Analysis of xx-mith-te3-00063288-base.sdk

Contents

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

Original Sudoku

level: hard

position: .2345....45...92..6.92.34...36....78.45....61.......42..269.....6........943.5... initial

Autosolve

position: .2345....45...92..6.92.34...36....78.45....61.......42..269...4.6........943.5.2. 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: 0:00:14.368282

The following important HDP chains were detected:

* PRF # I2: 6,7 # E2: 1,8 => SOL
* STA # I2: 6,7 + E2: 1,8
* CNT   1 HDP CHAINS /  60 HYP OPENED

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

Details

Positions

`.2345....45...92..6.92.34...36....78.45....61.......42..269.....6........943.5...`	initial
`.2345....45...92..6.92.34...36....78.45....61.......42..269...4.6........943.5.2.`	autosolve
`123456789457189236689273415236941578745832961918567342372698154561724893894315627`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
G1: 6,7
I3: 5,7
G4: 5,9
G5: 3,9
A7: 3,5
A8: 3,5
E8: 2,4
F8: 2,4
H7: 3,5
I9: 6,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A4,A5: 2.. / A4 = 2  => 13 pairs (_) / A5 = 2  => 15 pairs (_)
E8,F8: 2.. / E8 = 2  =>  9 pairs (_) / F8 = 2  => 10 pairs (_)
H2,I2: 3.. / H2 = 3  =>  9 pairs (_) / I2 = 3  => 12 pairs (_)
E5,E6: 3.. / E5 = 3  => 11 pairs (_) / E6 = 3  => 11 pairs (_)
G5,G6: 3.. / G5 = 3  => 11 pairs (_) / G6 = 3  => 11 pairs (_)
A7,A8: 3.. / A7 = 3  =>  9 pairs (_) / A8 = 3  => 10 pairs (_)
E5,G5: 3.. / E5 = 3  => 11 pairs (_) / G5 = 3  => 11 pairs (_)
E6,G6: 3.. / E6 = 3  => 11 pairs (_) / G6 = 3  => 11 pairs (_)
A7,H7: 3.. / A7 = 3  =>  9 pairs (_) / H7 = 3  => 10 pairs (_)
I2,I8: 3.. / I2 = 3  => 12 pairs (_) / I8 = 3  =>  9 pairs (_)
E4,F4: 4.. / E4 = 4  =>  9 pairs (_) / F4 = 4  => 10 pairs (_)
E8,F8: 4.. / E8 = 4  => 10 pairs (_) / F8 = 4  =>  9 pairs (_)
E4,E8: 4.. / E4 = 4  =>  9 pairs (_) / E8 = 4  => 10 pairs (_)
F4,F8: 4.. / F4 = 4  => 10 pairs (_) / F8 = 4  =>  9 pairs (_)
H3,I3: 5.. / H3 = 5  =>  8 pairs (_) / I3 = 5  => 11 pairs (_)
D4,D6: 5.. / D4 = 5  => 10 pairs (_) / D6 = 5  => 11 pairs (_)
G4,G6: 5.. / G4 = 5  => 11 pairs (_) / G6 = 5  => 10 pairs (_)
A7,A8: 5.. / A7 = 5  => 10 pairs (_) / A8 = 5  =>  9 pairs (_)
D4,G4: 5.. / D4 = 5  => 10 pairs (_) / G4 = 5  => 11 pairs (_)
D6,G6: 5.. / D6 = 5  => 11 pairs (_) / G6 = 5  => 10 pairs (_)
A7,H7: 5.. / A7 = 5  => 10 pairs (_) / H7 = 5  =>  9 pairs (_)
I3,I8: 5.. / I3 = 5  => 11 pairs (_) / I8 = 5  =>  8 pairs (_)
F1,E2: 6.. / F1 = 6  =>  0 pairs (*) / E2 = 6  =>  0 pairs (X)
E6,F6: 6.. / E6 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
G9,I9: 6.. / G9 = 6  => 21 pairs (_) / I9 = 6  => 10 pairs (_)
E2,I2: 6.. / E2 = 6  => 11 pairs (_) / I2 = 6  =>  0 pairs (*)
E2,E6: 6.. / E2 = 6  => 11 pairs (_) / E6 = 6  =>  0 pairs (*)
F1,F6: 6.. / F1 = 6  =>  0 pairs (*) / F6 = 6  =>  0 pairs (X)
G1,G9: 6.. / G1 = 6  => 10 pairs (_) / G9 = 6  => 21 pairs (_)
H1,I1: 9.. / H1 = 9  => 15 pairs (_) / I1 = 9  => 12 pairs (_)
H8,I8: 9.. / H8 = 9  => 12 pairs (_) / I8 = 9  => 15 pairs (_)
H1,H8: 9.. / H1 = 9  => 15 pairs (_) / H8 = 9  => 12 pairs (_)
I1,I8: 9.. / I1 = 9  => 12 pairs (_) / I8 = 9  => 15 pairs (_)
* DURATION: 0:00:11.815991  START: 09:37:07.490789  END: 09:37:19.306780 2025-04-06
* CP COUNT: (33)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:14.184729  START: 09:37:28.425241  END: 09:37:42.609970 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00063288-base-pr-002.dot
* REASONING
* PRF # I2: 6,7 # E2: 1,8 => SOL
* STA # I2: 6,7 + E2: 1,8
* CNT   1 HDP CHAINS /  60 HYP OPENED

Header Info

rating: 13896; r2: 372647; index: 63288

Solution

position: 123456789457189236689273415236941578745832961918567342372698154561724893894315627 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 # I1: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # F1: 1,8 => UNS
* INC # G9: 6,7 => UNS
* INC # G9: 1,8 => UNS
* INC # G6: 5,9 => UNS
* INC # G6: 3 => UNS
* INC # D4: 5,9 => UNS
* INC # D4: 1 => UNS
* INC # G6: 3,9 => UNS
* INC # G6: 5 => UNS
* INC # H8: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 1 => UNS
* INC # F4: 2,4 => UNS
* INC # F4: 1 => UNS
* INC # H8: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # G9: 6,7 => UNS
* INC # G9: 1,8 => UNS
* INC # I1: 6,7 => UNS
* INC # I2: 6,7 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # F1: 1,8 => UNS
* INC # G9: 6,7 => UNS
* INC # G9: 1,8 => UNS
* INC # G6: 5,9 => UNS
* INC # G6: 3 => UNS
* INC # D4: 5,9 => UNS
* INC # D4: 1 => UNS
* INC # G6: 3,9 => UNS
* INC # G6: 5 => UNS
* INC # H8: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 1 => UNS
* INC # F4: 2,4 => UNS
* INC # F4: 1 => UNS
* INC # H8: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # G9: 6,7 => UNS
* INC # G9: 1,8 => UNS
* INC # I1: 6,7 => UNS
* INC # I2: 6,7 => UNS
* CNT  24 HDP CHAINS /  24 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # F1: 6,7 => UNS
* INC # F1: 1,8 => UNS
* INC # G9: 6,7 => UNS
* INC # G9: 1,8 => UNS
* INC # G6: 5,9 => UNS
* INC # G6: 3 => UNS
* INC # D4: 5,9 => UNS
* INC # D4: 1 => UNS
* INC # G6: 3,9 => UNS
* INC # G6: 5 => UNS
* INC # H8: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # E4: 2,4 => UNS
* INC # E4: 1 => UNS
* INC # F4: 2,4 => UNS
* INC # F4: 1 => UNS
* INC # H8: 3,5 => UNS
* INC # I8: 3,5 => UNS
* INC # G9: 6,7 => UNS
* INC # G9: 1,8 => UNS
* INC # I1: 6,7 => UNS
* INC # I2: 6,7 => UNS
* INC # I1: 6,7 # C2: 1,8 => UNS
* INC # I1: 6,7 # B3: 1,8 => UNS
* INC # I1: 6,7 # A6: 1,8 => UNS
* INC # I1: 6,7 # A9: 1,8 => UNS
* INC # I1: 6,7 # D2: 1,8 => UNS
* INC # I1: 6,7 # E3: 1,8 => UNS
* INC # I1: 6,7 # F7: 1,8 => UNS
* INC # I1: 6,7 # F7: 7 => UNS
* INC # I1: 6,7 # G9: 6,7 => UNS
* INC # I1: 6,7 # G9: 1,8 => UNS
* INC # I1: 6,7 # C2: 1,8 => UNS
* INC # I1: 6,7 # D2: 1,8 => UNS
* INC # I1: 6,7 # B3: 1,8 => UNS
* INC # I1: 6,7 # E3: 1,8 => UNS
* INC # I1: 6,7 # G6: 5,9 => UNS
* INC # I1: 6,7 # G6: 3 => UNS
* INC # I1: 6,7 # D4: 5,9 => UNS
* INC # I1: 6,7 # D4: 1 => UNS
* INC # I1: 6,7 # G6: 3,9 => UNS
* INC # I1: 6,7 # G6: 5 => UNS
* INC # I1: 6,7 # E4: 2,4 => UNS
* INC # I1: 6,7 # E4: 1 => UNS
* INC # I1: 6,7 # F4: 2,4 => UNS
* INC # I1: 6,7 # F4: 1 => UNS
* INC # I1: 6,7 # G9: 6,7 => UNS
* INC # I1: 6,7 # G9: 1,8 => UNS
* INC # I1: 6,7 => UNS
* INC # I2: 6,7 # F1: 6,7 => UNS
* INC # I2: 6,7 # F1: 1,8 => UNS
* INC # I2: 6,7 # G9: 6,7 => UNS
* INC # I2: 6,7 # G9: 1,8 => UNS
* INC # I2: 6,7 # A1: 1,8 => UNS
* INC # I2: 6,7 # F1: 1,8 => UNS
* INC # I2: 6,7 # E2: 6,7 => UNS
* PRF # I2: 6,7 # E2: 1,8 => SOL
* STA # I2: 6,7 + E2: 1,8
* CNT  59 HDP CHAINS /  60 HYP OPENED