Analysis of xx-mith-te3-00104565-base.sdk

Contents

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

Original Sudoku

level: hard

position: ....56.8..5.18...6.8.7.2.15.74......36.......8.5.17...5.2.618.........21...27.65. initial

Autosolve

position: ....56.8..5.18...6.8.7.2.15.74......36.......8.5.17...5.2.618.........21..827.65. 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: 0:00:07.775168

The following important HDP chains were detected:

* DIS # A4: 2 # C2: 3,9 => CTR => C2: 7
* PRF # A4: 2 + C2: 7 # I1: 3,9 => SOL
* STA # A4: 2 + C2: 7 + I1: 3,9
* CNT   2 HDP CHAINS /  31 HYP OPENED

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

Details

Positions

`....56.8..5.18...6.8.7.2.15.74......36.......8.5.17...5.2.618.........21...27.65.`	initial
`....56.8..5.18...6.8.7.2.15.74......36.......8.5.17...5.2.618.........21..827.65.`	autosolve
`123456789457189236689732415274395168361824597895617342542961873736548921918273654`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (8)
C5: 1,9
B6: 2,9
G4: 1,5
G5: 1,5
A8: 6,7
C8: 6,7
D8: 5,8
F8: 5,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,C5: 1.. / A4 = 1  => 14 pairs (_) / C5 = 1  =>  7 pairs (_)
G4,G5: 1.. / G4 = 1  =>  7 pairs (_) / G5 = 1  => 14 pairs (_)
A9,B9: 1.. / A9 = 1  => 12 pairs (_) / B9 = 1  =>  9 pairs (_)
A4,G4: 1.. / A4 = 1  => 14 pairs (_) / G4 = 1  =>  7 pairs (_)
C5,G5: 1.. / C5 = 1  =>  7 pairs (_) / G5 = 1  => 14 pairs (_)
B1,B9: 1.. / B1 = 1  => 12 pairs (_) / B9 = 1  =>  9 pairs (_)
C1,C5: 1.. / C1 = 1  => 14 pairs (_) / C5 = 1  =>  7 pairs (_)
A4,B6: 2.. / A4 = 2  => 13 pairs (_) / B6 = 2  => 12 pairs (_)
E4,E5: 2.. / E4 = 2  => 11 pairs (_) / E5 = 2  =>  9 pairs (_)
A2,G2: 2.. / A2 = 2  => 11 pairs (_) / G2 = 2  =>  8 pairs (_)
E5,I5: 2.. / E5 = 2  =>  9 pairs (_) / I5 = 2  => 11 pairs (_)
B1,B6: 2.. / B1 = 2  => 13 pairs (_) / B6 = 2  => 12 pairs (_)
G4,G5: 5.. / G4 = 5  => 14 pairs (_) / G5 = 5  =>  7 pairs (_)
D8,F8: 5.. / D8 = 5  =>  6 pairs (_) / F8 = 5  =>  6 pairs (_)
A3,C3: 6.. / A3 = 6  =>  7 pairs (_) / C3 = 6  => 10 pairs (_)
D4,D6: 6.. / D4 = 6  => 10 pairs (_) / D6 = 6  =>  9 pairs (_)
H4,H6: 6.. / H4 = 6  =>  9 pairs (_) / H6 = 6  => 10 pairs (_)
A8,C8: 6.. / A8 = 6  => 10 pairs (_) / C8 = 6  =>  7 pairs (_)
D4,H4: 6.. / D4 = 6  => 10 pairs (_) / H4 = 6  =>  9 pairs (_)
D6,H6: 6.. / D6 = 6  =>  9 pairs (_) / H6 = 6  => 10 pairs (_)
A3,A8: 6.. / A3 = 6  =>  7 pairs (_) / A8 = 6  => 10 pairs (_)
C3,C8: 6.. / C3 = 6  => 10 pairs (_) / C8 = 6  =>  7 pairs (_)
G1,G2: 7.. / G1 = 7  =>  8 pairs (_) / G2 = 7  => 11 pairs (_)
H5,I5: 7.. / H5 = 7  =>  8 pairs (_) / I5 = 7  => 15 pairs (_)
A8,C8: 7.. / A8 = 7  =>  7 pairs (_) / C8 = 7  => 10 pairs (_)
H7,I7: 7.. / H7 = 7  => 15 pairs (_) / I7 = 7  =>  8 pairs (_)
H5,H7: 7.. / H5 = 7  =>  8 pairs (_) / H7 = 7  => 15 pairs (_)
I5,I7: 7.. / I5 = 7  => 15 pairs (_) / I7 = 7  =>  8 pairs (_)
I4,I5: 8.. / I4 = 8  =>  8 pairs (_) / I5 = 8  =>  9 pairs (_)
D8,F8: 8.. / D8 = 8  =>  6 pairs (_) / F8 = 8  =>  6 pairs (_)
* DURATION: 0:00:10.072182  START: 16:50:00.461710  END: 16:50:10.533892 2025-04-06
* CP COUNT: (30)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:07.633067  START: 16:50:15.729320  END: 16:50:23.362387 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00104565-base-pr-002.dot
* REASONING
* DIS # A4: 2 # C2: 3,9 => CTR => C2: 7
* PRF # A4: 2 + C2: 7 # I1: 3,9 => SOL
* STA # A4: 2 + C2: 7 + I1: 3,9
* CNT   2 HDP CHAINS /  31 HYP OPENED

Header Info

rating: 26239; r2: 531217; index: 104565

Solution

position: 123456789457189236689732415274395168361824597895617342542961873736548921918273654 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: 1,9 => UNS
* INC # A4: 2 => UNS
* INC # C1: 1,9 => UNS
* INC # C1: 3,7 => UNS
* INC # A4: 2,9 => UNS
* INC # A4: 1 => UNS
* INC # G6: 2,9 => UNS
* INC # I6: 2,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 1,4 => UNS
* INC # D4: 5,8 => UNS
* INC # D5: 5,8 => UNS
* INC # F4: 5,8 => UNS
* INC # F5: 5,8 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 1,9 => UNS
* INC # A4: 2 => UNS
* INC # C1: 1,9 => UNS
* INC # C1: 3,7 => UNS
* INC # A4: 2,9 => UNS
* INC # A4: 1 => UNS
* INC # G6: 2,9 => UNS
* INC # I6: 2,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 1,4 => UNS
* INC # D4: 5,8 => UNS
* INC # D5: 5,8 => UNS
* INC # F4: 5,8 => UNS
* INC # F5: 5,8 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A4: 1,9 => UNS
* INC # A4: 2 => UNS
* INC # C1: 1,9 => UNS
* INC # C1: 3,7 => UNS
* INC # A4: 2,9 => UNS
* INC # A4: 1 => UNS
* INC # G6: 2,9 => UNS
* INC # I6: 2,9 => UNS
* INC # B1: 2,9 => UNS
* INC # B1: 1,4 => UNS
* INC # D4: 5,8 => UNS
* INC # D5: 5,8 => UNS
* INC # F4: 5,8 => UNS
* INC # F5: 5,8 => UNS
* INC # A4: 1,9 # A1: 2,7 => UNS
* INC # A4: 1,9 # A1: 1,4,9 => UNS
* INC # A4: 1,9 # A2: 2,7 => UNS
* INC # A4: 1,9 # A2: 4,9 => UNS
* INC # A4: 1,9 # A1: 1,9 => UNS
* INC # A4: 1,9 # A9: 1,9 => UNS
* INC # A4: 1,9 # C1: 1,9 => UNS
* INC # A4: 1,9 # C1: 3,7 => UNS
* INC # A4: 1,9 # D4: 5,8 => UNS
* INC # A4: 1,9 # D5: 5,8 => UNS
* INC # A4: 1,9 # F4: 5,8 => UNS
* INC # A4: 1,9 # F5: 5,8 => UNS
* INC # A4: 1,9 => UNS
* DIS # A4: 2 # C2: 3,9 => CTR => C2: 7
* INC # A4: 2 + C2: 7 # D1: 3,9 => UNS
* PRF # A4: 2 + C2: 7 # I1: 3,9 => SOL
* STA # A4: 2 + C2: 7 + I1: 3,9
* CNT  30 HDP CHAINS /  31 HYP OPENED