Analysis of xx-mith-te3-00014561-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12....7..4.6..9...78....5......643.....9.547...43...6.3..64.95.5...936.7...5.7... initial

Autosolve

position: 12....7..4.6..9...78....5......643.....9.547...43...6.3..64.95.54..936.7...5.7... 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: 0:00:06.248130

The following important HDP chains were detected:

* PRF # C1: 3,5 # H1: 4,8 => SOL
* STA # C1: 3,5 + H1: 4,8
* CNT   1 HDP CHAINS /  28 HYP OPENED

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

Details

Positions

`12....7..4.6..9...78....5......643.....9.547...43...6.3..64.95.5...936.7...5.7...`	initial
`12....7..4.6..9...78....5......643.....9.547...43...6.3..64.95.54..936.7...5.7...`	autosolve
`123456789456789123789132546275864391631925478894371265317648952548293617962517834`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B2: 3,5
C3: 3,9
D1: 4,8
F1: 6,8
C5: 1,3
B7: 1,7
A9: 6,9
B9: 6,9
H9: 3,4
I9: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
B5,C5: 3.. / B5 = 3  => 16 pairs (_) / C5 = 3  => 13 pairs (_)
H9,I9: 3.. / H9 = 3  =>  8 pairs (_) / I9 = 3  => 14 pairs (_)
B2,B5: 3.. / B2 = 3  => 13 pairs (_) / B5 = 3  => 16 pairs (_)
D1,D3: 4.. / D1 = 4  => 10 pairs (_) / D3 = 4  => 11 pairs (_)
H9,I9: 4.. / H9 = 4  => 14 pairs (_) / I9 = 4  =>  8 pairs (_)
C1,B2: 5.. / C1 = 5  => 13 pairs (_) / B2 = 5  => 16 pairs (_)
E1,E2: 5.. / E1 = 5  => 16 pairs (_) / E2 = 5  => 13 pairs (_)
I4,I6: 5.. / I4 = 5  => 12 pairs (_) / I6 = 5  => 11 pairs (_)
C1,E1: 5.. / C1 = 5  => 13 pairs (_) / E1 = 5  => 16 pairs (_)
B2,E2: 5.. / B2 = 5  => 16 pairs (_) / E2 = 5  => 13 pairs (_)
B6,I6: 5.. / B6 = 5  => 12 pairs (_) / I6 = 5  => 11 pairs (_)
C1,C4: 5.. / C1 = 5  => 13 pairs (_) / C4 = 5  => 16 pairs (_)
F1,F3: 6.. / F1 = 6  => 10 pairs (_) / F3 = 6  => 13 pairs (_)
I1,I3: 6.. / I1 = 6  => 13 pairs (_) / I3 = 6  => 10 pairs (_)
A5,B5: 6.. / A5 = 6  => 16 pairs (_) / B5 = 6  => 12 pairs (_)
A9,B9: 6.. / A9 = 6  => 12 pairs (_) / B9 = 6  => 16 pairs (_)
F1,I1: 6.. / F1 = 6  => 10 pairs (_) / I1 = 6  => 13 pairs (_)
F3,I3: 6.. / F3 = 6  => 13 pairs (_) / I3 = 6  => 10 pairs (_)
A5,A9: 6.. / A5 = 6  => 16 pairs (_) / A9 = 6  => 12 pairs (_)
B5,B9: 6.. / B5 = 6  => 12 pairs (_) / B9 = 6  => 16 pairs (_)
D2,E2: 7.. / D2 = 7  => 10 pairs (_) / E2 = 7  =>  0 pairs (X)
D4,E6: 7.. / D4 = 7  =>  0 pairs (X) / E6 = 7  => 10 pairs (_)
B7,C7: 7.. / B7 = 7  => 11 pairs (_) / C7 = 7  => 15 pairs (_)
B6,E6: 7.. / B6 = 7  =>  0 pairs (X) / E6 = 7  => 10 pairs (_)
C4,C7: 7.. / C4 = 7  => 11 pairs (_) / C7 = 7  => 15 pairs (_)
D2,D4: 7.. / D2 = 7  => 10 pairs (_) / D4 = 7  =>  0 pairs (X)
E2,E6: 7.. / E2 = 7  =>  0 pairs (X) / E6 = 7  => 10 pairs (_)
C1,C3: 9.. / C1 = 9  => 17 pairs (_) / C3 = 9  => 10 pairs (_)
A9,B9: 9.. / A9 = 9  => 16 pairs (_) / B9 = 9  => 12 pairs (_)
* DURATION: 0:00:08.764141  START: 07:17:02.533685  END: 07:17:11.297826 2025-04-04
* CP COUNT: (29)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:06.116999  START: 07:17:18.848313  END: 07:17:24.965312 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00014561-base-pr-002.dot
* REASONING
* PRF # C1: 3,5 # H1: 4,8 => SOL
* STA # C1: 3,5 + H1: 4,8
* CNT   1 HDP CHAINS /  28 HYP OPENED

Header Info

rating: 3280; r2: 265635; index: 14561

Solution

position: 123456789456789123789132546275864391631925478894371265317648952548293617962517834 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 # C1: 3,5 => UNS
* INC # C1: 9 => UNS
* INC # E2: 3,5 => UNS
* INC # E2: 1,2,7,8 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 5 => UNS
* INC # H3: 3,9 => UNS
* INC # I3: 3,9 => UNS
* INC # H1: 4,8 => UNS
* INC # I1: 4,8 => UNS
* INC # I1: 6,8 => UNS
* INC # I1: 3,4,9 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 6 => UNS
* INC # C7: 1,7 => UNS
* INC # C7: 2,8 => UNS
* INC # B4: 1,7 => UNS
* INC # B6: 1,7 => UNS
* INC # H1: 3,4 => UNS
* INC # H3: 3,4 => UNS
* INC # I1: 3,4 => UNS
* INC # I3: 3,4 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 3,5 => UNS
* INC # C1: 9 => UNS
* INC # E2: 3,5 => UNS
* INC # E2: 1,2,7,8 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 5 => UNS
* INC # H3: 3,9 => UNS
* INC # I3: 3,9 => UNS
* INC # H1: 4,8 => UNS
* INC # I1: 4,8 => UNS
* INC # I1: 6,8 => UNS
* INC # I1: 3,4,9 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 6 => UNS
* INC # C7: 1,7 => UNS
* INC # C7: 2,8 => UNS
* INC # B4: 1,7 => UNS
* INC # B6: 1,7 => UNS
* INC # H1: 3,4 => UNS
* INC # H3: 3,4 => UNS
* INC # I1: 3,4 => UNS
* INC # I3: 3,4 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # C1: 3,5 => UNS
* INC # C1: 9 => UNS
* INC # E2: 3,5 => UNS
* INC # E2: 1,2,7,8 => UNS
* INC # C1: 3,9 => UNS
* INC # C1: 5 => UNS
* INC # H3: 3,9 => UNS
* INC # I3: 3,9 => UNS
* INC # H1: 4,8 => UNS
* INC # I1: 4,8 => UNS
* INC # I1: 6,8 => UNS
* INC # I1: 3,4,9 => UNS
* INC # B5: 1,3 => UNS
* INC # B5: 6 => UNS
* INC # C7: 1,7 => UNS
* INC # C7: 2,8 => UNS
* INC # B4: 1,7 => UNS
* INC # B6: 1,7 => UNS
* INC # H1: 3,4 => UNS
* INC # H3: 3,4 => UNS
* INC # I1: 3,4 => UNS
* INC # I3: 3,4 => UNS
* INC # C1: 3,5 # E1: 3,5 => UNS
* INC # C1: 3,5 # E1: 8 => UNS
* INC # C1: 3,5 # E2: 3,5 => UNS
* INC # C1: 3,5 # E2: 1,2,7,8 => UNS
* PRF # C1: 3,5 # H1: 4,8 => SOL
* STA # C1: 3,5 + H1: 4,8
* CNT  27 HDP CHAINS /  28 HYP OPENED