Analysis of xx-mith-te3-00021097-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1..4.6.8....1..2..6...72.14275......36........41.67....8..2167..1...8.4.....4.... initial

Autosolve

position: 1..4.6.8....1..2..6...72.14275......36........41.67....8..2167..1...8.4.....4.... autosolve

Pair Reduction Variants

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # I5: 8,9 => CTR => I5: 1,2,5,7
* DIS # C2: 8,9 => CTR => C2: 3,4,7
* DIS # D6: 8,9 => CTR => D6: 2,3,5
* DIS # A2: 8,9 => CTR => A2: 4,5,7
* DIS # I5: 1,8 => CTR => I5: 2,5,7,9
* CNT   5 HDP CHAINS /  23 HYP OPENED

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

Pair Reduction

The following important HDP chains were detected:

* DIS # I5: 8,9 => CTR => I5: 1,2,5,7
* DIS I5: 1,2,5,7 # C2: 8,9 => CTR => C2: 3,4,7
* DIS I5: 1,2,5,7 + C2: 3,4,7 # C3: 3 => CTR => C3: 8,9
* DIS I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 # D6: 8,9 => CTR => D6: 2,3,5
* DIS I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 # A2: 8,9 => CTR => A2: 4,5,7
* STA I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7
* CNT   5 HDP CHAINS /  49 HYP OPENED

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

Pair Reduction Position

position: 1..4.678....18.2.66.8.72.14275....6.369.....7841.67....8..2167..1...8.4.....4.... pair_reduction

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

Deep Pair Reduction

Time used: 0:00:14.684958

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

`1..4.6.8....1..2..6...72.14275......36........41.67....8..2167..1...8.4.....4....`	initial
`1..4.6.8....1..2..6...72.14275......36........41.67....8..2167..1...8.4.....4....`	autosolve
`1..4.678....18.2.66.8.72.14275....6.369.....7841.67....8..2167..1...8.4.....4....`	pair_reduction
`123456789457189236698372514275893461369214857841567392584921673712638945936745128`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
C5: 8,9
A6: 8,9
D8: 6,7
D9: 6,7
G9: 1,8
I9: 1,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E4,E5: 1.. / E4 = 1  =>  9 pairs (_) / E5 = 1  =>  6 pairs (_)
G9,I9: 1.. / G9 = 1  =>  4 pairs (_) / I9 = 1  => 12 pairs (_)
B1,C1: 2.. / B1 = 2  =>  8 pairs (_) / C1 = 2  => 12 pairs (_)
D5,D6: 2.. / D5 = 2  =>  7 pairs (_) / D6 = 2  =>  8 pairs (_)
I8,H9: 2.. / I8 = 2  =>  6 pairs (_) / H9 = 2  =>  6 pairs (_)
C8,I8: 2.. / C8 = 2  =>  6 pairs (_) / I8 = 2  =>  6 pairs (_)
B1,B9: 2.. / B1 = 2  =>  8 pairs (_) / B9 = 2  => 12 pairs (_)
A2,C2: 4.. / A2 = 4  => 12 pairs (_) / C2 = 4  =>  8 pairs (_)
F4,F5: 4.. / F4 = 4  => 15 pairs (_) / F5 = 4  =>  7 pairs (_)
G4,G5: 4.. / G4 = 4  =>  7 pairs (_) / G5 = 4  => 15 pairs (_)
A7,C7: 4.. / A7 = 4  =>  8 pairs (_) / C7 = 4  => 12 pairs (_)
F4,G4: 4.. / F4 = 4  => 15 pairs (_) / G4 = 4  =>  7 pairs (_)
F5,G5: 4.. / F5 = 4  =>  7 pairs (_) / G5 = 4  => 15 pairs (_)
A2,A7: 4.. / A2 = 4  => 12 pairs (_) / A7 = 4  =>  8 pairs (_)
C2,C7: 4.. / C2 = 4  =>  8 pairs (_) / C7 = 4  => 12 pairs (_)
H2,I2: 6.. / H2 = 6  =>  0 pairs (X) / I2 = 6  => 14 pairs (_)
H4,I4: 6.. / H4 = 6  => 14 pairs (_) / I4 = 6  =>  0 pairs (X)
C8,C9: 6.. / C8 = 6  =>  5 pairs (_) / C9 = 6  =>  5 pairs (_)
D8,D9: 6.. / D8 = 6  =>  5 pairs (_) / D9 = 6  =>  5 pairs (_)
C8,D8: 6.. / C8 = 6  =>  5 pairs (_) / D8 = 6  =>  5 pairs (_)
C9,D9: 6.. / C9 = 6  =>  5 pairs (_) / D9 = 6  =>  5 pairs (_)
H2,H4: 6.. / H2 = 6  =>  0 pairs (X) / H4 = 6  => 14 pairs (_)
I2,I4: 6.. / I2 = 6  => 14 pairs (_) / I4 = 6  =>  0 pairs (X)
G5,I5: 7.. / G5 = 7  =>  0 pairs (X) / I5 = 7  => 14 pairs (_)
D8,D9: 7.. / D8 = 7  =>  5 pairs (_) / D9 = 7  =>  5 pairs (_)
G1,G5: 7.. / G1 = 7  => 14 pairs (_) / G5 = 7  =>  0 pairs (X)
E2,D3: 8.. / E2 = 8  => 14 pairs (_) / D3 = 8  =>  0 pairs (X)
C5,A6: 8.. / C5 = 8  =>  0 pairs (X) / A6 = 8  => 14 pairs (_)
G9,I9: 8.. / G9 = 8  => 12 pairs (_) / I9 = 8  =>  4 pairs (_)
C3,D3: 8.. / C3 = 8  => 14 pairs (_) / D3 = 8  =>  0 pairs (X)
A2,A6: 8.. / A2 = 8  =>  0 pairs (X) / A6 = 8  => 14 pairs (_)
C5,A6: 9.. / C5 = 9  => 14 pairs (_) / A6 = 9  =>  0 pairs (X)
* DURATION: 0:00:09.139034  START: 06:10:09.580663  END: 06:10:18.719697 2025-04-06
* CP COUNT: (32)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.543446  START: 06:10:33.808641  END: 06:10:48.352087 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00021097-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: 365766; index: 21097

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 # D5: 8,9 => UNS
* INC # E5: 8,9 => UNS
* INC # G5: 8,9 => UNS
* DIS # I5: 8,9 => CTR => I5: 1,2,5,7
* INC # I5: 1,2,5,7 => UNS
* DIS # C2: 8,9 => CTR => C2: 3,4,7
* INC # C2: 3,4,7 => UNS
* INC # C3: 8,9 => UNS
* DIS # D6: 8,9 => CTR => D6: 2,3,5
* INC # D6: 2,3,5 => UNS
* INC # G6: 8,9 => UNS
* INC # I6: 8,9 => UNS
* DIS # A2: 8,9 => CTR => A2: 4,5,7
* INC # A2: 4,5,7 => UNS
* INC # C8: 6,7 => UNS
* INC # C8: 2,3,9 => UNS
* INC # C9: 6,7 => UNS
* INC # C9: 2,3,9 => UNS
* INC # G4: 1,8 => UNS
* INC # G5: 1,8 => UNS
* INC # I4: 1,8 => UNS
* DIS # I5: 1,8 => CTR => I5: 2,5,7,9
* INC # I5: 2,5,7,9 => UNS
* CNT  23 HDP CHAINS /  23 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D5: 8,9 => UNS
* INC # E5: 8,9 => UNS
* INC # G5: 8,9 => UNS
* DIS # I5: 8,9 => CTR => I5: 1,2,5,7
* DIS I5: 1,2,5,7 # C2: 8,9 => CTR => C2: 3,4,7
* INC I5: 1,2,5,7 + C2: 3,4,7 # C3: 8,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 # C3: 8,9 => UNS
* DIS I5: 1,2,5,7 + C2: 3,4,7 # C3: 3 => CTR => C3: 8,9
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 # D5: 8,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 # E5: 8,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 # G5: 8,9 => UNS
* DIS I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 # D6: 8,9 => CTR => D6: 2,3,5
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 # G6: 8,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 # I6: 8,9 => UNS
* DIS I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 # A2: 8,9 => CTR => A2: 4,5,7
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C8: 6,7 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C8: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C9: 6,7 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C9: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # G4: 1,8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # G5: 1,8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # B1: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # B1: 5,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C8: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C9: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # D5: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # D5: 8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # H6: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # I6: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # G4: 1,8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # G5: 1,8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # H6: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # I6: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # D5: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # D5: 8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # H9: 2,5 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # H9: 3,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C8: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C9: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # H9: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # H9: 5,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # B1: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # B1: 5,9 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C8: 6,7 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C8: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C9: 6,7 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # C9: 2,3 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # G4: 1,8 => UNS
* INC I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7 # G5: 1,8 => UNS
* STA I5: 1,2,5,7 + C2: 3,4,7 + C3: 8,9 + D6: 2,3,5 + A2: 4,5,7
* CNT  49 HDP CHAINS /  49 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