Analysis of xx-mith-te3-00054001-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12....78....7....3.......6421..73.5.3.........9.52...15..3.79...7..95...93.21.... initial

Autosolve

position: 12....78....7....3.......6421..73.5.3.........9.52...15..3.79...7..95...93.21.... autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C3: 7,8 => CTR => C3: 3,5,9
* DIS # C3: 5,8 => CTR => C3: 3,7,9
* DIS # G8: 1,2 => CTR => G8: 3,4,6,8
* CNT   3 HDP CHAINS /  21 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # C3: 7,8 => CTR => C3: 3,5,9
* DIS C3: 3,5,9 # G8: 1,2 => CTR => G8: 3,4,6,8
* STA C3: 3,5,9 + G8: 3,4,6,8
* CNT   2 HDP CHAINS /  37 HYP OPENED

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

Pair Reduction Position

position: 12....78....7....37......6421..73.5.3.........9.52...15..3.79...7..95...93.21.... pair_reduction

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

Deep Pair Reduction

Time used: 0:00:20.293699

The following important HDP chains were detected:

* DIS # B2: 5,8 # C1: 4,6 => CTR => C1: 3,9
* DIS # B2: 5,8 + C1: 3,9 # D5: 4,6 => CTR => D5: 1,8,9
* DIS # B2: 5,8 + C1: 3,9 + D5: 1,8,9 # F5: 4,6 => CTR => F5: 1,8,9
* PRF # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G3: 5 => SOL
* STA # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 + G3: 5
* CNT   4 HDP CHAINS /  62 HYP OPENED

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

Details

Positions

`12....78....7....3.......6421..73.5.3.........9.52...15..3.79...7..95...93.21....`	initial
`12....78....7....3.......6421..73.5.3.........9.52...15..3.79...7..95...93.21....`	autosolve
`12....78....7....37......6421..73.5.3.........9.52...15..3.79...7..95...93.21....`	pair_reduction
`123456789456789123789132564218973456345861297697524831562347918871695342934218675`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
A3: 7,8
B3: 5,8
I1: 5,9
C7: 1,2
C8: 1,2
H9: 4,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D5,F5: 1.. / D5 = 1  => 10 pairs (_) / F5 = 1  =>  8 pairs (_)
C7,C8: 1.. / C7 = 1  =>  8 pairs (_) / C8 = 1  =>  6 pairs (_)
C7,H7: 1.. / C7 = 1  =>  8 pairs (_) / H7 = 1  =>  6 pairs (_)
D3,D5: 1.. / D3 = 1  =>  8 pairs (_) / D5 = 1  => 10 pairs (_)
F2,F3: 2.. / F2 = 2  =>  8 pairs (_) / F3 = 2  =>  7 pairs (_)
C7,C8: 2.. / C7 = 2  =>  6 pairs (_) / C8 = 2  =>  8 pairs (_)
F3,G3: 2.. / F3 = 2  =>  7 pairs (_) / G3 = 2  =>  8 pairs (_)
C1,C3: 3.. / C1 = 3  =>  7 pairs (_) / C3 = 3  => 16 pairs (_)
E1,E3: 3.. / E1 = 3  => 16 pairs (_) / E3 = 3  =>  7 pairs (_)
G6,H6: 3.. / G6 = 3  => 10 pairs (_) / H6 = 3  =>  7 pairs (_)
G8,H8: 3.. / G8 = 3  =>  7 pairs (_) / H8 = 3  => 10 pairs (_)
C1,E1: 3.. / C1 = 3  =>  7 pairs (_) / E1 = 3  => 16 pairs (_)
C3,E3: 3.. / C3 = 3  => 16 pairs (_) / E3 = 3  =>  7 pairs (_)
G6,G8: 3.. / G6 = 3  => 10 pairs (_) / G8 = 3  =>  7 pairs (_)
H6,H8: 3.. / H6 = 3  =>  7 pairs (_) / H8 = 3  => 10 pairs (_)
B5,C5: 5.. / B5 = 5  => 11 pairs (_) / C5 = 5  =>  7 pairs (_)
G9,I9: 5.. / G9 = 5  => 10 pairs (_) / I9 = 5  => 11 pairs (_)
I1,I9: 5.. / I1 = 5  => 10 pairs (_) / I9 = 5  => 11 pairs (_)
A3,C3: 7.. / A3 = 7  =>  5 pairs (_) / C3 = 7  =>  0 pairs (X)
H9,I9: 7.. / H9 = 7  =>  9 pairs (_) / I9 = 7  => 15 pairs (_)
A3,A6: 7.. / A3 = 7  =>  5 pairs (_) / A6 = 7  =>  0 pairs (X)
I5,I9: 7.. / I5 = 7  =>  9 pairs (_) / I9 = 7  => 15 pairs (_)
I1,H2: 9.. / I1 = 9  => 11 pairs (_) / H2 = 9  => 10 pairs (_)
D4,I4: 9.. / D4 = 9  => 14 pairs (_) / I4 = 9  => 12 pairs (_)
H2,H5: 9.. / H2 = 9  => 10 pairs (_) / H5 = 9  => 11 pairs (_)
* DURATION: 0:00:05.859805  START: 16:00:58.889342  END: 16:01:04.749147 2025-04-04
* CP COUNT: (25)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:20.058566  START: 16:01:12.898507  END: 16:01:32.957073 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00054001-base-pr-002.dot
* REASONING
* DIS # B2: 5,8 # C1: 4,6 => CTR => C1: 3,9
* DIS # B2: 5,8 + C1: 3,9 # D5: 4,6 => CTR => D5: 1,8,9
* DIS # B2: 5,8 + C1: 3,9 + D5: 1,8,9 # F5: 4,6 => CTR => F5: 1,8,9
* PRF # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G3: 5 => SOL
* STA # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 + G3: 5
* CNT   4 HDP CHAINS /  62 HYP OPENED

Header Info

rating: 11022; r2: 289226; index: 54001

Solution

position: 123456789456789123789132564218973456345861297697524831562347918871695342934218675 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:

* DIS # C3: 7,8 => CTR => C3: 3,5,9
* INC # C3: 3,5,9 => UNS
* INC # A6: 7,8 => UNS
* INC # A6: 4,6 => UNS
* INC # B2: 5,8 => UNS
* INC # C2: 5,8 => UNS
* DIS # C3: 5,8 => CTR => C3: 3,7,9
* INC # C3: 3,7,9 => UNS
* INC # E3: 5,8 => UNS
* INC # E3: 3 => UNS
* INC # B5: 5,8 => UNS
* INC # B5: 4,6 => UNS
* INC # C1: 5,9 => UNS
* INC # C1: 3,4,6 => UNS
* INC # H7: 1,2 => UNS
* INC # H7: 4 => UNS
* DIS # G8: 1,2 => CTR => G8: 3,4,6,8
* INC # G8: 3,4,6,8 => UNS
* INC # H8: 1,2 => UNS
* INC # H5: 4,7 => UNS
* INC # H6: 4,7 => UNS
* CNT  21 HDP CHAINS /  21 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* DIS # C3: 7,8 => CTR => C3: 3,5,9
* INC C3: 3,5,9 # B2: 5,8 => UNS
* INC C3: 3,5,9 # C2: 5,8 => UNS
* INC C3: 3,5,9 # E3: 5,8 => UNS
* INC C3: 3,5,9 # E3: 3 => UNS
* INC C3: 3,5,9 # B5: 5,8 => UNS
* INC C3: 3,5,9 # B5: 4,6 => UNS
* INC C3: 3,5,9 # C1: 5,9 => UNS
* INC C3: 3,5,9 # C1: 3,4,6 => UNS
* INC C3: 3,5,9 # H7: 1,2 => UNS
* INC C3: 3,5,9 # H7: 4 => UNS
* DIS C3: 3,5,9 # G8: 1,2 => CTR => G8: 3,4,6,8
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 1,2 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 1,2 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 3,4 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 1,2 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 3,4 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H5: 4,7 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H6: 4,7 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # B2: 5,8 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # C2: 5,8 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # E3: 5,8 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # E3: 3 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # B5: 5,8 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # B5: 4,6 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # C1: 5,9 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # C1: 3,4,6 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # F2: 2,9 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # F2: 1,4,6,8 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H5: 2,9 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H5: 4,7 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H7: 1,2 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H7: 4 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 1,2 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H8: 3,4 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H5: 4,7 => UNS
* INC C3: 3,5,9 + G8: 3,4,6,8 # H6: 4,7 => UNS
* STA C3: 3,5,9 + G8: 3,4,6,8
* CNT  37 HDP CHAINS /  37 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B2: 5,8 => UNS
* INC # C2: 5,8 => UNS
* INC # E3: 5,8 => UNS
* INC # E3: 3 => UNS
* INC # B5: 5,8 => UNS
* INC # B5: 4,6 => UNS
* INC # C1: 5,9 => UNS
* INC # C1: 3,4,6 => UNS
* INC # F2: 2,9 => UNS
* INC # F2: 1,4,6,8 => UNS
* INC # H5: 2,9 => UNS
* INC # H5: 4,7 => UNS
* INC # H7: 1,2 => UNS
* INC # H7: 4 => UNS
* INC # H8: 1,2 => UNS
* INC # H8: 3,4 => UNS
* INC # H5: 4,7 => UNS
* INC # H6: 4,7 => UNS
* DIS # B2: 5,8 # C1: 4,6 => CTR => C1: 3,9
* INC # B2: 5,8 + C1: 3,9 # A6: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 # A8: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 # E3: 5,8 => UNS
* INC # B2: 5,8 + C1: 3,9 # E3: 3 => UNS
* INC # B2: 5,8 + C1: 3,9 # F2: 2,9 => UNS
* INC # B2: 5,8 + C1: 3,9 # F2: 1 => UNS
* INC # B2: 5,8 + C1: 3,9 # H5: 2,9 => UNS
* INC # B2: 5,8 + C1: 3,9 # H5: 4,7 => UNS
* INC # B2: 5,8 + C1: 3,9 # C4: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 # A6: 4,6 => UNS
* DIS # B2: 5,8 + C1: 3,9 # D5: 4,6 => CTR => D5: 1,8,9
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 # E5: 4,6 => UNS
* DIS # B2: 5,8 + C1: 3,9 + D5: 1,8,9 # F5: 4,6 => CTR => F5: 1,8,9
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G5: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # C4: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # A6: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E5: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G5: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G6: 3,4 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G6: 6,8 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H8: 3,4 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H8: 1,2 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # A8: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # C9: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E7: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E7: 8 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H7: 1,2 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H7: 4 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H8: 1,2 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H8: 3,4 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H5: 4,7 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # H5: 2,9 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # A6: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # A8: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # C4: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # C9: 4,6 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E3: 5,8 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E3: 3 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E3: 5,8 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # E3: 3 => UNS
* INC # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G3: 1,2 => UNS
* PRF # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 # G3: 5 => SOL
* STA # B2: 5,8 + C1: 3,9 + D5: 1,8,9 + F5: 1,8,9 + G3: 5
* CNT  61 HDP CHAINS /  62 HYP OPENED