Analysis of xx-mith-te3-00154973-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1...56....5.......68.3.7..1...6.381........947.....6235.17.83..83..61....7.53.1.. initial

Autosolve

position: 1...56....5.......68.3.7..1...6.381........947.....6235.17.83..83..61....7.53.1.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # C5: 2,3 => CTR => C5: 5,6,8
* CNT   1 HDP CHAINS /  20 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 # C5: 2,3 => CTR => C5: 5,6,8
* STA C5: 5,6,8
* CNT   1 HDP CHAINS /  33 HYP OPENED

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

Pair Reduction Position

position: 1...56....5.......68.3.7..1...6.381.3......947.....6235.17.83..83..61....7.53.1.. pair_reduction
Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:24.798289

The following important HDP chains were detected:

* DIS # H1: 3,7 # H9: 4,6 => CTR => H9: 8
* DIS # H1: 4,8 # H9: 8 => CTR => H9: 4,6
* DIS # H2: 4,6,8 # H9: 4,6 => CTR => H9: 8
* PRF # G3: 4,5 # C9: 2,9 => SOL
* STA # G3: 4,5 + C9: 2,9
* CNT   4 HDP CHAINS / 127 HYP OPENED

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

Details

Positions

1...56....5.......68.3.7..1...6.381........947.....6235.17.83..83..61....7.53.1.. initial
1...56....5.......68.3.7..1...6.381........947.....6235.17.83..83..61....7.53.1.. autosolve
1...56....5.......68.3.7..1...6.381.3......947.....6235.17.83..83..61....7.53.1.. pair_reduction
123456789457189236689327451295643817316872594748915623561798342834261975972534168 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (6)
H3: 4,5
A5: 2,3
F5: 2,5
I4: 5,7
G5: 5,7
H7: 4,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,E2: 1.. / D2 = 1  =>  7 pairs (_) / E2 = 1  =>  7 pairs (_)
B5,B6: 1.. / B5 = 1  => 15 pairs (_) / B6 = 1  =>  7 pairs (_)
H1,H2: 3.. / H1 = 3  =>  6 pairs (_) / H2 = 3  =>  8 pairs (_)
A5,C5: 3.. / A5 = 3  =>  7 pairs (_) / C5 = 3  =>  0 pairs (X)
C1,H1: 3.. / C1 = 3  =>  8 pairs (_) / H1 = 3  =>  6 pairs (_)
A2,A5: 3.. / A2 = 3  =>  0 pairs (X) / A5 = 3  =>  7 pairs (_)
G3,H3: 5.. / G3 = 5  => 19 pairs (_) / H3 = 5  =>  6 pairs (_)
F5,F6: 5.. / F5 = 5  => 13 pairs (_) / F6 = 5  => 10 pairs (_)
I4,G5: 5.. / I4 = 5  => 13 pairs (_) / G5 = 5  => 13 pairs (_)
C4,I4: 5.. / C4 = 5  => 13 pairs (_) / I4 = 5  => 13 pairs (_)
C6,F6: 5.. / C6 = 5  => 13 pairs (_) / F6 = 5  => 10 pairs (_)
H3,H8: 5.. / H3 = 5  =>  6 pairs (_) / H8 = 5  => 19 pairs (_)
I4,I8: 5.. / I4 = 5  => 13 pairs (_) / I8 = 5  => 13 pairs (_)
H2,I2: 6.. / H2 = 6  =>  5 pairs (_) / I2 = 6  =>  7 pairs (_)
B5,C5: 6.. / B5 = 6  =>  7 pairs (_) / C5 = 6  => 15 pairs (_)
B7,C9: 6.. / B7 = 6  => 15 pairs (_) / C9 = 6  =>  7 pairs (_)
B5,B7: 6.. / B5 = 6  =>  7 pairs (_) / B7 = 6  => 15 pairs (_)
C5,C9: 6.. / C5 = 6  => 15 pairs (_) / C9 = 6  =>  7 pairs (_)
C1,C2: 7.. / C1 = 7  =>  6 pairs (_) / C2 = 7  =>  6 pairs (_)
E4,E5: 7.. / E4 = 7  => 13 pairs (_) / E5 = 7  => 13 pairs (_)
I4,G5: 7.. / I4 = 7  => 13 pairs (_) / G5 = 7  => 13 pairs (_)
E4,I4: 7.. / E4 = 7  => 13 pairs (_) / I4 = 7  => 13 pairs (_)
E5,G5: 7.. / E5 = 7  => 13 pairs (_) / G5 = 7  => 13 pairs (_)
C5,C6: 8.. / C5 = 8  =>  9 pairs (_) / C6 = 8  => 11 pairs (_)
H9,I9: 8.. / H9 = 8  =>  6 pairs (_) / I9 = 8  =>  9 pairs (_)
* DURATION: 0:00:06.174761  START: 22:57:20.689015  END: 22:57:26.863776 2025-04-06
* CP COUNT: (25)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:24.518216  START: 22:57:34.612475  END: 22:57:59.130691 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00154973-base-pr-002.dot
* REASONING
* DIS # H1: 3,7 # H9: 4,6 => CTR => H9: 8
* DIS # H1: 4,8 # H9: 8 => CTR => H9: 4,6
* DIS # H2: 4,6,8 # H9: 4,6 => CTR => H9: 8
* PRF # G3: 4,5 # C9: 2,9 => SOL
* STA # G3: 4,5 + C9: 2,9
* CNT   4 HDP CHAINS / 127 HYP OPENED

Header Info

rating: 42753; r2: 789638; index: 154973

Solution

position: 123456789457189236689327451295643817316872594748915623561798342834261975972534168 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 # G3: 4,5 => UNS
* INC # G3: 2,9 => UNS
* INC # H8: 4,5 => UNS
* INC # H8: 7 => UNS
* DIS # C5: 2,3 => CTR => C5: 5,6,8
* INC # C5: 5,6,8 => UNS
* INC # A2: 2,3 => UNS
* INC # A2: 4,9 => UNS
* INC # C5: 2,5 => UNS
* INC # C5: 3,6,8 => UNS
* INC # I8: 5,7 => UNS
* INC # I8: 2,9 => UNS
* INC # G8: 5,7 => UNS
* INC # G8: 2,4,9 => UNS
* INC # H9: 4,6 => UNS
* INC # H9: 8 => UNS
* INC # B7: 4,6 => UNS
* INC # B7: 2,9 => UNS
* INC # H2: 4,6 => UNS
* INC # H2: 3,7,8 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G3: 4,5 => UNS
* INC # G3: 2,9 => UNS
* INC # H8: 4,5 => UNS
* INC # H8: 7 => UNS
* DIS # C5: 2,3 => CTR => C5: 5,6,8
* INC C5: 5,6,8 # I8: 5,7 => UNS
* INC C5: 5,6,8 # I8: 2,9 => UNS
* INC C5: 5,6,8 # G8: 5,7 => UNS
* INC C5: 5,6,8 # G8: 2,4,9 => UNS
* INC C5: 5,6,8 # H9: 4,6 => UNS
* INC C5: 5,6,8 # H9: 8 => UNS
* INC C5: 5,6,8 # B7: 4,6 => UNS
* INC C5: 5,6,8 # B7: 2,9 => UNS
* INC C5: 5,6,8 # H2: 4,6 => UNS
* INC C5: 5,6,8 # H2: 3,7,8 => UNS
* INC C5: 5,6,8 # H1: 3,7 => UNS
* INC C5: 5,6,8 # H1: 4,8 => UNS
* INC C5: 5,6,8 # H2: 3,7 => UNS
* INC C5: 5,6,8 # H2: 4,6,8 => UNS
* INC C5: 5,6,8 # G3: 4,5 => UNS
* INC C5: 5,6,8 # G3: 2,9 => UNS
* INC C5: 5,6,8 # H8: 4,5 => UNS
* INC C5: 5,6,8 # H8: 7 => UNS
* INC C5: 5,6,8 # I8: 5,7 => UNS
* INC C5: 5,6,8 # I8: 2,9 => UNS
* INC C5: 5,6,8 # G8: 5,7 => UNS
* INC C5: 5,6,8 # G8: 2,4,9 => UNS
* INC C5: 5,6,8 # H9: 4,6 => UNS
* INC C5: 5,6,8 # H9: 8 => UNS
* INC C5: 5,6,8 # B7: 4,6 => UNS
* INC C5: 5,6,8 # B7: 2,9 => UNS
* INC C5: 5,6,8 # H2: 4,6 => UNS
* INC C5: 5,6,8 # H2: 3,7,8 => UNS
* STA C5: 5,6,8
* CNT  33 HDP CHAINS /  33 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 3,7 => UNS
* INC # H1: 4,8 => UNS
* INC # H2: 3,7 => UNS
* INC # H2: 4,6,8 => UNS
* INC # G3: 4,5 => UNS
* INC # G3: 2,9 => UNS
* INC # H8: 4,5 => UNS
* INC # H8: 7 => UNS
* INC # I8: 5,7 => UNS
* INC # I8: 2,9 => UNS
* INC # G8: 5,7 => UNS
* INC # G8: 2,4,9 => UNS
* INC # H9: 4,6 => UNS
* INC # H9: 8 => UNS
* INC # B7: 4,6 => UNS
* INC # B7: 2,9 => UNS
* INC # H2: 4,6 => UNS
* INC # H2: 3,7,8 => UNS
* INC # H1: 3,7 # H2: 3,7 => UNS
* INC # H1: 3,7 # H2: 4,6,8 => UNS
* INC # H1: 3,7 # H2: 3,7 => UNS
* INC # H1: 3,7 # H2: 4,6,8 => UNS
* INC # H1: 3,7 # G3: 4,5 => UNS
* INC # H1: 3,7 # G3: 2,9 => UNS
* INC # H1: 3,7 # H8: 4,5 => UNS
* INC # H1: 3,7 # H8: 7 => UNS
* INC # H1: 3,7 # I8: 5,7 => UNS
* INC # H1: 3,7 # I8: 2,9 => UNS
* INC # H1: 3,7 # G8: 5,7 => UNS
* INC # H1: 3,7 # G8: 2,4,9 => UNS
* DIS # H1: 3,7 # H9: 4,6 => CTR => H9: 8
* INC # H1: 3,7 + H9: 8 # B7: 4,6 => UNS
* INC # H1: 3,7 + H9: 8 # B7: 2,9 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 4,6 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 3,7 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 3,7 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 4,6 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 3,7 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 4,6 => UNS
* INC # H1: 3,7 + H9: 8 # G3: 4,5 => UNS
* INC # H1: 3,7 + H9: 8 # G3: 2,9 => UNS
* INC # H1: 3,7 + H9: 8 # H8: 4,5 => UNS
* INC # H1: 3,7 + H9: 8 # H8: 7 => UNS
* INC # H1: 3,7 + H9: 8 # I8: 5,7 => UNS
* INC # H1: 3,7 + H9: 8 # I8: 2,9 => UNS
* INC # H1: 3,7 + H9: 8 # G8: 5,7 => UNS
* INC # H1: 3,7 + H9: 8 # G8: 2,4,9 => UNS
* INC # H1: 3,7 + H9: 8 # B7: 4,6 => UNS
* INC # H1: 3,7 + H9: 8 # B7: 2,9 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 4,6 => UNS
* INC # H1: 3,7 + H9: 8 # H2: 3,7 => UNS
* INC # H1: 3,7 + H9: 8 => UNS
* INC # H1: 4,8 # D5: 1,8 => UNS
* INC # H1: 4,8 # D6: 1,8 => UNS
* INC # H1: 4,8 # E5: 1,8 => UNS
* INC # H1: 4,8 # E6: 1,8 => UNS
* INC # H1: 4,8 # H9: 4,8 => UNS
* INC # H1: 4,8 # H9: 6 => UNS
* INC # H1: 4,8 # H9: 4,6 => UNS
* DIS # H1: 4,8 # H9: 8 => CTR => H9: 4,6
* INC # H1: 4,8 + H9: 4,6 # B7: 4,6 => UNS
* INC # H1: 4,8 + H9: 4,6 # B7: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # G8: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # I8: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # B7: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # E7: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # I1: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # I1: 7 => UNS
* INC # H1: 4,8 + H9: 4,6 # D5: 1,8 => UNS
* INC # H1: 4,8 + H9: 4,6 # D6: 1,8 => UNS
* INC # H1: 4,8 + H9: 4,6 # E5: 1,8 => UNS
* INC # H1: 4,8 + H9: 4,6 # E6: 1,8 => UNS
* INC # H1: 4,8 + H9: 4,6 # B7: 4,6 => UNS
* INC # H1: 4,8 + H9: 4,6 # B7: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # G8: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # I8: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # B7: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # E7: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # I1: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 # I1: 7 => UNS
* INC # H1: 4,8 + H9: 4,6 # C9: 4,6 => UNS
* INC # H1: 4,8 + H9: 4,6 # C9: 2,9 => UNS
* INC # H1: 4,8 + H9: 4,6 => UNS
* INC # H2: 3,7 # H1: 3,7 => UNS
* INC # H2: 3,7 # H1: 4,8 => UNS
* INC # H2: 3,7 # D5: 1,8 => UNS
* INC # H2: 3,7 # D6: 1,8 => UNS
* INC # H2: 3,7 # E5: 1,8 => UNS
* INC # H2: 3,7 # E6: 1,8 => UNS
* INC # H2: 3,7 # H1: 3,7 => UNS
* INC # H2: 3,7 # H1: 4,8 => UNS
* INC # H2: 3,7 # G3: 4,5 => UNS
* INC # H2: 3,7 # G3: 2,9 => UNS
* INC # H2: 3,7 # H8: 4,5 => UNS
* INC # H2: 3,7 # H8: 7 => UNS
* INC # H2: 3,7 # I8: 5,7 => UNS
* INC # H2: 3,7 # I8: 2,9 => UNS
* INC # H2: 3,7 # G8: 5,7 => UNS
* INC # H2: 3,7 # G8: 2,4,9 => UNS
* INC # H2: 3,7 # H9: 4,6 => UNS
* INC # H2: 3,7 # H9: 8 => UNS
* INC # H2: 3,7 # B7: 4,6 => UNS
* INC # H2: 3,7 # B7: 2,9 => UNS
* INC # H2: 3,7 # G8: 2,9 => UNS
* INC # H2: 3,7 # I8: 2,9 => UNS
* INC # H2: 3,7 # I9: 2,9 => UNS
* INC # H2: 3,7 # B7: 2,9 => UNS
* INC # H2: 3,7 # E7: 2,9 => UNS
* INC # H2: 3,7 # I1: 2,9 => UNS
* INC # H2: 3,7 # I1: 7,8 => UNS
* INC # H2: 3,7 => UNS
* DIS # H2: 4,6,8 # H9: 4,6 => CTR => H9: 8
* INC # H2: 4,6,8 + H9: 8 # B7: 4,6 => UNS
* INC # H2: 4,6,8 + H9: 8 # B7: 2,9 => UNS
* INC # H2: 4,6,8 + H9: 8 # B7: 4,6 => UNS
* INC # H2: 4,6,8 + H9: 8 # B7: 2,9 => UNS
* INC # H2: 4,6,8 + H9: 8 => UNS
* INC # G3: 4,5 # H1: 3,7 => UNS
* INC # G3: 4,5 # H1: 8 => UNS
* INC # G3: 4,5 # H2: 3,7 => UNS
* INC # G3: 4,5 # H2: 6,8 => UNS
* INC # G3: 4,5 # B1: 2,9 => UNS
* INC # G3: 4,5 # A2: 2,9 => UNS
* INC # G3: 4,5 # C4: 2,9 => UNS
* INC # G3: 4,5 # C8: 2,9 => UNS
* PRF # G3: 4,5 # C9: 2,9 => SOL
* STA # G3: 4,5 + C9: 2,9
* CNT 126 HDP CHAINS / 127 HYP OPENED