Analysis of xx-mith-te3-00106709-base.sdk

Contents

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

Original Sudoku

level: hard

position: ...4.67.9......23..8........91..8.7..........87..9416..4.9.7...71.86...49...41..7 initial

Autosolve

position: ...4.67.94.....23..8.....4..916.847...4......87..9416..4.9.7...71.86...49...41..7 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: 0:00:20.577610

The following important HDP chains were detected:

* PRF # I2: 5,6 # I7: 2,3,8 => SOL
* STA # I2: 5,6 + I7: 2,3,8
* CNT   1 HDP CHAINS /  79 HYP OPENED

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

Details

Positions

`...4.67.9......23..8........91..8.7..........87..9416..4.9.7...71.86...49...41..7`	initial
`...4.67.94.....23..8.....4..916.847...4......87..9416..4.9.7...71.86...49...41..7`	autosolve
`123456789457189236689372541291638475364715892875294163546927318712863954938541627`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
B2: 5,6
C2: 7,9
C3: 7,9
F2: 5,9
G3: 5,6
D5: 1,7
E5: 1,7
C7: 6,8
C9: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A3: 1.. / A1 = 1  => 10 pairs (_) / A3 = 1  => 12 pairs (_)
D5,E5: 1.. / D5 = 1  =>  9 pairs (_) / E5 = 1  =>  8 pairs (_)
H7,I7: 1.. / H7 = 1  => 10 pairs (_) / I7 = 1  => 10 pairs (_)
H1,H7: 1.. / H1 = 1  => 10 pairs (_) / H7 = 1  => 10 pairs (_)
B2,A3: 6.. / B2 = 6  =>  8 pairs (_) / A3 = 6  => 12 pairs (_)
A5,B5: 6.. / A5 = 6  =>  8 pairs (_) / B5 = 6  => 12 pairs (_)
C7,C9: 6.. / C7 = 6  => 11 pairs (_) / C9 = 6  =>  7 pairs (_)
B2,I2: 6.. / B2 = 6  =>  8 pairs (_) / I2 = 6  => 12 pairs (_)
C9,G9: 6.. / C9 = 6  =>  7 pairs (_) / G9 = 6  => 11 pairs (_)
A3,A5: 6.. / A3 = 6  => 12 pairs (_) / A5 = 6  =>  8 pairs (_)
B2,B5: 6.. / B2 = 6  =>  8 pairs (_) / B5 = 6  => 12 pairs (_)
C2,C3: 7.. / C2 = 7  =>  7 pairs (_) / C3 = 7  => 10 pairs (_)
D5,E5: 7.. / D5 = 7  =>  8 pairs (_) / E5 = 7  =>  9 pairs (_)
E1,E2: 8.. / E1 = 8  => 14 pairs (_) / E2 = 8  => 11 pairs (_)
H1,I2: 8.. / H1 = 8  => 11 pairs (_) / I2 = 8  => 14 pairs (_)
C7,C9: 8.. / C7 = 8  =>  7 pairs (_) / C9 = 8  => 11 pairs (_)
E1,H1: 8.. / E1 = 8  => 14 pairs (_) / H1 = 8  => 11 pairs (_)
E2,I2: 8.. / E2 = 8  => 11 pairs (_) / I2 = 8  => 14 pairs (_)
C2,C3: 9.. / C2 = 9  => 10 pairs (_) / C3 = 9  =>  7 pairs (_)
F2,F3: 9.. / F2 = 9  =>  7 pairs (_) / F3 = 9  => 10 pairs (_)
G5,H5: 9.. / G5 = 9  => 12 pairs (_) / H5 = 9  => 10 pairs (_)
G8,H8: 9.. / G8 = 9  => 10 pairs (_) / H8 = 9  => 12 pairs (_)
C2,F2: 9.. / C2 = 9  => 10 pairs (_) / F2 = 9  =>  7 pairs (_)
C3,F3: 9.. / C3 = 9  =>  7 pairs (_) / F3 = 9  => 10 pairs (_)
G5,G8: 9.. / G5 = 9  => 12 pairs (_) / G8 = 9  => 10 pairs (_)
H5,H8: 9.. / H5 = 9  => 10 pairs (_) / H8 = 9  => 12 pairs (_)
* DURATION: 0:00:10.153363  START: 17:07:45.782463  END: 17:07:55.935826 2025-04-06
* CP COUNT: (26)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:20.371399  START: 17:08:05.412287  END: 17:08:25.783686 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00106709-base-pr-002.dot
* REASONING
* PRF # I2: 5,6 # I7: 2,3,8 => SOL
* STA # I2: 5,6 + I7: 2,3,8
* CNT   1 HDP CHAINS /  79 HYP OPENED

Header Info

rating: 26762; r2: 540416; index: 106709

Solution

position: 123456789457189236689372541291638475364715892875294163546927318712863954938541627 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 # A3: 5,6 => UNS
* INC # A3: 1,2,3 => UNS
* INC # I2: 5,6 => UNS
* INC # I2: 1,8 => UNS
* INC # B5: 5,6 => UNS
* INC # B5: 2,3 => UNS
* INC # F3: 5,9 => UNS
* INC # F3: 2,3 => UNS
* INC # I2: 5,6 => UNS
* INC # I3: 5,6 => UNS
* INC # A3: 5,6 => UNS
* INC # A3: 1,2,3 => UNS
* INC # G7: 5,6 => UNS
* INC # G9: 5,6 => UNS
* INC # D2: 1,7 => UNS
* INC # D3: 1,7 => UNS
* INC # E2: 1,7 => UNS
* INC # E3: 1,7 => UNS
* INC # G7: 6,8 => UNS
* INC # I7: 6,8 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 3,5 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 5,6 => UNS
* INC # A3: 1,2,3 => UNS
* INC # I2: 5,6 => UNS
* INC # I2: 1,8 => UNS
* INC # B5: 5,6 => UNS
* INC # B5: 2,3 => UNS
* INC # F3: 5,9 => UNS
* INC # F3: 2,3 => UNS
* INC # I2: 5,6 => UNS
* INC # I3: 5,6 => UNS
* INC # A3: 5,6 => UNS
* INC # A3: 1,2,3 => UNS
* INC # G7: 5,6 => UNS
* INC # G9: 5,6 => UNS
* INC # D2: 1,7 => UNS
* INC # D3: 1,7 => UNS
* INC # E2: 1,7 => UNS
* INC # E3: 1,7 => UNS
* INC # G7: 6,8 => UNS
* INC # I7: 6,8 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 3,5 => UNS
* CNT  22 HDP CHAINS /  22 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A3: 5,6 => UNS
* INC # A3: 1,2,3 => UNS
* INC # I2: 5,6 => UNS
* INC # I2: 1,8 => UNS
* INC # B5: 5,6 => UNS
* INC # B5: 2,3 => UNS
* INC # F3: 5,9 => UNS
* INC # F3: 2,3 => UNS
* INC # I2: 5,6 => UNS
* INC # I3: 5,6 => UNS
* INC # A3: 5,6 => UNS
* INC # A3: 1,2,3 => UNS
* INC # G7: 5,6 => UNS
* INC # G9: 5,6 => UNS
* INC # D2: 1,7 => UNS
* INC # D3: 1,7 => UNS
* INC # E2: 1,7 => UNS
* INC # E3: 1,7 => UNS
* INC # G7: 6,8 => UNS
* INC # I7: 6,8 => UNS
* INC # G9: 6,8 => UNS
* INC # G9: 3,5 => UNS
* INC # A3: 5,6 # B5: 2,3 => UNS
* INC # A3: 5,6 # B9: 2,3 => UNS
* INC # A3: 5,6 # C6: 2,3 => UNS
* INC # A3: 5,6 # C8: 2,3 => UNS
* INC # A3: 5,6 # I2: 5,6 => UNS
* INC # A3: 5,6 # I2: 8 => UNS
* INC # A3: 5,6 # B5: 5,6 => UNS
* INC # A3: 5,6 # B5: 2,3 => UNS
* INC # A3: 5,6 # A5: 5,6 => UNS
* INC # A3: 5,6 # A5: 2,3 => UNS
* INC # A3: 5,6 # E2: 5,8 => UNS
* INC # A3: 5,6 # E2: 1,7 => UNS
* INC # A3: 5,6 # I2: 5,8 => UNS
* INC # A3: 5,6 # I2: 6 => UNS
* INC # A3: 5,6 # H5: 5,8 => UNS
* INC # A3: 5,6 # H9: 5,8 => UNS
* INC # A3: 5,6 # I2: 5,6 => UNS
* INC # A3: 5,6 # I2: 8 => UNS
* INC # A3: 5,6 # G7: 5,6 => UNS
* INC # A3: 5,6 # G9: 5,6 => UNS
* INC # A3: 5,6 # D2: 1,7 => UNS
* INC # A3: 5,6 # D2: 5 => UNS
* INC # A3: 5,6 # E2: 1,7 => UNS
* INC # A3: 5,6 # E2: 5,8 => UNS
* INC # A3: 5,6 # G7: 6,8 => UNS
* INC # A3: 5,6 # I7: 6,8 => UNS
* INC # A3: 5,6 # G9: 6,8 => UNS
* INC # A3: 5,6 # G9: 3,5 => UNS
* INC # A3: 5,6 => UNS
* INC # A3: 1,2,3 # F3: 5,9 => UNS
* INC # A3: 1,2,3 # F3: 2,3 => UNS
* INC # A3: 1,2,3 # I2: 1,8 => UNS
* INC # A3: 1,2,3 # I2: 5 => UNS
* INC # A3: 1,2,3 # E1: 1,8 => UNS
* INC # A3: 1,2,3 # E1: 2,3 => UNS
* INC # A3: 1,2,3 # H7: 1,8 => UNS
* INC # A3: 1,2,3 # H7: 2,5 => UNS
* INC # A3: 1,2,3 # I3: 5,6 => UNS
* INC # A3: 1,2,3 # I3: 1 => UNS
* INC # A3: 1,2,3 # G7: 5,6 => UNS
* INC # A3: 1,2,3 # G9: 5,6 => UNS
* INC # A3: 1,2,3 # D2: 1,7 => UNS
* INC # A3: 1,2,3 # D3: 1,7 => UNS
* INC # A3: 1,2,3 # E2: 1,7 => UNS
* INC # A3: 1,2,3 # E3: 1,7 => UNS
* INC # A3: 1,2,3 # G7: 6,8 => UNS
* INC # A3: 1,2,3 # I7: 6,8 => UNS
* INC # A3: 1,2,3 # G9: 6,8 => UNS
* INC # A3: 1,2,3 # G9: 3,5 => UNS
* INC # A3: 1,2,3 => UNS
* INC # I2: 5,6 # A3: 5,6 => UNS
* INC # I2: 5,6 # A3: 2,3 => UNS
* INC # I2: 5,6 # B5: 5,6 => UNS
* INC # I2: 5,6 # B5: 2,3 => UNS
* INC # I2: 5,6 # I7: 5,6 => UNS
* PRF # I2: 5,6 # I7: 2,3,8 => SOL
* STA # I2: 5,6 + I7: 2,3,8
* CNT  78 HDP CHAINS /  79 HYP OPENED