Analysis of xx-mith-te3-00157877-base.sdk

Contents

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

Original Sudoku

level: hard

position: ....567.94.6789.....921.....47...5.65....749.96...5.733......546...3.9.7......... initial

Autosolve

position: ....567.94.6789.....921.....47...5.65....749.96...5.733......546...3.9.7......... 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: 0:00:04.988914

The following important HDP chains were detected:

* PRF # B3: 7,8 # A4: 1,2 => SOL
* STA # B3: 7,8 + A4: 1,2
* CNT   1 HDP CHAINS /  24 HYP OPENED

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

Details

Positions

`....567.94.6789.....921.....47...5.65....749.96...5.733......546...3.9.7.........`	initial
`....567.94.6789.....921.....47...5.65....749.96...5.733......546...3.9.7.........`	autosolve
`123456789456789132789213645247398516531627498968145273372961854615834927894572361`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A3: 7,8
D1: 3,4
F3: 3,4
I3: 5,8
E4: 2,9
E5: 2,6
E6: 2,4
C8: 4,5
C9: 4,5

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D1,F3: 3.. / D1 = 3  => 14 pairs (_) / F3 = 3  => 11 pairs (_)
B5,C5: 3.. / B5 = 3  => 11 pairs (_) / C5 = 3  =>  9 pairs (_)
D4,F4: 3.. / D4 = 3  => 11 pairs (_) / F4 = 3  => 14 pairs (_)
G9,H9: 3.. / G9 = 3  => 11 pairs (_) / H9 = 3  => 14 pairs (_)
C1,C5: 3.. / C1 = 3  => 11 pairs (_) / C5 = 3  =>  9 pairs (_)
D1,D4: 3.. / D1 = 3  => 14 pairs (_) / D4 = 3  => 11 pairs (_)
F3,F4: 3.. / F3 = 3  => 11 pairs (_) / F4 = 3  => 14 pairs (_)
D1,F3: 4.. / D1 = 4  => 11 pairs (_) / F3 = 4  => 14 pairs (_)
H1,H3: 4.. / H1 = 4  => 14 pairs (_) / H3 = 4  => 11 pairs (_)
D6,E6: 4.. / D6 = 4  =>  9 pairs (_) / E6 = 4  =>  9 pairs (_)
C8,C9: 4.. / C8 = 4  =>  7 pairs (_) / C9 = 4  =>  8 pairs (_)
D1,H1: 4.. / D1 = 4  => 11 pairs (_) / H1 = 4  => 14 pairs (_)
F3,H3: 4.. / F3 = 4  => 14 pairs (_) / H3 = 4  => 11 pairs (_)
E6,E9: 4.. / E6 = 4  =>  9 pairs (_) / E9 = 4  =>  9 pairs (_)
B2,B3: 5.. / B2 = 5  => 11 pairs (_) / B3 = 5  => 12 pairs (_)
I2,I3: 5.. / I2 = 5  => 12 pairs (_) / I3 = 5  => 11 pairs (_)
C8,C9: 5.. / C8 = 5  =>  8 pairs (_) / C9 = 5  =>  7 pairs (_)
D8,D9: 5.. / D8 = 5  =>  7 pairs (_) / D9 = 5  =>  8 pairs (_)
B2,I2: 5.. / B2 = 5  => 11 pairs (_) / I2 = 5  => 12 pairs (_)
B3,I3: 5.. / B3 = 5  => 12 pairs (_) / I3 = 5  => 11 pairs (_)
C8,D8: 5.. / C8 = 5  =>  8 pairs (_) / D8 = 5  =>  7 pairs (_)
C9,D9: 5.. / C9 = 5  =>  7 pairs (_) / D9 = 5  =>  8 pairs (_)
G3,H3: 6.. / G3 = 6  => 12 pairs (_) / H3 = 6  => 14 pairs (_)
D5,E5: 6.. / D5 = 6  => 10 pairs (_) / E5 = 6  =>  9 pairs (_)
H3,H9: 6.. / H3 = 6  => 14 pairs (_) / H9 = 6  => 12 pairs (_)
A3,B3: 7.. / A3 = 7  => 10 pairs (_) / B3 = 7  =>  0 pairs (X)
E7,E9: 7.. / E7 = 7  =>  9 pairs (_) / E9 = 7  =>  8 pairs (_)
B7,E7: 7.. / B7 = 7  =>  8 pairs (_) / E7 = 7  =>  9 pairs (_)
A3,A9: 7.. / A3 = 7  => 10 pairs (_) / A9 = 7  =>  0 pairs (X)
D4,E4: 9.. / D4 = 9  => 17 pairs (_) / E4 = 9  =>  8 pairs (_)
B7,B9: 9.. / B7 = 9  =>  9 pairs (_) / B9 = 9  =>  9 pairs (_)
* DURATION: 0:00:08.321885  START: 23:23:03.123860  END: 23:23:11.445745 2025-04-06
* CP COUNT: (31)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:04.830602  START: 23:23:17.506633  END: 23:23:22.337235 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00157877-base-pr-002.dot
* REASONING
* PRF # B3: 7,8 # A4: 1,2 => SOL
* STA # B3: 7,8 + A4: 1,2
* CNT   1 HDP CHAINS /  24 HYP OPENED

Header Info

rating: 44061; r2: 836635; index: 157877

Solution

position: 123456789456789132789213645247398516531627498968145273372961854615834927894572361 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 # B3: 7,8 => UNS
* INC # B3: 3,5 => UNS
* INC # A9: 7,8 => UNS
* INC # A9: 1,2 => UNS
* INC # H1: 3,4 => UNS
* INC # H1: 1,2,8 => UNS
* INC # H3: 3,4 => UNS
* INC # H3: 6,8 => UNS
* INC # B3: 5,8 => UNS
* INC # B3: 3,7 => UNS
* INC # E7: 2,9 => UNS
* INC # E9: 2,9 => UNS
* INC # E7: 2,6 => UNS
* INC # E9: 2,6 => UNS
* INC # E9: 2,4 => UNS
* INC # E9: 6,7,9 => UNS
* INC # D8: 4,5 => UNS
* INC # D8: 1,8 => UNS
* INC # D9: 4,5 => UNS
* INC # D9: 1,6,8,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # B3: 7,8 => UNS
* INC # B3: 3,5 => UNS
* INC # A9: 7,8 => UNS
* INC # A9: 1,2 => UNS
* INC # H1: 3,4 => UNS
* INC # H1: 1,2,8 => UNS
* INC # H3: 3,4 => UNS
* INC # H3: 6,8 => UNS
* INC # B3: 5,8 => UNS
* INC # B3: 3,7 => UNS
* INC # E7: 2,9 => UNS
* INC # E9: 2,9 => UNS
* INC # E7: 2,6 => UNS
* INC # E9: 2,6 => UNS
* INC # E9: 2,4 => UNS
* INC # E9: 6,7,9 => UNS
* INC # D8: 4,5 => UNS
* INC # D8: 1,8 => UNS
* INC # D9: 4,5 => UNS
* INC # D9: 1,6,8,9 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # B3: 7,8 => UNS
* INC # B3: 3,5 => UNS
* INC # A9: 7,8 => UNS
* INC # A9: 1,2 => UNS
* INC # H1: 3,4 => UNS
* INC # H1: 1,2,8 => UNS
* INC # H3: 3,4 => UNS
* INC # H3: 6,8 => UNS
* INC # B3: 5,8 => UNS
* INC # B3: 3,7 => UNS
* INC # E7: 2,9 => UNS
* INC # E9: 2,9 => UNS
* INC # E7: 2,6 => UNS
* INC # E9: 2,6 => UNS
* INC # E9: 2,4 => UNS
* INC # E9: 6,7,9 => UNS
* INC # D8: 4,5 => UNS
* INC # D8: 1,8 => UNS
* INC # D9: 4,5 => UNS
* INC # D9: 1,6,8,9 => UNS
* INC # B3: 7,8 # B1: 1,2 => UNS
* INC # B3: 7,8 # C1: 1,2 => UNS
* PRF # B3: 7,8 # A4: 1,2 => SOL
* STA # B3: 7,8 + A4: 1,2
* CNT  23 HDP CHAINS /  24 HYP OPENED