Analysis of xx-mith-te3-00134025-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12..567.9...1.926.6..27..15.4........16...95.8..9.7.....1...5.2..2...19........76 initial

Autosolve

position: 12..567.9...1.926.6..27..15.4........16...95.8..9.7.....1.9.5.2..2...19........76 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: 0:00:10.583272

The following important HDP chains were detected:

* PRF # A4: 2 # G4: 3,8 => SOL
* STA # A4: 2 + G4: 3,8
* CNT   1 HDP CHAINS /  40 HYP OPENED

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

Details

Positions

`12..567.9...1.926.6..27..15.4........16...95.8..9.7.....1...5.2..2...19........76`	initial
`12..567.9...1.926.6..27..15.4........16...95.8..9.7.....1.9.5.2..2...19........76`	autosolve
`123456789457189263698273415249615837716832954835947621361798542572364198984521376`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
C4: 7,9
A5: 2,7
B6: 3,5
C6: 3,5
G6: 4,6
H6: 2,4
I6: 1,4
E9: 1,2
F9: 1,2

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
I4,I6: 1.. / I4 = 1  => 10 pairs (_) / I6 = 1  =>  8 pairs (_)
E9,F9: 1.. / E9 = 1  =>  8 pairs (_) / F9 = 1  =>  7 pairs (_)
E6,I6: 1.. / E6 = 1  => 10 pairs (_) / I6 = 1  =>  8 pairs (_)
F4,F9: 1.. / F4 = 1  =>  8 pairs (_) / F9 = 1  =>  7 pairs (_)
A4,A5: 2.. / A4 = 2  => 12 pairs (_) / A5 = 2  => 12 pairs (_)
H4,H6: 2.. / H4 = 2  => 10 pairs (_) / H6 = 2  =>  9 pairs (_)
E9,F9: 2.. / E9 = 2  =>  7 pairs (_) / F9 = 2  =>  8 pairs (_)
E6,H6: 2.. / E6 = 2  => 10 pairs (_) / H6 = 2  =>  9 pairs (_)
B6,C6: 3.. / B6 = 3  =>  8 pairs (_) / C6 = 3  =>  8 pairs (_)
B6,C6: 5.. / B6 = 5  =>  8 pairs (_) / C6 = 5  =>  8 pairs (_)
D4,F4: 5.. / D4 = 5  => 11 pairs (_) / F4 = 5  => 10 pairs (_)
F4,F8: 5.. / F4 = 5  => 10 pairs (_) / F8 = 5  => 11 pairs (_)
G4,G6: 6.. / G4 = 6  => 11 pairs (_) / G6 = 6  =>  9 pairs (_)
B7,B8: 6.. / B7 = 6  =>  9 pairs (_) / B8 = 6  =>  9 pairs (_)
E6,G6: 6.. / E6 = 6  => 11 pairs (_) / G6 = 6  =>  9 pairs (_)
B7,D7: 6.. / B7 = 6  =>  9 pairs (_) / D7 = 6  =>  9 pairs (_)
I4,I5: 7.. / I4 = 7  => 12 pairs (_) / I5 = 7  => 12 pairs (_)
D7,D8: 7.. / D7 = 7  => 10 pairs (_) / D8 = 7  =>  9 pairs (_)
A5,I5: 7.. / A5 = 7  => 12 pairs (_) / I5 = 7  => 12 pairs (_)
C2,C4: 7.. / C2 = 7  => 14 pairs (_) / C4 = 7  => 10 pairs (_)
B3,C3: 9.. / B3 = 9  =>  9 pairs (_) / C3 = 9  => 11 pairs (_)
A4,C4: 9.. / A4 = 9  => 10 pairs (_) / C4 = 9  => 14 pairs (_)
A4,A9: 9.. / A4 = 9  => 10 pairs (_) / A9 = 9  => 14 pairs (_)
B3,B9: 9.. / B3 = 9  =>  9 pairs (_) / B9 = 9  => 11 pairs (_)
* DURATION: 0:00:07.965727  START: 20:15:27.030903  END: 20:15:34.996630 2025-04-06
* CP COUNT: (24)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:10.394970  START: 20:15:42.303770  END: 20:15:52.698740 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00134025-base-pr-002.dot
* REASONING
* PRF # A4: 2 # G4: 3,8 => SOL
* STA # A4: 2 + G4: 3,8
* CNT   1 HDP CHAINS /  40 HYP OPENED

Header Info

rating: 35495; r2: 735830; index: 134025

Solution

position: 123456789457189263698273415249615837716832954835947621361798542572364198984521376 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 # A4: 7,9 => UNS
* INC # A4: 2 => UNS
* INC # A4: 2,7 => UNS
* INC # A4: 9 => UNS
* INC # B2: 3,5 => UNS
* INC # B8: 3,5 => UNS
* INC # B9: 3,5 => UNS
* INC # C2: 3,5 => UNS
* INC # C9: 3,5 => UNS
* INC # E6: 4,6 => UNS
* INC # E6: 1,2 => UNS
* INC # E6: 2,4 => UNS
* INC # E6: 1,6 => UNS
* INC # E6: 1,4 => UNS
* INC # E6: 2,6 => UNS
* INC # E4: 1,2 => UNS
* INC # E6: 1,2 => UNS
* INC # F4: 1,2 => UNS
* INC # F4: 3,5,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 7,9 => UNS
* INC # A4: 2 => UNS
* INC # A4: 2,7 => UNS
* INC # A4: 9 => UNS
* INC # B2: 3,5 => UNS
* INC # B8: 3,5 => UNS
* INC # B9: 3,5 => UNS
* INC # C2: 3,5 => UNS
* INC # C9: 3,5 => UNS
* INC # E6: 4,6 => UNS
* INC # E6: 1,2 => UNS
* INC # E6: 2,4 => UNS
* INC # E6: 1,6 => UNS
* INC # E6: 1,4 => UNS
* INC # E6: 2,6 => UNS
* INC # E4: 1,2 => UNS
* INC # E6: 1,2 => UNS
* INC # F4: 1,2 => UNS
* INC # F4: 3,5,8 => UNS
* CNT  19 HDP CHAINS /  19 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 7,9 => UNS
* INC # A4: 2 => UNS
* INC # A4: 2,7 => UNS
* INC # A4: 9 => UNS
* INC # B2: 3,5 => UNS
* INC # B8: 3,5 => UNS
* INC # B9: 3,5 => UNS
* INC # C2: 3,5 => UNS
* INC # C9: 3,5 => UNS
* INC # E6: 4,6 => UNS
* INC # E6: 1,2 => UNS
* INC # E6: 2,4 => UNS
* INC # E6: 1,6 => UNS
* INC # E6: 1,4 => UNS
* INC # E6: 2,6 => UNS
* INC # E4: 1,2 => UNS
* INC # E6: 1,2 => UNS
* INC # F4: 1,2 => UNS
* INC # F4: 3,5,8 => UNS
* INC # A4: 7,9 # B2: 3,5 => UNS
* INC # A4: 7,9 # B9: 3,5 => UNS
* INC # A4: 7,9 # C2: 3,5 => UNS
* INC # A4: 7,9 # C9: 3,5 => UNS
* INC # A4: 7,9 # E4: 1,2 => UNS
* INC # A4: 7,9 # E6: 1,2 => UNS
* INC # A4: 7,9 # B7: 6,7 => UNS
* INC # A4: 7,9 # B7: 3,8 => UNS
* INC # A4: 7,9 # B8: 6,7 => UNS
* INC # A4: 7,9 # B8: 3,8 => UNS
* INC # A4: 7,9 # E4: 1,2 => UNS
* INC # A4: 7,9 # E6: 1,2 => UNS
* INC # A4: 7,9 => UNS
* INC # A4: 2 # B2: 3,5 => UNS
* INC # A4: 2 # B9: 3,5 => UNS
* INC # A4: 2 # C9: 3,5 => UNS
* INC # A4: 2 # C9: 4,8 => UNS
* INC # A4: 2 # E8: 4,6 => UNS
* INC # A4: 2 # E8: 3,8 => UNS
* PRF # A4: 2 # G4: 3,8 => SOL
* STA # A4: 2 + G4: 3,8
* CNT  39 HDP CHAINS /  40 HYP OPENED