC # I9: 1,2 => UNS
* INC # C8: 2,3 => UNS
* INC # C8: 9 => UNS
* INC # G7: 2,3 => UNS
* INC # I7: 2,3 => UNS
* INC # A4: 2,3 => UNS
* INC # A5: 2,3 => UNS
* INC # C8: 3,9 => UNS
* INC # C8: 2 => UNS
* INC # B4: 3,9 => UNS
* INC # B6: 3,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G9: 1,2 => UNS
* INC # G9: 3,4 => UNS
* INC # I8: 1,2 => UNS
* INC # I9: 1,2 => UNS
* INC # C8: 2,3 => UNS
* INC # C8: 9 => UNS
* INC # G7: 2,3 => UNS
* INC # I7: 2,3 => UNS
* INC # A4: 2,3 => UNS
* INC # A5: 2,3 => UNS
* INC # C8: 3,9 => UNS
* INC # C8: 2 => UNS
* INC # B4: 3,9 => UNS
* INC # B6: 3,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G9: 1,2 => UNS
* INC # G9: 3,4 => UNS
* INC # I8: 1,2 => UNS
* INC # I9: 1,2 => UNS
* INC # C8: 2,3 => UNS
* INC # C8: 9 => UNS
* INC # G7: 2,3 => UNS
* INC # I7: 2,3 => UNS
* INC # A4: 2,3 => UNS
* INC # A5: 2,3 => UNS
* INC # C8: 3,9 => UNS
* INC # C8: 2 => UNS
* INC # B4: 3,9 => UNS
* INC # B6: 3,9 => UNS
* INC # G9: 1,2 # I8: 1,2 => UNS
* INC # G9: 1,2 # I9: 1,2 => UNS
* INC # G9: 1,2 # A4: 4,9 => UNS
* INC # G9: 1,2 # B4: 4,9 => UNS
* INC # G9: 1,2 # A6: 4,9 => UNS
* INC # G9: 1,2 # B6: 4,9 => UNS
* INC # G9: 1,2 # C8: 2,3 => UNS
* INC # G9: 1,2 # C8: 9 => UNS
* INC # G9: 1,2 # I7: 2,3 => UNS
* INC # G9: 1,2 # I7: 6,7 => UNS
* INC # G9: 1,2 # A4: 2,3 => UNS
* INC # G9: 1,2 # A5: 2,3 => UNS
* INC # G9: 1,2 # C8: 3,9 => UNS
* INC # G9: 1,2 # C8: 2 => UNS
* INC # G9: 1,2 # B4: 3,9 => UNS
* INC # G9: 1,2 # B6: 3,9 => UNS
* INC # G9: 1,2 # I8: 1,2 => UNS
* INC # G9: 1,2 # I9: 1,2 => UNS
* INC # G9: 1,2 => UNS
* INC # G9: 3,4 # F1: 3,6 => UNS
* DIS # G9: 3,4 # G1: 3,6 => CTR => G1: 7
* PRF # G9: 3,4 + G1: 7 # E4: 3,6 => SOL
* STA # G9: 3,4 + G1: 7 + E4: 3,6
* CNT  36 HDP CHAINS /  37 HYP OPENED