Analysis of xx-mith-te3-00048306-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1.3.567....718....8..7.3....81....75.3.......7.68....1...5..697675.....3......54. initial

Autosolve

position: 1.3.567....718....8..7.3....81....7553.......7.68.5..1...5..697675.....3......54. 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: 0:00:12.328553

The following important HDP chains were detected:

* DIS # H2: 2,3 # G2: 4,9 => CTR => G2: 2,3
* PRF # H2: 2,3 + G2: 2,3 # E4: 2,4,9 => SOL
* STA # H2: 2,3 + G2: 2,3 + E4: 2,4,9
* CNT   2 HDP CHAINS /  58 HYP OPENED

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

Details

Positions

`1.3.567....718....8..7.3....81....75.3.......7.68....1...5..697675.....3......54.`	initial
`1.3.567....718....8..7.3....81....7553.......7.68.5..1...5..697675.....3......54.`	autosolve
`123456789457189236869723154281694375534271968796835421342518697675942813918367542`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B2: 5,6
B3: 5,6
H1: 2,8
D4: 3,6
E5: 1,7
F5: 1,7
H6: 2,3
D9: 3,6
I9: 2,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,H3: 1.. / G3 = 1  => 10 pairs (_) / H3 = 1  =>  9 pairs (_)
E5,F5: 1.. / E5 = 1  =>  6 pairs (_) / F5 = 1  =>  9 pairs (_)
B7,B9: 1.. / B7 = 1  => 12 pairs (_) / B9 = 1  => 10 pairs (_)
G8,H8: 1.. / G8 = 1  =>  9 pairs (_) / H8 = 1  => 10 pairs (_)
G3,G8: 1.. / G3 = 1  => 10 pairs (_) / G8 = 1  =>  9 pairs (_)
H3,H8: 1.. / H3 = 1  =>  9 pairs (_) / H8 = 1  => 10 pairs (_)
G2,H2: 3.. / G2 = 3  => 10 pairs (_) / H2 = 3  =>  7 pairs (_)
A7,A9: 3.. / A7 = 3  => 11 pairs (_) / A9 = 3  =>  9 pairs (_)
A7,E7: 3.. / A7 = 3  => 11 pairs (_) / E7 = 3  =>  9 pairs (_)
D4,D9: 3.. / D4 = 3  =>  8 pairs (_) / D9 = 3  =>  8 pairs (_)
H2,H6: 3.. / H2 = 3  =>  7 pairs (_) / H6 = 3  => 10 pairs (_)
B2,B3: 5.. / B2 = 5  =>  8 pairs (_) / B3 = 5  =>  8 pairs (_)
H2,H3: 5.. / H2 = 5  =>  8 pairs (_) / H3 = 5  =>  8 pairs (_)
B2,H2: 5.. / B2 = 5  =>  8 pairs (_) / H2 = 5  =>  8 pairs (_)
B3,H3: 5.. / B3 = 5  =>  8 pairs (_) / H3 = 5  =>  8 pairs (_)
B2,B3: 6.. / B2 = 6  =>  8 pairs (_) / B3 = 6  =>  8 pairs (_)
D4,E4: 6.. / D4 = 6  =>  8 pairs (_) / E4 = 6  =>  8 pairs (_)
H5,I5: 6.. / H5 = 6  =>  9 pairs (_) / I5 = 6  => 14 pairs (_)
D9,E9: 6.. / D9 = 6  =>  8 pairs (_) / E9 = 6  =>  8 pairs (_)
D4,D9: 6.. / D4 = 6  =>  8 pairs (_) / D9 = 6  =>  8 pairs (_)
E4,E9: 6.. / E4 = 6  =>  8 pairs (_) / E9 = 6  =>  8 pairs (_)
E5,F5: 7.. / E5 = 7  =>  9 pairs (_) / F5 = 7  =>  6 pairs (_)
E9,F9: 7.. / E9 = 7  =>  6 pairs (_) / F9 = 7  =>  9 pairs (_)
E5,E9: 7.. / E5 = 7  =>  9 pairs (_) / E9 = 7  =>  6 pairs (_)
F5,F9: 7.. / F5 = 7  =>  6 pairs (_) / F9 = 7  =>  9 pairs (_)
H1,I1: 8.. / H1 = 8  => 10 pairs (_) / I1 = 8  => 19 pairs (_)
C7,C9: 8.. / C7 = 8  => 11 pairs (_) / C9 = 8  => 15 pairs (_)
C7,F7: 8.. / C7 = 8  => 11 pairs (_) / F7 = 8  => 15 pairs (_)
G5,G8: 8.. / G5 = 8  => 11 pairs (_) / G8 = 8  => 16 pairs (_)
* DURATION: 0:00:09.476955  START: 15:09:56.223499  END: 15:10:05.700454 2025-04-04
* CP COUNT: (29)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:12.148670  START: 15:10:15.756948  END: 15:10:27.905618 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00048306-base-pr-002.dot
* REASONING
* DIS # H2: 2,3 # G2: 4,9 => CTR => G2: 2,3
* PRF # H2: 2,3 + G2: 2,3 # E4: 2,4,9 => SOL
* STA # H2: 2,3 + G2: 2,3 + E4: 2,4,9
* CNT   2 HDP CHAINS /  58 HYP OPENED

Header Info

rating: 10012; r2: 369419; index: 48306

Solution

position: 123456789457189236869723154281694375534271968796835421342518697675942813918367542 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 # H2: 5,6 => UNS
* INC # H2: 2,3 => UNS
* INC # H3: 5,6 => UNS
* INC # H3: 1,2 => UNS
* INC # I1: 2,8 => UNS
* INC # I1: 4,9 => UNS
* INC # H5: 2,8 => UNS
* INC # H8: 2,8 => UNS
* INC # E4: 3,6 => UNS
* INC # E4: 2,4,9 => UNS
* INC # E9: 1,7 => UNS
* INC # E9: 2,3,6 => UNS
* INC # F9: 1,7 => UNS
* INC # F9: 2,8 => UNS
* INC # G4: 2,3 => UNS
* INC # G6: 2,3 => UNS
* INC # E6: 2,3 => UNS
* INC # E6: 4,9 => UNS
* INC # H2: 2,3 => UNS
* INC # H2: 5,6 => UNS
* INC # E9: 3,6 => UNS
* INC # E9: 1,2,7 => UNS
* INC # G8: 2,8 => UNS
* INC # H8: 2,8 => UNS
* INC # C9: 2,8 => UNS
* INC # F9: 2,8 => UNS
* INC # I1: 2,8 => UNS
* INC # I5: 2,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 5,6 => UNS
* INC # H2: 2,3 => UNS
* INC # H3: 5,6 => UNS
* INC # H3: 1,2 => UNS
* INC # I1: 2,8 => UNS
* INC # I1: 4,9 => UNS
* INC # H5: 2,8 => UNS
* INC # H8: 2,8 => UNS
* INC # E4: 3,6 => UNS
* INC # E4: 2,4,9 => UNS
* INC # E9: 1,7 => UNS
* INC # E9: 2,3,6 => UNS
* INC # F9: 1,7 => UNS
* INC # F9: 2,8 => UNS
* INC # G4: 2,3 => UNS
* INC # G6: 2,3 => UNS
* INC # E6: 2,3 => UNS
* INC # E6: 4,9 => UNS
* INC # H2: 2,3 => UNS
* INC # H2: 5,6 => UNS
* INC # E9: 3,6 => UNS
* INC # E9: 1,2,7 => UNS
* INC # G8: 2,8 => UNS
* INC # H8: 2,8 => UNS
* INC # C9: 2,8 => UNS
* INC # F9: 2,8 => UNS
* INC # I1: 2,8 => UNS
* INC # I5: 2,8 => UNS
* CNT  28 HDP CHAINS /  28 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H2: 5,6 => UNS
* INC # H2: 2,3 => UNS
* INC # H3: 5,6 => UNS
* INC # H3: 1,2 => UNS
* INC # I1: 2,8 => UNS
* INC # I1: 4,9 => UNS
* INC # H5: 2,8 => UNS
* INC # H8: 2,8 => UNS
* INC # E4: 3,6 => UNS
* INC # E4: 2,4,9 => UNS
* INC # E9: 1,7 => UNS
* INC # E9: 2,3,6 => UNS
* INC # F9: 1,7 => UNS
* INC # F9: 2,8 => UNS
* INC # G4: 2,3 => UNS
* INC # G6: 2,3 => UNS
* INC # E6: 2,3 => UNS
* INC # E6: 4,9 => UNS
* INC # H2: 2,3 => UNS
* INC # H2: 5,6 => UNS
* INC # E9: 3,6 => UNS
* INC # E9: 1,2,7 => UNS
* INC # G8: 2,8 => UNS
* INC # H8: 2,8 => UNS
* INC # C9: 2,8 => UNS
* INC # F9: 2,8 => UNS
* INC # I1: 2,8 => UNS
* INC # I5: 2,8 => UNS
* INC # H2: 5,6 # H3: 5,6 => UNS
* INC # H2: 5,6 # H3: 1,2 => UNS
* INC # H2: 5,6 # I1: 2,8 => UNS
* INC # H2: 5,6 # I1: 4,9 => UNS
* INC # H2: 5,6 # H5: 2,8 => UNS
* INC # H2: 5,6 # H8: 2,8 => UNS
* INC # H2: 5,6 # H3: 5,6 => UNS
* INC # H2: 5,6 # H3: 1,2 => UNS
* INC # H2: 5,6 # E9: 3,6 => UNS
* INC # H2: 5,6 # E9: 1,7 => UNS
* INC # H2: 5,6 # E9: 1,7 => UNS
* INC # H2: 5,6 # E9: 3,6 => UNS
* INC # H2: 5,6 # F9: 1,7 => UNS
* INC # H2: 5,6 # F9: 2,8 => UNS
* INC # H2: 5,6 # E9: 1,3 => UNS
* INC # H2: 5,6 # E9: 6,7 => UNS
* INC # H2: 5,6 # E9: 3,6 => UNS
* INC # H2: 5,6 # E9: 1,7 => UNS
* INC # H2: 5,6 # G8: 2,8 => UNS
* INC # H2: 5,6 # H8: 2,8 => UNS
* INC # H2: 5,6 # C9: 2,8 => UNS
* INC # H2: 5,6 # F9: 2,8 => UNS
* INC # H2: 5,6 # I1: 2,8 => UNS
* INC # H2: 5,6 # I5: 2,8 => UNS
* INC # H2: 5,6 => UNS
* INC # H2: 2,3 # G2: 2,3 => UNS
* DIS # H2: 2,3 # G2: 4,9 => CTR => G2: 2,3
* INC # H2: 2,3 + G2: 2,3 # E4: 3,6 => UNS
* PRF # H2: 2,3 + G2: 2,3 # E4: 2,4,9 => SOL
* STA # H2: 2,3 + G2: 2,3 + E4: 2,4,9
* CNT  57 HDP CHAINS /  58 HYP OPENED