Analysis of xx-mith-te3-00112710-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12..5..89........69.6....5.2..8.5.......47.21....23..5.92...5.856.2..91.8.15...62 initial

Autosolve

position: 12..5..89........69.6....5.2..8.5.......47.21....23..5.92...5.856.2..91.8.15...62 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: 0:00:04.214712

The following important HDP chains were detected:

* PRF # D1: 4,6 # C2: 3,7 => SOL
* STA # D1: 4,6 + C2: 3,7
* CNT   1 HDP CHAINS /  20 HYP OPENED

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

Details

Positions

`12..5..89........69.6....5.2..8.5.......47.21....23..5.92...5.856.2..91.8.15...62`	initial
`12..5..89........69.6....5.2..8.5.......47.21....23..5.92...5.856.2..91.8.15...62`	autosolve
`123456789457189236986372154249815673635947821718623495392761548564238917871594362`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
F1: 4,6
G2: 1,2
G3: 1,2
A5: 3,6
D5: 6,9
F8: 4,8
F9: 4,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G2,G3: 1.. / G2 = 1  =>  5 pairs (_) / G3 = 1  =>  5 pairs (_)
B4,B6: 1.. / B4 = 1  =>  8 pairs (_) / B6 = 1  =>  9 pairs (_)
E4,D6: 1.. / E4 = 1  =>  9 pairs (_) / D6 = 1  =>  8 pairs (_)
B4,E4: 1.. / B4 = 1  =>  8 pairs (_) / E4 = 1  =>  9 pairs (_)
B6,D6: 1.. / B6 = 1  =>  9 pairs (_) / D6 = 1  =>  8 pairs (_)
F2,F3: 2.. / F2 = 2  =>  5 pairs (_) / F3 = 2  =>  5 pairs (_)
G2,G3: 2.. / G2 = 2  =>  5 pairs (_) / G3 = 2  =>  5 pairs (_)
F2,G2: 2.. / F2 = 2  =>  5 pairs (_) / G2 = 2  =>  5 pairs (_)
F3,G3: 2.. / F3 = 2  =>  5 pairs (_) / G3 = 2  =>  5 pairs (_)
B2,C2: 5.. / B2 = 5  =>  9 pairs (_) / C2 = 5  =>  7 pairs (_)
B5,C5: 5.. / B5 = 5  =>  7 pairs (_) / C5 = 5  =>  9 pairs (_)
B2,B5: 5.. / B2 = 5  =>  9 pairs (_) / B5 = 5  =>  7 pairs (_)
C2,C5: 5.. / C2 = 5  =>  7 pairs (_) / C5 = 5  =>  9 pairs (_)
D1,F1: 6.. / D1 = 6  => 17 pairs (_) / F1 = 6  =>  7 pairs (_)
A5,A6: 6.. / A5 = 6  =>  9 pairs (_) / A6 = 6  => 11 pairs (_)
E4,G4: 6.. / E4 = 6  => 13 pairs (_) / G4 = 6  =>  9 pairs (_)
E4,E7: 6.. / E4 = 6  => 13 pairs (_) / E7 = 6  =>  9 pairs (_)
F1,F7: 6.. / F1 = 6  =>  7 pairs (_) / F7 = 6  => 17 pairs (_)
G5,G6: 8.. / G5 = 8  =>  8 pairs (_) / G6 = 8  => 12 pairs (_)
E8,F8: 8.. / E8 = 8  =>  9 pairs (_) / F8 = 8  =>  7 pairs (_)
H4,H6: 9.. / H4 = 9  => 11 pairs (_) / H6 = 9  =>  8 pairs (_)
E9,F9: 9.. / E9 = 9  =>  6 pairs (_) / F9 = 9  =>  7 pairs (_)
C5,D5: 9.. / C5 = 9  => 11 pairs (_) / D5 = 9  =>  8 pairs (_)
F2,F9: 9.. / F2 = 9  =>  6 pairs (_) / F9 = 9  =>  7 pairs (_)
* DURATION: 0:00:05.806931  START: 17:29:52.945666  END: 17:29:58.752597 2025-04-06
* CP COUNT: (24)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:04.087836  START: 17:30:03.371898  END: 17:30:07.459734 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00112710-base-pr-002.dot
* REASONING
* PRF # D1: 4,6 # C2: 3,7 => SOL
* STA # D1: 4,6 + C2: 3,7
* CNT   1 HDP CHAINS /  20 HYP OPENED

Header Info

rating: 28757; r2: 555460; index: 112710

Solution

position: 123456789457189236986372154249815673635947821718623495392761548564238917871594362 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 # D1: 4,6 => UNS
* INC # D1: 3,7 => UNS
* INC # F7: 4,6 => UNS
* INC # F7: 1 => UNS
* INC # F2: 1,2 => UNS
* INC # F2: 4,8,9 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 4,8 => UNS
* INC # G5: 3,6 => UNS
* INC # G5: 8 => UNS
* INC # E4: 6,9 => UNS
* INC # D6: 6,9 => UNS
* INC # F2: 4,8 => UNS
* INC # F3: 4,8 => UNS
* INC # F2: 4,9 => UNS
* INC # F2: 1,2,8 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 4,6 => UNS
* INC # D1: 3,7 => UNS
* INC # F7: 4,6 => UNS
* INC # F7: 1 => UNS
* INC # F2: 1,2 => UNS
* INC # F2: 4,8,9 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 4,8 => UNS
* INC # G5: 3,6 => UNS
* INC # G5: 8 => UNS
* INC # E4: 6,9 => UNS
* INC # D6: 6,9 => UNS
* INC # F2: 4,8 => UNS
* INC # F3: 4,8 => UNS
* INC # F2: 4,9 => UNS
* INC # F2: 1,2,8 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 4,6 => UNS
* INC # D1: 3,7 => UNS
* INC # F7: 4,6 => UNS
* INC # F7: 1 => UNS
* INC # F2: 1,2 => UNS
* INC # F2: 4,8,9 => UNS
* INC # F3: 1,2 => UNS
* INC # F3: 4,8 => UNS
* INC # G5: 3,6 => UNS
* INC # G5: 8 => UNS
* INC # E4: 6,9 => UNS
* INC # D6: 6,9 => UNS
* INC # F2: 4,8 => UNS
* INC # F3: 4,8 => UNS
* INC # F2: 4,9 => UNS
* INC # F2: 1,2,8 => UNS
* INC # D1: 4,6 # A2: 3,7 => UNS
* INC # D1: 4,6 # B2: 3,7 => UNS
* PRF # D1: 4,6 # C2: 3,7 => SOL
* STA # D1: 4,6 + C2: 3,7
* CNT  19 HDP CHAINS /  20 HYP OPENED