Analysis of xx-mith-te3-00021098-base.sdk

Contents

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

Original Sudoku

level: hard

position: ...4.678....1..2..6...72.1.275......369.....7.4..67....8..2167..1...8.4.....4.... initial

Autosolve

position: 1..4.678....18.2.66.8.72.14275....6.369.....7841.67....8..2167..1...8.4.....4.... 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: 0:00:12.653470

The following important HDP chains were detected:

* PRF # B1: 2,3 # I8: 5,9 => SOL
* STA # B1: 2,3 + I8: 5,9
* CNT   1 HDP CHAINS /  44 HYP OPENED

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

Details

Positions

`...4.678....1..2..6...72.1.275......369.....7.4..67....8..2167..1...8.4.....4....`	initial
`1..4.678....18.2.66.8.72.14275....6.369.....7841.67....8..2167..1...8.4.....4....`	autosolve
`123456789457189236698372514275893461369214857841567392584921673712638945936745128`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
C1: 2,3
A2: 4,7
C2: 4,7
E5: 1,5
F5: 4,5
D6: 2,5
I4: 1,8
H5: 2,5
C7: 3,4
B9: 2,3
D8: 6,7
D9: 6,7
G9: 1,8
I9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E5: 1.. / E4 = 1  => 11 pairs (_) / E5 = 1  => 15 pairs (_)
G9,I9: 1.. / G9 = 1  => 13 pairs (_) / I9 = 1  => 12 pairs (_)
E5,G5: 1.. / E5 = 1  => 15 pairs (_) / G5 = 1  => 11 pairs (_)
I4,I9: 1.. / I4 = 1  => 13 pairs (_) / I9 = 1  => 12 pairs (_)
B1,C1: 2.. / B1 = 2  => 17 pairs (_) / C1 = 2  => 12 pairs (_)
D5,D6: 2.. / D5 = 2  => 13 pairs (_) / D6 = 2  => 13 pairs (_)
I8,H9: 2.. / I8 = 2  => 14 pairs (_) / H9 = 2  => 15 pairs (_)
D5,H5: 2.. / D5 = 2  => 13 pairs (_) / H5 = 2  => 13 pairs (_)
C8,I8: 2.. / C8 = 2  => 15 pairs (_) / I8 = 2  => 14 pairs (_)
B1,B9: 2.. / B1 = 2  => 17 pairs (_) / B9 = 2  => 12 pairs (_)
I6,I8: 2.. / I6 = 2  => 15 pairs (_) / I8 = 2  => 14 pairs (_)
A2,C2: 4.. / A2 = 4  => 12 pairs (_) / C2 = 4  => 15 pairs (_)
F4,F5: 4.. / F4 = 4  => 15 pairs (_) / F5 = 4  => 15 pairs (_)
G4,G5: 4.. / G4 = 4  => 15 pairs (_) / G5 = 4  => 15 pairs (_)
A7,C7: 4.. / A7 = 4  => 15 pairs (_) / C7 = 4  => 12 pairs (_)
F4,G4: 4.. / F4 = 4  => 15 pairs (_) / G4 = 4  => 15 pairs (_)
F5,G5: 4.. / F5 = 4  => 15 pairs (_) / G5 = 4  => 15 pairs (_)
A2,A7: 4.. / A2 = 4  => 12 pairs (_) / A7 = 4  => 15 pairs (_)
C2,C7: 4.. / C2 = 4  => 15 pairs (_) / C7 = 4  => 12 pairs (_)
C8,C9: 6.. / C8 = 6  => 13 pairs (_) / C9 = 6  => 13 pairs (_)
D8,D9: 6.. / D8 = 6  => 13 pairs (_) / D9 = 6  => 13 pairs (_)
C8,D8: 6.. / C8 = 6  => 13 pairs (_) / D8 = 6  => 13 pairs (_)
C9,D9: 6.. / C9 = 6  => 13 pairs (_) / D9 = 6  => 13 pairs (_)
A2,C2: 7.. / A2 = 7  => 15 pairs (_) / C2 = 7  => 12 pairs (_)
D8,D9: 7.. / D8 = 7  => 13 pairs (_) / D9 = 7  => 13 pairs (_)
D4,D5: 8.. / D4 = 8  => 14 pairs (_) / D5 = 8  => 14 pairs (_)
G9,I9: 8.. / G9 = 8  => 12 pairs (_) / I9 = 8  => 13 pairs (_)
D5,G5: 8.. / D5 = 8  => 14 pairs (_) / G5 = 8  => 14 pairs (_)
I4,I9: 8.. / I4 = 8  => 12 pairs (_) / I9 = 8  => 13 pairs (_)
* DURATION: 0:00:11.220143  START: 08:42:47.854106  END: 08:42:59.074249 2025-04-04
* CP COUNT: (29)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.525665  START: 08:43:10.543348  END: 08:43:23.069013 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00021098-base-pr-002.dot
* REASONING
* PRF # B1: 2,3 # I8: 5,9 => SOL
* STA # B1: 2,3 + I8: 5,9
* CNT   1 HDP CHAINS /  44 HYP OPENED

Header Info

rating: 4357; r2: 366162; index: 21098

Solution

position: 123456789457189236698372514275893461369214857841567392584921673712638945936745128 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 # B1: 2,3 => UNS
* INC # B1: 5,9 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 2,3 => UNS
* INC # D5: 2,5 => UNS
* INC # D5: 8 => UNS
* INC # H6: 2,5 => UNS
* INC # I6: 2,5 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* INC # H6: 2,5 => UNS
* INC # I6: 2,5 => UNS
* INC # D5: 2,5 => UNS
* INC # D5: 8 => UNS
* INC # H9: 2,5 => UNS
* INC # H9: 3,9 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 2,3 => UNS
* INC # H9: 2,3 => UNS
* INC # H9: 5,9 => UNS
* INC # B1: 2,3 => UNS
* INC # B1: 5,9 => UNS
* INC # C8: 6,7 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 6,7 => UNS
* INC # C9: 2,3 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,3 => UNS
* INC # B1: 5,9 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 2,3 => UNS
* INC # D5: 2,5 => UNS
* INC # D5: 8 => UNS
* INC # H6: 2,5 => UNS
* INC # I6: 2,5 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* INC # H6: 2,5 => UNS
* INC # I6: 2,5 => UNS
* INC # D5: 2,5 => UNS
* INC # D5: 8 => UNS
* INC # H9: 2,5 => UNS
* INC # H9: 3,9 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 2,3 => UNS
* INC # H9: 2,3 => UNS
* INC # H9: 5,9 => UNS
* INC # B1: 2,3 => UNS
* INC # B1: 5,9 => UNS
* INC # C8: 6,7 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 6,7 => UNS
* INC # C9: 2,3 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B1: 2,3 => UNS
* INC # B1: 5,9 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 2,3 => UNS
* INC # D5: 2,5 => UNS
* INC # D5: 8 => UNS
* INC # H6: 2,5 => UNS
* INC # I6: 2,5 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* INC # H6: 2,5 => UNS
* INC # I6: 2,5 => UNS
* INC # D5: 2,5 => UNS
* INC # D5: 8 => UNS
* INC # H9: 2,5 => UNS
* INC # H9: 3,9 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 2,3 => UNS
* INC # H9: 2,3 => UNS
* INC # H9: 5,9 => UNS
* INC # B1: 2,3 => UNS
* INC # B1: 5,9 => UNS
* INC # C8: 6,7 => UNS
* INC # C8: 2,3 => UNS
* INC # C9: 6,7 => UNS
* INC # C9: 2,3 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* INC # B1: 2,3 # C8: 2,3 => UNS
* INC # B1: 2,3 # C9: 2,3 => UNS
* INC # B1: 2,3 # F2: 5,9 => UNS
* INC # B1: 2,3 # H2: 5,9 => UNS
* INC # B1: 2,3 # D3: 5,9 => UNS
* INC # B1: 2,3 # G3: 5,9 => UNS
* INC # B1: 2,3 # F2: 5,9 => UNS
* INC # B1: 2,3 # D3: 5,9 => UNS
* INC # B1: 2,3 # E8: 5,9 => UNS
* INC # B1: 2,3 # E8: 3 => UNS
* INC # B1: 2,3 # H2: 5,9 => UNS
* INC # B1: 2,3 # G3: 5,9 => UNS
* INC # B1: 2,3 # I6: 5,9 => UNS
* INC # B1: 2,3 # I7: 5,9 => UNS
* PRF # B1: 2,3 # I8: 5,9 => SOL
* STA # B1: 2,3 + I8: 5,9
* CNT  43 HDP CHAINS /  44 HYP OPENED