Analysis of xx-mith-te3-00066636-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1...56..9.5.1.9..6.9.27....27....8.....5.....51....34.7..6.21....1.9.6.....71.... initial

Autosolve

position: 1...56..9.5.1.9..6.9.27....27....8.....5.....51....34.7..6.21....1.9.6.....71.... 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: 0:00:03.848160

The following important HDP chains were detected:

* PRF # I3: 4,5 # C1: 3,4,8 => SOL
* STA # I3: 4,5 + C1: 3,4,8
* CNT   1 HDP CHAINS /  20 HYP OPENED

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

Details

Positions

`1...56..9.5.1.9..6.9.27....27....8.....5.....51....34.7..6.21....1.9.6.....71....`	initial
`1...56..9.5.1.9..6.9.27....27....8.....5.....51....34.7..6.21....1.9.6.....71....`	autosolve
`123456789457189236698273514274931865386524971519867342735642198841395627962718453`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
G3: 4,5
D6: 8,9
F6: 7,8
I4: 1,5
I6: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H3,I3: 1.. / H3 = 1  =>  5 pairs (_) / I3 = 1  => 11 pairs (_)
F4,F5: 1.. / F4 = 1  =>  7 pairs (_) / F5 = 1  => 10 pairs (_)
E5,E6: 2.. / E5 = 2  =>  6 pairs (_) / E6 = 2  =>  9 pairs (_)
E6,I6: 2.. / E6 = 2  =>  9 pairs (_) / I6 = 2  =>  6 pairs (_)
H4,I4: 5.. / H4 = 5  =>  8 pairs (_) / I4 = 5  =>  6 pairs (_)
C7,C9: 5.. / C7 = 5  =>  5 pairs (_) / C9 = 5  =>  6 pairs (_)
F8,F9: 5.. / F8 = 5  =>  5 pairs (_) / F9 = 5  => 11 pairs (_)
G3,G9: 5.. / G3 = 5  =>  4 pairs (_) / G9 = 5  => 15 pairs (_)
A3,C3: 6.. / A3 = 6  =>  5 pairs (_) / C3 = 6  =>  6 pairs (_)
H4,H5: 6.. / H4 = 6  =>  7 pairs (_) / H5 = 6  =>  5 pairs (_)
C6,E6: 6.. / C6 = 6  =>  6 pairs (_) / E6 = 6  =>  7 pairs (_)
B5,B9: 6.. / B5 = 6  =>  8 pairs (_) / B9 = 6  =>  5 pairs (_)
C1,C2: 7.. / C1 = 7  =>  6 pairs (_) / C2 = 7  =>  7 pairs (_)
F5,F6: 7.. / F5 = 7  =>  9 pairs (_) / F6 = 7  =>  6 pairs (_)
H8,I8: 7.. / H8 = 7  =>  6 pairs (_) / I8 = 7  =>  6 pairs (_)
F6,I6: 7.. / F6 = 7  =>  6 pairs (_) / I6 = 7  =>  9 pairs (_)
D4,D6: 9.. / D4 = 9  =>  6 pairs (_) / D6 = 9  =>  6 pairs (_)
C6,D6: 9.. / C6 = 9  =>  6 pairs (_) / D6 = 9  =>  6 pairs (_)
C7,H7: 9.. / C7 = 9  =>  8 pairs (_) / H7 = 9  =>  5 pairs (_)
A5,A9: 9.. / A5 = 9  =>  8 pairs (_) / A9 = 9  =>  5 pairs (_)
G5,G9: 9.. / G5 = 9  =>  5 pairs (_) / G9 = 9  =>  8 pairs (_)
* DURATION: 0:00:04.716146  START: 09:47:59.657435  END: 09:48:04.373581 2025-04-06
* CP COUNT: (21)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:03.718035  START: 09:48:08.909663  END: 09:48:12.627698 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00066636-base-pr-002.dot
* REASONING
* PRF # I3: 4,5 # C1: 3,4,8 => SOL
* STA # I3: 4,5 + C1: 3,4,8
* CNT   1 HDP CHAINS /  20 HYP OPENED

Header Info

rating: 14679; r2: 440709; index: 66636

Solution

position: 123456789457189236698273514274931865386524971519867342735642198841395627962718453 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 # I3: 4,5 => UNS
* INC # I3: 1,3,8 => UNS
* INC # G9: 4,5 => UNS
* INC # G9: 2,9 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 6 => UNS
* INC # F5: 7,8 => UNS
* INC # F5: 1,3,4 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 6,9 => UNS
* INC # I3: 1,5 => UNS
* INC # I3: 3,4,8 => UNS
* INC # G5: 2,7 => UNS
* INC # H5: 2,7 => UNS
* INC # I5: 2,7 => UNS
* INC # I8: 2,7 => UNS
* INC # I8: 3,4,5,8 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I3: 4,5 => UNS
* INC # I3: 1,3,8 => UNS
* INC # G9: 4,5 => UNS
* INC # G9: 2,9 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 6 => UNS
* INC # F5: 7,8 => UNS
* INC # F5: 1,3,4 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 6,9 => UNS
* INC # I3: 1,5 => UNS
* INC # I3: 3,4,8 => UNS
* INC # G5: 2,7 => UNS
* INC # H5: 2,7 => UNS
* INC # I5: 2,7 => UNS
* INC # I8: 2,7 => UNS
* INC # I8: 3,4,5,8 => UNS
* CNT  17 HDP CHAINS /  17 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I3: 4,5 => UNS
* INC # I3: 1,3,8 => UNS
* INC # G9: 4,5 => UNS
* INC # G9: 2,9 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 6 => UNS
* INC # F5: 7,8 => UNS
* INC # F5: 1,3,4 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 6,9 => UNS
* INC # I3: 1,5 => UNS
* INC # I3: 3,4,8 => UNS
* INC # G5: 2,7 => UNS
* INC # H5: 2,7 => UNS
* INC # I5: 2,7 => UNS
* INC # I8: 2,7 => UNS
* INC # I8: 3,4,5,8 => UNS
* INC # I3: 4,5 # C1: 2,7 => UNS
* PRF # I3: 4,5 # C1: 3,4,8 => SOL
* STA # I3: 4,5 + C1: 3,4,8
* CNT  19 HDP CHAINS /  20 HYP OPENED