Analysis of xx-mith-te3-00082882-base.sdk

Contents

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

Original Sudoku

level: hard

position: ....56..9...18.2.66.....5....6.9.8.1..96.8.52..5.21...3...1.....718.....9.2...1.8 initial

Autosolve

position: ....56..9...18.2.66.....5....6.9.8.1..96.8.52..5.21...3...1.....718.....9.2...1.8 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: 0:00:15.636142

The following important HDP chains were detected:

* DIS # F3: 3,4,7 # I6: 3,4 => CTR => I6: 7
* PRF # F3: 3,4,7 + I6: 7 # G8: 3,4 => SOL
* STA # F3: 3,4,7 + I6: 7 + G8: 3,4
* CNT   2 HDP CHAINS /  55 HYP OPENED

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

Details

Positions

`....56..9...18.2.66.....5....6.9.8.1..96.8.52..5.21...3...1.....718.....9.2...1.8`	initial
`....56..9...18.2.66.....5....6.9.8.1..96.8.52..5.21...3...1.....718.....9.2...1.8`	autosolve
`123456789457189236698273514236795841719648352845321967384917625571862493962534178`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (14)
A2: 4,5
B2: 5,9
D3: 2,9
H1: 1,8
H3: 1,8
A4: 2,7
A5: 1,7
A6: 7,8
G6: 6,9
H6: 6,9
C7: 4,8
A8: 4,5
B9: 5,6
D7: 2,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 14 pairs (_) / H3 = 1  => 15 pairs (_)
A5,B5: 1.. / A5 = 1  => 15 pairs (_) / B5 = 1  => 14 pairs (_)
B3,H3: 1.. / B3 = 1  => 14 pairs (_) / H3 = 1  => 15 pairs (_)
A1,A5: 1.. / A1 = 1  => 14 pairs (_) / A5 = 1  => 15 pairs (_)
A1,B1: 2.. / A1 = 2  => 15 pairs (_) / B1 = 2  => 15 pairs (_)
D3,F3: 2.. / D3 = 2  => 12 pairs (_) / F3 = 2  => 12 pairs (_)
A4,B4: 2.. / A4 = 2  => 15 pairs (_) / B4 = 2  => 15 pairs (_)
H7,H8: 2.. / H7 = 2  => 12 pairs (_) / H8 = 2  => 14 pairs (_)
F8,H8: 2.. / F8 = 2  => 12 pairs (_) / H8 = 2  => 14 pairs (_)
A1,A4: 2.. / A1 = 2  => 15 pairs (_) / A4 = 2  => 15 pairs (_)
B1,B4: 2.. / B1 = 2  => 15 pairs (_) / B4 = 2  => 15 pairs (_)
D3,D7: 2.. / D3 = 2  => 12 pairs (_) / D7 = 2  => 12 pairs (_)
C7,A8: 4.. / C7 = 4  => 15 pairs (_) / A8 = 4  => 15 pairs (_)
A2,A8: 4.. / A2 = 4  => 15 pairs (_) / A8 = 4  => 15 pairs (_)
A2,B2: 5.. / A2 = 5  => 15 pairs (_) / B2 = 5  => 15 pairs (_)
D4,F4: 5.. / D4 = 5  => 14 pairs (_) / F4 = 5  => 15 pairs (_)
I7,I8: 5.. / I7 = 5  => 16 pairs (_) / I8 = 5  => 15 pairs (_)
A2,A8: 5.. / A2 = 5  => 15 pairs (_) / A8 = 5  => 15 pairs (_)
D4,D9: 5.. / D4 = 5  => 14 pairs (_) / D9 = 5  => 15 pairs (_)
G6,H6: 6.. / G6 = 6  => 12 pairs (_) / H6 = 6  => 15 pairs (_)
B7,B9: 6.. / B7 = 6  => 14 pairs (_) / B9 = 6  => 15 pairs (_)
E8,E9: 6.. / E8 = 6  => 14 pairs (_) / E9 = 6  => 22 pairs (_)
H1,H3: 8.. / H1 = 8  => 15 pairs (_) / H3 = 8  => 14 pairs (_)
A6,B6: 8.. / A6 = 8  => 15 pairs (_) / B6 = 8  => 13 pairs (_)
B7,C7: 8.. / B7 = 8  => 15 pairs (_) / C7 = 8  => 15 pairs (_)
A1,A6: 8.. / A1 = 8  => 13 pairs (_) / A6 = 8  => 15 pairs (_)
C3,C7: 8.. / C3 = 8  => 15 pairs (_) / C7 = 8  => 15 pairs (_)
B2,B3: 9.. / B2 = 9  => 15 pairs (_) / B3 = 9  => 15 pairs (_)
G6,H6: 9.. / G6 = 9  => 15 pairs (_) / H6 = 9  => 12 pairs (_)
B2,F2: 9.. / B2 = 9  => 15 pairs (_) / F2 = 9  => 15 pairs (_)
D3,D7: 9.. / D3 = 9  => 12 pairs (_) / D7 = 9  => 12 pairs (_)
* DURATION: 0:00:10.738435  START: 21:45:25.937919  END: 21:45:36.676354 2025-04-04
* CP COUNT: (31)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:15.457566  START: 21:45:44.555119  END: 21:46:00.012685 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00082882-base-pr-002.dot
* REASONING
* DIS # F3: 3,4,7 # I6: 3,4 => CTR => I6: 7
* PRF # F3: 3,4,7 + I6: 7 # G8: 3,4 => SOL
* STA # F3: 3,4,7 + I6: 7 + G8: 3,4
* CNT   2 HDP CHAINS /  55 HYP OPENED

Header Info

rating: 20344; r2: 427958; index: 82882

Solution

position: 123456789457189236698273514236795841719648352845321967384917625571862493962534178 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 # F3: 2,9 => UNS
* INC # F3: 3,4,7 => UNS
* INC # A1: 1,8 => UNS
* INC # B1: 1,8 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 9 => UNS
* INC # G7: 6,9 => UNS
* INC # G8: 6,9 => UNS
* INC # H7: 6,9 => UNS
* INC # H8: 6,9 => UNS
* INC # C3: 4,8 => UNS
* INC # C3: 3,7 => UNS
* INC # F8: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # B7: 5,6 => UNS
* INC # B7: 8 => UNS
* INC # F7: 2,9 => UNS
* INC # F8: 2,9 => UNS
* INC # H7: 2,9 => UNS
* INC # H7: 4,6,7 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # F3: 2,9 => UNS
* INC # F3: 3,4,7 => UNS
* INC # A1: 1,8 => UNS
* INC # B1: 1,8 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 9 => UNS
* INC # G7: 6,9 => UNS
* INC # G8: 6,9 => UNS
* INC # H7: 6,9 => UNS
* INC # H8: 6,9 => UNS
* INC # C3: 4,8 => UNS
* INC # C3: 3,7 => UNS
* INC # F8: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # B7: 5,6 => UNS
* INC # B7: 8 => UNS
* INC # F7: 2,9 => UNS
* INC # F8: 2,9 => UNS
* INC # H7: 2,9 => UNS
* INC # H7: 4,6,7 => UNS
* CNT  20 HDP CHAINS /  20 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # F3: 2,9 => UNS
* INC # F3: 3,4,7 => UNS
* INC # A1: 1,8 => UNS
* INC # B1: 1,8 => UNS
* INC # B3: 1,8 => UNS
* INC # B3: 9 => UNS
* INC # G7: 6,9 => UNS
* INC # G8: 6,9 => UNS
* INC # H7: 6,9 => UNS
* INC # H8: 6,9 => UNS
* INC # C3: 4,8 => UNS
* INC # C3: 3,7 => UNS
* INC # F8: 4,5 => UNS
* INC # I8: 4,5 => UNS
* INC # B7: 5,6 => UNS
* INC # B7: 8 => UNS
* INC # F7: 2,9 => UNS
* INC # F8: 2,9 => UNS
* INC # H7: 2,9 => UNS
* INC # H7: 4,6,7 => UNS
* INC # F3: 2,9 # A1: 1,8 => UNS
* INC # F3: 2,9 # B1: 1,8 => UNS
* INC # F3: 2,9 # F7: 2,9 => UNS
* INC # F3: 2,9 # F8: 2,9 => UNS
* INC # F3: 2,9 # A1: 1,8 => UNS
* INC # F3: 2,9 # B1: 1,8 => UNS
* INC # F3: 2,9 # G7: 6,9 => UNS
* INC # F3: 2,9 # G8: 6,9 => UNS
* INC # F3: 2,9 # H7: 6,9 => UNS
* INC # F3: 2,9 # H8: 6,9 => UNS
* INC # F3: 2,9 # F7: 2,9 => UNS
* INC # F3: 2,9 # F8: 2,9 => UNS
* INC # F3: 2,9 # H7: 2,9 => UNS
* INC # F3: 2,9 # H7: 4,6,7 => UNS
* INC # F3: 2,9 # E9: 3,6 => UNS
* INC # F3: 2,9 # E9: 4,7 => UNS
* INC # F3: 2,9 # G8: 3,6 => UNS
* INC # F3: 2,9 # H8: 3,6 => UNS
* INC # F3: 2,9 # F8: 3,5 => UNS
* INC # F3: 2,9 # F8: 2,9 => UNS
* INC # F3: 2,9 => UNS
* INC # F3: 3,4,7 # D1: 3,7 => UNS
* INC # F3: 3,4,7 # G1: 3,7 => UNS
* INC # F3: 3,4,7 # G1: 3,7 => UNS
* INC # F3: 3,4,7 # I3: 3,7 => UNS
* INC # F3: 3,4,7 # H4: 3,7 => UNS
* INC # F3: 3,4,7 # H9: 3,7 => UNS
* INC # F3: 3,4,7 # B4: 3,4 => UNS
* INC # F3: 3,4,7 # B5: 3,4 => UNS
* INC # F3: 3,4,7 # D6: 3,4 => UNS
* DIS # F3: 3,4,7 # I6: 3,4 => CTR => I6: 7
* INC # F3: 3,4,7 + I6: 7 # B4: 3,4 => UNS
* INC # F3: 3,4,7 + I6: 7 # B5: 3,4 => UNS
* PRF # F3: 3,4,7 + I6: 7 # G8: 3,4 => SOL
* STA # F3: 3,4,7 + I6: 7 + G8: 3,4
* CNT  54 HDP CHAINS /  55 HYP OPENED