Analysis of xx-mith-te3-00115226-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ..34.67..4.718....6...37......6.1..4..6....92..8....5.3.1.64..8..4......86.71...3 initial

Autosolve

position: ..34.67..4.718....6...37......6.1..4..6....92..8....5.3.1.64..8..4......86.71...3 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # G6: 1,3 => CTR => G6: 6
* DIS # H8: 2,7 => CTR => H8: 1,6
* CNT   2 HDP CHAINS /  18 HYP OPENED

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

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # G6: 1,3 => CTR => G6: 6
* DIS G6: 6 # H8: 2,7 => CTR => H8: 1,6
* DIS G6: 6 + H8: 1,6 # B6: 1,7 => CTR => B6: 2,3,4,9
* STA G6: 6 + H8: 1,6 + B6: 2,3,4,9
* CNT   3 HDP CHAINS /  62 HYP OPENED

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

Pair Reduction Position

position: ..34.67..4.718....6...37......6.1..4..6....92..8...65.3.1.64..8..4......86.71...3 pair_reduction
Pair Reduction

See section Pair Reduction for the HDP chains leading to this result.

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:13.055913

The following important HDP chains were detected:

* DIS # H4: 7 # A1: 5,9 => CTR => A1: 1,2
* DIS # H4: 7 + A1: 1,2 # B1: 5,9 => CTR => B1: 1,2,8
* DIS # H4: 7 + A1: 1,2 + B1: 1,2,8 # B8: 2 => CTR => B8: 5,9
* DIS # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 # B1: 1,8 => CTR => B1: 2
* PRF # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 + B1: 2 # F9: 5,9 => SOL
* STA # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 + B1: 2 + F9: 5,9
* CNT   5 HDP CHAINS /  52 HYP OPENED

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

Details

Positions

..34.67..4.718....6...37......6.1..4..6....92..8....5.3.1.64..8..4......86.71...3 initial
..34.67..4.718....6...37......6.1..4..6....92..8....5.3.1.64..8..4......86.71...3 autosolve
..34.67..4.718....6...37......6.1..4..6....92..8...65.3.1.64..8..4......86.71...3 pair_reduction
123456789457189236689237415235691874716548392948372651371964528594823167862715943 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
G4: 3,8
G5: 1,3
D8: 3,8
F8: 3,8
H7: 2,7
H9: 2,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,H2: 3.. / G2 = 3  => 13 pairs (_) / H2 = 3  => 17 pairs (_)
D8,F8: 3.. / D8 = 3  =>  6 pairs (_) / F8 = 3  =>  6 pairs (_)
H2,H4: 3.. / H2 = 3  => 17 pairs (_) / H4 = 3  => 13 pairs (_)
G3,H3: 4.. / G3 = 4  =>  5 pairs (_) / H3 = 4  => 21 pairs (_)
B5,B6: 4.. / B5 = 4  =>  7 pairs (_) / B6 = 4  =>  6 pairs (_)
E5,E6: 4.. / E5 = 4  =>  6 pairs (_) / E6 = 4  =>  7 pairs (_)
G9,H9: 4.. / G9 = 4  => 21 pairs (_) / H9 = 4  =>  5 pairs (_)
B5,E5: 4.. / B5 = 4  =>  7 pairs (_) / E5 = 4  =>  6 pairs (_)
B6,E6: 4.. / B6 = 4  =>  6 pairs (_) / E6 = 4  =>  7 pairs (_)
G3,G9: 4.. / G3 = 4  =>  5 pairs (_) / G9 = 4  => 21 pairs (_)
H3,H9: 4.. / H3 = 4  => 21 pairs (_) / H9 = 4  =>  5 pairs (_)
G6,I6: 6.. / G6 = 6  =>  7 pairs (_) / I6 = 6  =>  0 pairs (X)
H2,H8: 6.. / H2 = 6  => 12 pairs (_) / H8 = 6  => 17 pairs (_)
H4,I6: 7.. / H4 = 7  => 19 pairs (_) / I6 = 7  => 14 pairs (_)
B7,H7: 7.. / B7 = 7  => 19 pairs (_) / H7 = 7  => 14 pairs (_)
I6,I8: 7.. / I6 = 7  => 14 pairs (_) / I8 = 7  => 19 pairs (_)
B1,B3: 8.. / B1 = 8  =>  9 pairs (_) / B3 = 8  =>  7 pairs (_)
D5,F5: 8.. / D5 = 8  =>  6 pairs (_) / F5 = 8  =>  6 pairs (_)
G4,H4: 8.. / G4 = 8  =>  6 pairs (_) / H4 = 8  => 17 pairs (_)
D8,F8: 8.. / D8 = 8  =>  6 pairs (_) / F8 = 8  =>  6 pairs (_)
B1,H1: 8.. / B1 = 8  =>  9 pairs (_) / H1 = 8  =>  7 pairs (_)
D5,D8: 8.. / D5 = 8  =>  6 pairs (_) / D8 = 8  =>  6 pairs (_)
F5,F8: 8.. / F5 = 8  =>  6 pairs (_) / F8 = 8  =>  6 pairs (_)
G3,G4: 8.. / G3 = 8  => 17 pairs (_) / G4 = 8  =>  6 pairs (_)
* DURATION: 0:00:06.025858  START: 17:39:36.901502  END: 17:39:42.927360 2025-04-06
* CP COUNT: (24)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.853282  START: 17:39:55.613373  END: 17:40:08.466655 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00115226-base-pr-002.dot
* REASONING
* DIS # H4: 7 # A1: 5,9 => CTR => A1: 1,2
* DIS # H4: 7 + A1: 1,2 # B1: 5,9 => CTR => B1: 1,2,8
* DIS # H4: 7 + A1: 1,2 + B1: 1,2,8 # B8: 2 => CTR => B8: 5,9
* DIS # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 # B1: 1,8 => CTR => B1: 2
* PRF # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 + B1: 2 # F9: 5,9 => SOL
* STA # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 + B1: 2 + F9: 5,9
* CNT   5 HDP CHAINS /  52 HYP OPENED

Header Info

rating: 29351; r2: 579560; index: 115226

Solution

position: 123456789457189236689237415235691874716548392948372651371964528594823167862715943 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 # H4: 3,8 => UNS
* INC # H4: 7 => UNS
* DIS # G6: 1,3 => CTR => G6: 6
* INC # G6: 6 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 4,5,7 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 5 => UNS
* INC # F5: 3,8 => UNS
* INC # F5: 5 => UNS
* DIS # H8: 2,7 => CTR => H8: 1,6
* INC # H8: 1,6 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 5,9 => UNS
* INC # G9: 2,4 => UNS
* INC # G9: 5,9 => UNS
* INC # H3: 2,4 => UNS
* INC # H3: 1,8 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H4: 3,8 => UNS
* INC # H4: 7 => UNS
* DIS # G6: 1,3 => CTR => G6: 6
* INC G6: 6 # B5: 1,3 => UNS
* INC G6: 6 # B5: 4,5,7 => UNS
* INC G6: 6 # D5: 3,8 => UNS
* INC G6: 6 # D5: 5 => UNS
* INC G6: 6 # F5: 3,8 => UNS
* INC G6: 6 # F5: 5 => UNS
* DIS G6: 6 # H8: 2,7 => CTR => H8: 1,6
* INC G6: 6 + H8: 1,6 # B7: 2,7 => UNS
* INC G6: 6 + H8: 1,6 # B7: 5,9 => UNS
* INC G6: 6 + H8: 1,6 # G9: 2,4 => UNS
* INC G6: 6 + H8: 1,6 # G9: 5,9 => UNS
* INC G6: 6 + H8: 1,6 # H3: 2,4 => UNS
* INC G6: 6 + H8: 1,6 # H3: 1,8 => UNS
* INC G6: 6 + H8: 1,6 # H4: 3,8 => UNS
* INC G6: 6 + H8: 1,6 # H4: 7 => UNS
* INC G6: 6 + H8: 1,6 # B5: 1,3 => UNS
* INC G6: 6 + H8: 1,6 # B5: 4,5,7 => UNS
* INC G6: 6 + H8: 1,6 # A6: 1,7 => UNS
* DIS G6: 6 + H8: 1,6 # B6: 1,7 => CTR => B6: 2,3,4,9
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # A6: 1,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # A6: 2,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 1,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 5,6,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # A6: 1,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # A6: 2,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 1,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 5,6,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # D5: 3,8 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # D5: 5 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # F5: 3,8 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # F5: 5 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # B7: 2,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # B7: 5,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 1,6 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 5,7,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # G9: 2,4 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # G9: 5,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # H3: 2,4 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # H3: 1,8 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # H4: 3,8 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # H4: 7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # B5: 1,3 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # B5: 4,5,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # A6: 1,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # A6: 2,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 1,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 5,6,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # D5: 3,8 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # D5: 5 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # F5: 3,8 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # F5: 5 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # B7: 2,7 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # B7: 5,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 1,6 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # I8: 5,7,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # G9: 2,4 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # G9: 5,9 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # H3: 2,4 => UNS
* INC G6: 6 + H8: 1,6 + B6: 2,3,4,9 # H3: 1,8 => UNS
* STA G6: 6 + H8: 1,6 + B6: 2,3,4,9
* CNT  62 HDP CHAINS /  62 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H4: 3,8 => UNS
* INC # H4: 7 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 4,5,7 => UNS
* INC # A6: 1,7 => UNS
* INC # A6: 2,9 => UNS
* INC # I8: 1,7 => UNS
* INC # I8: 5,6,9 => UNS
* INC # D5: 3,8 => UNS
* INC # D5: 5 => UNS
* INC # F5: 3,8 => UNS
* INC # F5: 5 => UNS
* INC # B7: 2,7 => UNS
* INC # B7: 5,9 => UNS
* INC # I8: 1,6 => UNS
* INC # I8: 5,7,9 => UNS
* INC # G9: 2,4 => UNS
* INC # G9: 5,9 => UNS
* INC # H3: 2,4 => UNS
* INC # H3: 1,8 => UNS
* INC # H4: 3,8 # H1: 1,8 => UNS
* INC # H4: 3,8 # H1: 2 => UNS
* INC # H4: 3,8 # H3: 1,8 => UNS
* INC # H4: 3,8 # H3: 2,4 => UNS
* INC # H4: 3,8 # H2: 2,3 => UNS
* INC # H4: 3,8 # H2: 6 => UNS
* INC # H4: 3,8 # A4: 5,7 => UNS
* INC # H4: 3,8 # B4: 5,7 => UNS
* INC # H4: 3,8 # E5: 5,7 => UNS
* INC # H4: 3,8 # E5: 4 => UNS
* INC # H4: 3,8 # A8: 5,7 => UNS
* INC # H4: 3,8 # A8: 2,9 => UNS
* INC # H4: 3,8 # E5: 5,7 => UNS
* INC # H4: 3,8 # E5: 4 => UNS
* INC # H4: 3,8 # A4: 5,7 => UNS
* INC # H4: 3,8 # B4: 5,7 => UNS
* INC # H4: 3,8 # D5: 3,8 => UNS
* INC # H4: 3,8 # D5: 5 => UNS
* INC # H4: 3,8 # F5: 3,8 => UNS
* INC # H4: 3,8 # F5: 5 => UNS
* INC # H4: 3,8 # G9: 2,4 => UNS
* INC # H4: 3,8 # G9: 5,9 => UNS
* INC # H4: 3,8 # H3: 2,4 => UNS
* INC # H4: 3,8 # H3: 1,8 => UNS
* INC # H4: 3,8 => UNS
* DIS # H4: 7 # A1: 5,9 => CTR => A1: 1,2
* DIS # H4: 7 + A1: 1,2 # B1: 5,9 => CTR => B1: 1,2,8
* INC # H4: 7 + A1: 1,2 + B1: 1,2,8 # B8: 5,9 => UNS
* DIS # H4: 7 + A1: 1,2 + B1: 1,2,8 # B8: 2 => CTR => B8: 5,9
* DIS # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 # B1: 1,8 => CTR => B1: 2
* PRF # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 + B1: 2 # F9: 5,9 => SOL
* STA # H4: 7 + A1: 1,2 + B1: 1,2,8 + B8: 5,9 + B1: 2 + F9: 5,9
* CNT  51 HDP CHAINS /  52 HYP OPENED