Analysis of xx-mith-te3-00066637-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..66..27....27....8.....5..9...1....34.7..6.2.9...1.956.....71.... initial

Autosolve

position: 1...56..9.5.1.9..66..27....27....8.....5..9...1....34.7..6.2.9...1.956.....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: 0:00:05.968156

The following important HDP chains were detected:

* PRF # C6: 5,9 # C1: 3,4 => SOL
* STA # C6: 5,9 + C1: 3,4
* CNT   1 HDP CHAINS /  34 HYP OPENED

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

Details

Positions

`1...56..9.5.1.9..66..27....27....8.....5..9...1....34.7..6.2.9...1.956.....71....`	initial
`1...56..9.5.1.9..66..27....27....8.....5..9...1....34.7..6.2.9...1.956.....71....`	autosolve
`123456789457189236698273514274931865386524971519867342735642198841395627962718453`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
A6: 5,9
D6: 8,9
F6: 7,8
I4: 1,5
A9: 5,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F4,F5: 1.. / F4 = 1  =>  8 pairs (_) / F5 = 1  =>  7 pairs (_)
G7,I7: 1.. / G7 = 1  =>  6 pairs (_) / I7 = 1  => 11 pairs (_)
G3,G7: 1.. / G3 = 1  => 11 pairs (_) / G7 = 1  =>  6 pairs (_)
E5,E6: 2.. / E5 = 2  =>  6 pairs (_) / E6 = 2  =>  9 pairs (_)
E6,I6: 2.. / E6 = 2  =>  9 pairs (_) / I6 = 2  =>  6 pairs (_)
A6,A9: 5.. / A6 = 5  =>  4 pairs (_) / A9 = 5  => 14 pairs (_)
H4,H5: 6.. / H4 = 6  =>  8 pairs (_) / H5 = 6  => 10 pairs (_)
B9,C9: 6.. / B9 = 6  =>  5 pairs (_) / C9 = 6  =>  8 pairs (_)
C6,E6: 6.. / C6 = 6  =>  9 pairs (_) / E6 = 6  =>  6 pairs (_)
B5,B9: 6.. / B5 = 6  =>  8 pairs (_) / B9 = 6  =>  5 pairs (_)
C1,C2: 7.. / C1 = 7  =>  6 pairs (_) / C2 = 7  =>  7 pairs (_)
G1,G2: 7.. / G1 = 7  =>  7 pairs (_) / G2 = 7  =>  6 pairs (_)
F5,F6: 7.. / F5 = 7  =>  6 pairs (_) / F6 = 7  =>  5 pairs (_)
H8,I8: 7.. / H8 = 7  =>  5 pairs (_) / I8 = 7  =>  4 pairs (_)
C1,G1: 7.. / C1 = 7  =>  6 pairs (_) / G1 = 7  =>  7 pairs (_)
C2,G2: 7.. / C2 = 7  =>  7 pairs (_) / G2 = 7  =>  6 pairs (_)
F6,I6: 7.. / F6 = 7  =>  5 pairs (_) / I6 = 7  =>  6 pairs (_)
H5,H8: 7.. / H5 = 7  =>  4 pairs (_) / H8 = 7  =>  5 pairs (_)
B3,C3: 9.. / B3 = 9  =>  5 pairs (_) / C3 = 9  =>  8 pairs (_)
D4,D6: 9.. / D4 = 9  =>  7 pairs (_) / D6 = 9  =>  5 pairs (_)
C4,D4: 9.. / C4 = 9  =>  5 pairs (_) / D4 = 9  =>  7 pairs (_)
A6,A9: 9.. / A6 = 9  => 14 pairs (_) / A9 = 9  =>  4 pairs (_)
B3,B9: 9.. / B3 = 9  =>  5 pairs (_) / B9 = 9  =>  8 pairs (_)
* DURATION: 0:00:05.305176  START: 18:32:10.305575  END: 18:32:15.610751 2025-04-04
* CP COUNT: (23)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:05.839633  START: 18:32:18.965051  END: 18:32:24.804684 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00066637-base-pr-002.dot
* REASONING
* PRF # C6: 5,9 # C1: 3,4 => SOL
* STA # C6: 5,9 + C1: 3,4
* CNT   1 HDP CHAINS /  34 HYP OPENED

Header Info

rating: 14679; r2: 436939; index: 66637

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 # C4: 5,9 => UNS
* INC # C6: 5,9 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 5,6 => UNS
* INC # F5: 7,8 => UNS
* INC # F5: 1,3,4 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 6 => UNS
* INC # I3: 1,5 => UNS
* INC # I7: 1,5 => UNS
* INC # C9: 5,9 => UNS
* INC # C9: 2,3,4,6,8 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 5,9 => UNS
* INC # C6: 5,9 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 5,6 => UNS
* INC # F5: 7,8 => UNS
* INC # F5: 1,3,4 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 6 => UNS
* INC # I3: 1,5 => UNS
* INC # I7: 1,5 => UNS
* INC # C9: 5,9 => UNS
* INC # C9: 2,3,4,6,8 => UNS
* CNT  12 HDP CHAINS /  12 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C4: 5,9 => UNS
* INC # C6: 5,9 => UNS
* INC # C6: 8,9 => UNS
* INC # C6: 5,6 => UNS
* INC # F5: 7,8 => UNS
* INC # F5: 1,3,4 => UNS
* INC # H4: 1,5 => UNS
* INC # H4: 6 => UNS
* INC # I3: 1,5 => UNS
* INC # I7: 1,5 => UNS
* INC # C9: 5,9 => UNS
* INC # C9: 2,3,4,6,8 => UNS
* INC # C4: 5,9 # C9: 5,9 => UNS
* INC # C4: 5,9 # C9: 2,3,4,6,8 => UNS
* INC # C4: 5,9 # B5: 6,8 => UNS
* INC # C4: 5,9 # C5: 6,8 => UNS
* INC # C4: 5,9 # E6: 6,8 => UNS
* INC # C4: 5,9 # E6: 2 => UNS
* INC # C4: 5,9 # C9: 6,8 => UNS
* INC # C4: 5,9 # C9: 2,3,4,5,9 => UNS
* INC # C4: 5,9 # F5: 7,8 => UNS
* INC # C4: 5,9 # F5: 1 => UNS
* INC # C4: 5,9 # H4: 1,5 => UNS
* INC # C4: 5,9 # H4: 6 => UNS
* INC # C4: 5,9 # I3: 1,5 => UNS
* INC # C4: 5,9 # I7: 1,5 => UNS
* INC # C4: 5,9 # C9: 5,9 => UNS
* INC # C4: 5,9 # C9: 2,3,4,6,8 => UNS
* INC # C4: 5,9 => UNS
* INC # C6: 5,9 # E2: 3,4 => UNS
* INC # C6: 5,9 # F3: 3,4 => UNS
* INC # C6: 5,9 # B1: 3,4 => UNS
* PRF # C6: 5,9 # C1: 3,4 => SOL
* STA # C6: 5,9 + C1: 3,4
* CNT  33 HDP CHAINS /  34 HYP OPENED