Analysis of xx-mith-te3-00081398-base.sdk

Contents

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

Original Sudoku

level: hard

position: .2.4.........89.2....21.6..2.4.7.3.567..3.24.........73.75..4..54.3...7..62...53. initial

Autosolve

position: .2.45........89.2....21.65.2.4.7.3.567..3524.........73.75..4..54.3...7..62...53. 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: 0:00:16.435763

The following important HDP chains were detected:

* DIS # F1: 6,7 # H6: 8,9 => CTR => H6: 1,6
* PRF # F1: 6,7 + H6: 1,6 # I9: 1 => SOL
* STA # F1: 6,7 + H6: 1,6 + I9: 1
* CNT   2 HDP CHAINS /  44 HYP OPENED

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

Details

Positions

`.2.4.........89.2....21.6..2.4.7.3.567..3.24.........73.75..4..54.3...7..62...53.`	initial
`.2.45........89.2....21.65.2.4.7.3.567..3524.........73.75..4..54.3...7..62...53.`	autosolve
`123456789456789123798213654214978365679135248835624917387561492541392876962847531`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
D2: 6,7
F3: 3,7
G2: 1,7
B6: 3,5
C6: 3,5
E6: 2,4
F6: 2,4
E9: 4,9
I7: 2,6
I8: 2,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
E6,F6: 2.. / E6 = 2  =>  9 pairs (_) / F6 = 2  => 13 pairs (_)
I7,I8: 2.. / I7 = 2  => 10 pairs (_) / I8 = 2  => 10 pairs (_)
F1,F3: 3.. / F1 = 3  => 11 pairs (_) / F3 = 3  => 18 pairs (_)
B6,C6: 3.. / B6 = 3  =>  9 pairs (_) / C6 = 3  => 10 pairs (_)
A2,A3: 4.. / A2 = 4  => 12 pairs (_) / A3 = 4  => 16 pairs (_)
I2,I3: 4.. / I2 = 4  => 16 pairs (_) / I3 = 4  => 12 pairs (_)
E6,F6: 4.. / E6 = 4  => 13 pairs (_) / F6 = 4  =>  9 pairs (_)
E9,F9: 4.. / E9 = 4  =>  9 pairs (_) / F9 = 4  => 13 pairs (_)
A2,I2: 4.. / A2 = 4  => 12 pairs (_) / I2 = 4  => 16 pairs (_)
A3,I3: 4.. / A3 = 4  => 16 pairs (_) / I3 = 4  => 12 pairs (_)
E6,E9: 4.. / E6 = 4  => 13 pairs (_) / E9 = 4  =>  9 pairs (_)
F6,F9: 4.. / F6 = 4  =>  9 pairs (_) / F9 = 4  => 13 pairs (_)
B2,C2: 5.. / B2 = 5  =>  9 pairs (_) / C2 = 5  => 10 pairs (_)
B6,C6: 5.. / B6 = 5  => 10 pairs (_) / C6 = 5  =>  9 pairs (_)
B2,B6: 5.. / B2 = 5  =>  9 pairs (_) / B6 = 5  => 10 pairs (_)
C2,C6: 5.. / C2 = 5  => 10 pairs (_) / C6 = 5  =>  9 pairs (_)
C1,C2: 6.. / C1 = 6  => 10 pairs (_) / C2 = 6  => 16 pairs (_)
F1,D2: 6.. / F1 = 6  => 16 pairs (_) / D2 = 6  => 10 pairs (_)
H4,H6: 6.. / H4 = 6  =>  0 pairs (*) / H6 = 6  =>  0 pairs (X)
E7,E8: 6.. / E7 = 6  => 10 pairs (_) / E8 = 6  => 10 pairs (_)
I7,I8: 6.. / I7 = 6  => 10 pairs (_) / I8 = 6  => 10 pairs (_)
C1,F1: 6.. / C1 = 6  => 10 pairs (_) / F1 = 6  => 16 pairs (_)
C2,D2: 6.. / C2 = 6  => 16 pairs (_) / D2 = 6  => 10 pairs (_)
D6,H6: 6.. / D6 = 6  =>  0 pairs (*) / H6 = 6  =>  0 pairs (X)
E7,I7: 6.. / E7 = 6  => 10 pairs (_) / I7 = 6  => 10 pairs (_)
E8,I8: 6.. / E8 = 6  => 10 pairs (_) / I8 = 6  => 10 pairs (_)
F1,F4: 6.. / F1 = 6  => 16 pairs (_) / F4 = 6  => 10 pairs (_)
G1,G2: 7.. / G1 = 7  => 18 pairs (_) / G2 = 7  => 10 pairs (_)
D9,F9: 7.. / D9 = 7  => 10 pairs (_) / F9 = 7  => 16 pairs (_)
A3,F3: 7.. / A3 = 7  => 18 pairs (_) / F3 = 7  => 11 pairs (_)
D2,D9: 7.. / D2 = 7  => 16 pairs (_) / D9 = 7  => 10 pairs (_)
* DURATION: 0:00:11.387929  START: 11:33:19.557486  END: 11:33:30.945415 2025-04-06
* CP COUNT: (31)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:16.284626  START: 11:33:37.574998  END: 11:33:53.859624 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00081398-base-pr-002.dot
* REASONING
* DIS # F1: 6,7 # H6: 8,9 => CTR => H6: 1,6
* PRF # F1: 6,7 + H6: 1,6 # I9: 1 => SOL
* STA # F1: 6,7 + H6: 1,6 + I9: 1
* CNT   2 HDP CHAINS /  44 HYP OPENED

Header Info

rating: 19636; r2: 843820; index: 81398

Solution

position: 123456789456789123798213654214978365679135248835624917387561492541392876962847531 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 # F1: 6,7 => UNS
* INC # F1: 3 => UNS
* INC # F1: 3,7 => UNS
* INC # F1: 6 => UNS
* INC # G1: 1,7 => UNS
* INC # G1: 8,9 => UNS
* INC # A2: 1,7 => UNS
* INC # A2: 4 => UNS
* INC # B2: 3,5 => UNS
* INC # B2: 1 => UNS
* INC # C2: 3,5 => UNS
* INC # C2: 1,6 => UNS
* INC # E7: 2,6 => UNS
* INC # E7: 9 => UNS
* INC # E8: 2,6 => UNS
* INC # E8: 9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 6,7 => UNS
* INC # F1: 3 => UNS
* INC # F1: 3,7 => UNS
* INC # F1: 6 => UNS
* INC # G1: 1,7 => UNS
* INC # G1: 8,9 => UNS
* INC # A2: 1,7 => UNS
* INC # A2: 4 => UNS
* INC # B2: 3,5 => UNS
* INC # B2: 1 => UNS
* INC # C2: 3,5 => UNS
* INC # C2: 1,6 => UNS
* INC # E7: 2,6 => UNS
* INC # E7: 9 => UNS
* INC # E8: 2,6 => UNS
* INC # E8: 9 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F1: 6,7 => UNS
* INC # F1: 3 => UNS
* INC # F1: 3,7 => UNS
* INC # F1: 6 => UNS
* INC # G1: 1,7 => UNS
* INC # G1: 8,9 => UNS
* INC # A2: 1,7 => UNS
* INC # A2: 4 => UNS
* INC # B2: 3,5 => UNS
* INC # B2: 1 => UNS
* INC # C2: 3,5 => UNS
* INC # C2: 1,6 => UNS
* INC # E7: 2,6 => UNS
* INC # E7: 9 => UNS
* INC # E8: 2,6 => UNS
* INC # E8: 9 => UNS
* INC # F1: 6,7 # C2: 3,6 => UNS
* INC # F1: 6,7 # C2: 5 => UNS
* INC # F1: 6,7 # C2: 3,5 => UNS
* INC # F1: 6,7 # C2: 6 => UNS
* INC # F1: 6,7 # B4: 8,9 => UNS
* INC # F1: 6,7 # B7: 8,9 => UNS
* INC # F1: 6,7 # C5: 8,9 => UNS
* INC # F1: 6,7 # C8: 8,9 => UNS
* INC # F1: 6,7 # G1: 8,9 => UNS
* INC # F1: 6,7 # I1: 8,9 => UNS
* INC # F1: 6,7 # H4: 8,9 => UNS
* DIS # F1: 6,7 # H6: 8,9 => CTR => H6: 1,6
* INC # F1: 6,7 + H6: 1,6 # H7: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # G1: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # I1: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # H4: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # H7: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # B4: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # C5: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # D6: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # G6: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # C2: 3,5 => UNS
* INC # F1: 6,7 + H6: 1,6 # C2: 6 => UNS
* INC # F1: 6,7 + H6: 1,6 # B7: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # C8: 8,9 => UNS
* INC # F1: 6,7 + H6: 1,6 # I9: 8,9 => UNS
* PRF # F1: 6,7 + H6: 1,6 # I9: 1 => SOL
* STA # F1: 6,7 + H6: 1,6 + I9: 1
* CNT  43 HDP CHAINS /  44 HYP OPENED