Analysis of xx-mith-te3-00115829-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: .2.4.6...45.....3...97.3......3.5.78.7.86........743..5.....6..7..6..85.8..5...43 initial

Autosolve

position: .2.4.6...45.....36..97.3......3.5.78.7.86........7436.5....86.77..6..85.8..5.7.43 autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:14.027233

The following important HDP chains were detected:

* PRF # C1: 3 # D2: 1,2 => SOL
* STA # C1: 3 + D2: 1,2
* CNT   1 HDP CHAINS /  63 HYP OPENED

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

Details

Positions

.2.4.6...45.....3...97.3......3.5.78.7.86........743..5.....6..7..6..85.8..5...43 initial
.2.4.6...45.....36..97.3......3.5.78.7.86........7436.5....86.77..6..85.8..5.7.43 autosolve
123456789457189236689723514246395178375861492918274365531948627794632851862517943 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
A1: 1,3
C2: 7,8
A3: 1,6
C5: 3,5
B6: 1,8
C6: 5,8
E7: 3,4
E8: 3,4

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,C1: 3.. / A1 = 3  =>  9 pairs (_) / C1 = 3  => 13 pairs (_)
A5,C5: 3.. / A5 = 3  => 13 pairs (_) / C5 = 3  =>  9 pairs (_)
B7,B8: 3.. / B7 = 3  =>  7 pairs (_) / B8 = 3  =>  7 pairs (_)
E7,E8: 3.. / E7 = 3  =>  7 pairs (_) / E8 = 3  =>  7 pairs (_)
B7,E7: 3.. / B7 = 3  =>  7 pairs (_) / E7 = 3  =>  7 pairs (_)
B8,E8: 3.. / B8 = 3  =>  7 pairs (_) / E8 = 3  =>  7 pairs (_)
A1,A5: 3.. / A1 = 3  =>  9 pairs (_) / A5 = 3  => 13 pairs (_)
C1,C5: 3.. / C1 = 3  => 13 pairs (_) / C5 = 3  =>  9 pairs (_)
G3,I3: 4.. / G3 = 4  =>  8 pairs (_) / I3 = 4  =>  9 pairs (_)
B4,C4: 4.. / B4 = 4  =>  9 pairs (_) / C4 = 4  => 15 pairs (_)
G5,I5: 4.. / G5 = 4  =>  9 pairs (_) / I5 = 4  =>  8 pairs (_)
E7,E8: 4.. / E7 = 4  =>  7 pairs (_) / E8 = 4  =>  7 pairs (_)
G3,G5: 4.. / G3 = 4  =>  8 pairs (_) / G5 = 4  =>  9 pairs (_)
I3,I5: 4.. / I3 = 4  =>  9 pairs (_) / I5 = 4  =>  8 pairs (_)
E1,E3: 5.. / E1 = 5  => 12 pairs (_) / E3 = 5  =>  8 pairs (_)
C5,C6: 5.. / C5 = 5  => 13 pairs (_) / C6 = 5  =>  9 pairs (_)
C6,I6: 5.. / C6 = 5  =>  9 pairs (_) / I6 = 5  => 13 pairs (_)
A3,B3: 6.. / A3 = 6  => 11 pairs (_) / B3 = 6  => 14 pairs (_)
B9,C9: 6.. / B9 = 6  => 11 pairs (_) / C9 = 6  => 10 pairs (_)
A3,A4: 6.. / A3 = 6  => 11 pairs (_) / A4 = 6  => 14 pairs (_)
C4,C9: 6.. / C4 = 6  => 11 pairs (_) / C9 = 6  => 10 pairs (_)
C1,C2: 7.. / C1 = 7  =>  9 pairs (_) / C2 = 7  => 10 pairs (_)
G1,G2: 7.. / G1 = 7  => 10 pairs (_) / G2 = 7  =>  9 pairs (_)
C1,G1: 7.. / C1 = 7  =>  9 pairs (_) / G1 = 7  => 10 pairs (_)
C2,G2: 7.. / C2 = 7  => 10 pairs (_) / G2 = 7  =>  9 pairs (_)
H1,H3: 8.. / H1 = 8  => 10 pairs (_) / H3 = 8  => 10 pairs (_)
B6,C6: 8.. / B6 = 8  =>  9 pairs (_) / C6 = 8  => 13 pairs (_)
C2,E2: 8.. / C2 = 8  =>  9 pairs (_) / E2 = 8  => 10 pairs (_)
B3,B6: 8.. / B3 = 8  => 13 pairs (_) / B6 = 8  =>  9 pairs (_)
* DURATION: 0:00:10.328126  START: 05:47:08.059302  END: 05:47:18.387428 2025-04-05
* CP COUNT: (29)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:13.808988  START: 05:47:24.013761  END: 05:47:37.822749 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00115829-base-pr-002.dot
* REASONING
* PRF # C1: 3 # D2: 1,2 => SOL
* STA # C1: 3 + D2: 1,2
* CNT   1 HDP CHAINS /  63 HYP OPENED

Header Info

rating: 29562; r2: 586234; index: 115829

Solution

position: 123456789457189236689723514246395178375861492918274365531948627794632851862517943 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 # A5: 1,3 => UNS
* INC # A5: 2,9 => UNS
* INC # C1: 7,8 => UNS
* INC # C1: 3 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 8 => UNS
* INC # A4: 1,6 => UNS
* INC # A4: 2,9 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 6 => UNS
* INC # B7: 3,4 => UNS
* INC # B7: 1,9 => UNS
* INC # B8: 3,4 => UNS
* INC # B8: 1,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 1,3 => UNS
* INC # A5: 2,9 => UNS
* INC # C1: 7,8 => UNS
* INC # C1: 3 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 8 => UNS
* INC # A4: 1,6 => UNS
* INC # A4: 2,9 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 6 => UNS
* INC # B7: 3,4 => UNS
* INC # B7: 1,9 => UNS
* INC # B8: 3,4 => UNS
* INC # B8: 1,9 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 1,3 => UNS
* INC # A5: 2,9 => UNS
* INC # C1: 7,8 => UNS
* INC # C1: 3 => UNS
* INC # B3: 1,6 => UNS
* INC # B3: 8 => UNS
* INC # A4: 1,6 => UNS
* INC # A4: 2,9 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 6 => UNS
* INC # B7: 3,4 => UNS
* INC # B7: 1,9 => UNS
* INC # B8: 3,4 => UNS
* INC # B8: 1,9 => UNS
* INC # A5: 1,3 # C1: 7,8 => UNS
* INC # A5: 1,3 # C1: 3 => UNS
* INC # A5: 1,3 # E3: 1,8 => UNS
* INC # A5: 1,3 # H3: 1,8 => UNS
* INC # A5: 1,3 # E4: 2,9 => UNS
* INC # A5: 1,3 # G4: 2,9 => UNS
* INC # A5: 1,3 # D6: 2,9 => UNS
* INC # A5: 1,3 # I6: 2,9 => UNS
* INC # A5: 1,3 # B7: 3,4 => UNS
* INC # A5: 1,3 # B7: 9 => UNS
* INC # A5: 1,3 # B8: 3,4 => UNS
* INC # A5: 1,3 # B8: 9 => UNS
* INC # A5: 1,3 => UNS
* INC # A5: 2,9 # A4: 1,6 => UNS
* INC # A5: 2,9 # A4: 2,9 => UNS
* INC # A5: 2,9 # B4: 1,6 => UNS
* INC # A5: 2,9 # B9: 1,6 => UNS
* INC # A5: 2,9 # E3: 2,8 => UNS
* INC # A5: 2,9 # E3: 5 => UNS
* INC # A5: 2,9 # A4: 2,9 => UNS
* INC # A5: 2,9 # A6: 2,9 => UNS
* INC # A5: 2,9 # F5: 2,9 => UNS
* INC # A5: 2,9 # H5: 2,9 => UNS
* INC # A5: 2,9 # G3: 4,5 => UNS
* INC # A5: 2,9 # G3: 2 => UNS
* INC # A5: 2,9 # I3: 4,5 => UNS
* INC # A5: 2,9 # I3: 2 => UNS
* INC # A5: 2,9 # B7: 3,4 => UNS
* INC # A5: 2,9 # B7: 1,9 => UNS
* INC # A5: 2,9 # B8: 3,4 => UNS
* INC # A5: 2,9 # B8: 1,9 => UNS
* INC # A5: 2,9 => UNS
* INC # C1: 7,8 # A4: 1,6 => UNS
* INC # C1: 7,8 # A4: 2,9 => UNS
* INC # C1: 7,8 # B4: 1,6 => UNS
* INC # C1: 7,8 # B9: 1,6 => UNS
* INC # C1: 7,8 # E3: 2,8 => UNS
* INC # C1: 7,8 # E3: 5 => UNS
* INC # C1: 7,8 # G3: 4,5 => UNS
* INC # C1: 7,8 # G3: 2 => UNS
* INC # C1: 7,8 # I3: 4,5 => UNS
* INC # C1: 7,8 # I3: 2 => UNS
* INC # C1: 7,8 # B7: 3,4 => UNS
* INC # C1: 7,8 # B7: 1,9 => UNS
* INC # C1: 7,8 # B8: 3,4 => UNS
* INC # C1: 7,8 # B8: 1,9 => UNS
* INC # C1: 7,8 => UNS
* PRF # C1: 3 # D2: 1,2 => SOL
* STA # C1: 3 + D2: 1,2
* CNT  62 HDP CHAINS /  63 HYP OPENED