Analysis of xx-mith-te3-00146664-base.sdk

Contents

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

Original Sudoku

level: hard

position: 1.....7.....189.36.......51.1..98....346.19..9.8..........64....6.8.3..484.91...3 initial

Autosolve

position: 1.....7.....189.36.......51.1..9834..346.19..9.8..........64....6.8.3..484.91...3 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: 0:00:17.288727

The following important HDP chains were detected:

* DIS # I1: 2,8 # E1: 5 => CTR => E1: 3,4
* DIS # A3: 3,6 # C4: 5,7 => CTR => C4: 2,6
* PRF # A3: 3,6 + C4: 2,6 # C7: 5,7 => SOL
* STA # A3: 3,6 + C4: 2,6 + C7: 5,7
* CNT   3 HDP CHAINS /  69 HYP OPENED

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

Details

Positions

`1.....7.....189.36.......51.1..98....346.19..9.8..........64....6.8.3..484.91...3`	initial
`1.....7.....189.36.......51.1..9834..346.19..9.8..........64....6.8.3..484.91...3`	autosolve
`123456789457189236689237451216598347534671928978342165395764812761823594842915673`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
B1: 2,8
C1: 3,6
B3: 8,9
F1: 5,6
G2: 2,4
G3: 4,8
D6: 3,4
E6: 3,4
G6: 1,6
H6: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G6,H6: 1.. / G6 = 1  => 12 pairs (_) / H6 = 1  =>  9 pairs (_)
C7,C8: 1.. / C7 = 1  => 11 pairs (_) / C8 = 1  => 12 pairs (_)
D6,E6: 3.. / D6 = 3  => 10 pairs (_) / E6 = 3  => 10 pairs (_)
A7,C7: 3.. / A7 = 3  => 11 pairs (_) / C7 = 3  =>  0 pairs (X)
A3,A7: 3.. / A3 = 3  =>  0 pairs (X) / A7 = 3  => 11 pairs (_)
A2,A3: 4.. / A2 = 4  => 14 pairs (_) / A3 = 4  => 12 pairs (_)
D1,E1: 4.. / D1 = 4  => 10 pairs (_) / E1 = 4  => 10 pairs (_)
G2,G3: 4.. / G2 = 4  => 12 pairs (_) / G3 = 4  => 14 pairs (_)
D6,E6: 4.. / D6 = 4  => 10 pairs (_) / E6 = 4  => 10 pairs (_)
A2,G2: 4.. / A2 = 4  => 14 pairs (_) / G2 = 4  => 12 pairs (_)
A3,G3: 4.. / A3 = 4  => 12 pairs (_) / G3 = 4  => 14 pairs (_)
D1,D6: 4.. / D1 = 4  => 10 pairs (_) / D6 = 4  => 10 pairs (_)
E1,E6: 4.. / E1 = 4  => 10 pairs (_) / E6 = 4  => 10 pairs (_)
F1,F3: 6.. / F1 = 6  => 13 pairs (_) / F3 = 6  => 17 pairs (_)
A4,C4: 6.. / A4 = 6  => 12 pairs (_) / C4 = 6  => 15 pairs (_)
G6,H6: 6.. / G6 = 6  =>  9 pairs (_) / H6 = 6  => 12 pairs (_)
G9,H9: 6.. / G9 = 6  => 12 pairs (_) / H9 = 6  =>  9 pairs (_)
C1,F1: 6.. / C1 = 6  => 17 pairs (_) / F1 = 6  => 13 pairs (_)
A3,A4: 6.. / A3 = 6  => 15 pairs (_) / A4 = 6  => 12 pairs (_)
G6,G9: 6.. / G6 = 6  =>  9 pairs (_) / G9 = 6  => 12 pairs (_)
H6,H9: 6.. / H6 = 6  => 12 pairs (_) / H9 = 6  =>  9 pairs (_)
B1,B3: 8.. / B1 = 8  => 12 pairs (_) / B3 = 8  => 14 pairs (_)
H5,I5: 8.. / H5 = 8  => 13 pairs (_) / I5 = 8  => 12 pairs (_)
B3,G3: 8.. / B3 = 8  => 14 pairs (_) / G3 = 8  => 12 pairs (_)
G3,G7: 8.. / G3 = 8  => 12 pairs (_) / G7 = 8  => 14 pairs (_)
B3,C3: 9.. / B3 = 9  => 12 pairs (_) / C3 = 9  => 14 pairs (_)
H1,I1: 9.. / H1 = 9  => 14 pairs (_) / I1 = 9  => 11 pairs (_)
C8,H8: 9.. / C8 = 9  => 15 pairs (_) / H8 = 9  => 11 pairs (_)
B3,B7: 9.. / B3 = 9  => 12 pairs (_) / B7 = 9  => 14 pairs (_)
I1,I7: 9.. / I1 = 9  => 11 pairs (_) / I7 = 9  => 14 pairs (_)
* DURATION: 0:00:11.338081  START: 14:08:29.741968  END: 14:08:41.080049 2025-04-05
* CP COUNT: (30)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:17.122989  START: 14:08:45.428572  END: 14:09:02.551561 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00146664-base-pr-002.dot
* REASONING
* DIS # I1: 2,8 # E1: 5 => CTR => E1: 3,4
* DIS # A3: 3,6 # C4: 5,7 => CTR => C4: 2,6
* PRF # A3: 3,6 + C4: 2,6 # C7: 5,7 => SOL
* STA # A3: 3,6 + C4: 2,6 + C7: 5,7
* CNT   3 HDP CHAINS /  69 HYP OPENED

Header Info

rating: 39260; r2: 749458; index: 146664

Solution

position: 123456789457189236689237451216598347534671928978342165395764812761823594842915673 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 # H1: 2,8 => UNS
* INC # I1: 2,8 => UNS
* INC # A3: 3,6 => UNS
* INC # C3: 3,6 => UNS
* INC # A2: 2,4 => UNS
* INC # A2: 5,7 => UNS
* INC # D1: 3,4 => UNS
* INC # D1: 5 => UNS
* INC # E1: 3,4 => UNS
* INC # E1: 5 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 2,8 => UNS
* INC # I1: 2,8 => UNS
* INC # A3: 3,6 => UNS
* INC # C3: 3,6 => UNS
* INC # A2: 2,4 => UNS
* INC # A2: 5,7 => UNS
* INC # D1: 3,4 => UNS
* INC # D1: 5 => UNS
* INC # E1: 3,4 => UNS
* INC # E1: 5 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # H1: 2,8 => UNS
* INC # I1: 2,8 => UNS
* INC # A3: 3,6 => UNS
* INC # C3: 3,6 => UNS
* INC # A2: 2,4 => UNS
* INC # A2: 5,7 => UNS
* INC # D1: 3,4 => UNS
* INC # D1: 5 => UNS
* INC # E1: 3,4 => UNS
* INC # E1: 5 => UNS
* INC # H1: 2,8 # A3: 3,6 => UNS
* INC # H1: 2,8 # C3: 3,6 => UNS
* INC # H1: 2,8 # H5: 2,8 => UNS
* INC # H1: 2,8 # H7: 2,8 => UNS
* INC # H1: 2,8 # A2: 2,4 => UNS
* INC # H1: 2,8 # A2: 5,7 => UNS
* INC # H1: 2,8 # D1: 3,4 => UNS
* INC # H1: 2,8 # D1: 5 => UNS
* INC # H1: 2,8 # E1: 3,4 => UNS
* INC # H1: 2,8 # E1: 5 => UNS
* INC # H1: 2,8 => UNS
* INC # I1: 2,8 # C4: 5,7 => UNS
* INC # I1: 2,8 # B6: 5,7 => UNS
* INC # I1: 2,8 # A2: 5,7 => UNS
* INC # I1: 2,8 # A8: 5,7 => UNS
* INC # I1: 2,8 # D4: 5,7 => UNS
* INC # I1: 2,8 # F6: 5,7 => UNS
* INC # I1: 2,8 # E8: 5,7 => UNS
* INC # I1: 2,8 # E8: 2 => UNS
* INC # I1: 2,8 # D1: 3,4 => UNS
* INC # I1: 2,8 # D1: 5 => UNS
* INC # I1: 2,8 # E1: 3,4 => UNS
* DIS # I1: 2,8 # E1: 5 => CTR => E1: 3,4
* INC # I1: 2,8 + E1: 3,4 # C4: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # D4: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # B6: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # F6: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # G8: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # G9: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # B7: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # D7: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # D1: 3,4 => UNS
* INC # I1: 2,8 + E1: 3,4 # D1: 5 => UNS
* INC # I1: 2,8 + E1: 3,4 # D3: 2,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # F3: 2,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # E8: 2,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # E8: 5 => UNS
* INC # I1: 2,8 + E1: 3,4 # C4: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # B6: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # A2: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # A8: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # D4: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # F6: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # E8: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # E8: 2 => UNS
* INC # I1: 2,8 + E1: 3,4 # D1: 3,4 => UNS
* INC # I1: 2,8 + E1: 3,4 # D1: 5 => UNS
* INC # I1: 2,8 + E1: 3,4 # C4: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # D4: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # B6: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # F6: 5,7 => UNS
* INC # I1: 2,8 + E1: 3,4 # G8: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # G9: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # B7: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 # D7: 2,5 => UNS
* INC # I1: 2,8 + E1: 3,4 => UNS
* DIS # A3: 3,6 # C4: 5,7 => CTR => C4: 2,6
* PRF # A3: 3,6 + C4: 2,6 # C7: 5,7 => SOL
* STA # A3: 3,6 + C4: 2,6 + C7: 5,7
* CNT  68 HDP CHAINS /  69 HYP OPENED