Analysis of xx-mith-te3-00144227-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12.........7..9...689....5....59..73.......1..3..17..4...9.1.45...74.39...4.351.7 initial

Autosolve

position: 12......9..7..9...689....5....59..73.......1..3..17..4...9.1.45...74.39...4.351.7 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: 0:00:11.464869

The following important HDP chains were detected:

* PRF # A2: 4 # C4: 2,8 => SOL
* STA # A2: 4 + C4: 2,8
* CNT   1 HDP CHAINS /  51 HYP OPENED

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

Details

Positions

`12.........7..9...689....5....59..73.......1..3..17..4...9.1.45...74.39...4.351.7`	initial
`12......9..7..9...689....5....59..73.......1..3..17..4...9.1.45...74.39...4.351.7`	autosolve
`123456789457189236689372451218594673745623918936817524372961845561748392894235167`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
C1: 3,5
B2: 4,5
E3: 2,7
G1: 4,7
G3: 4,7
I3: 1,2
G5: 5,9
G6: 5,9
B7: 6,7
B9: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  9 pairs (_) / D3 = 1  => 10 pairs (_)
I2,I3: 1.. / I2 = 1  => 10 pairs (_) / I3 = 1  =>  9 pairs (_)
B4,C4: 1.. / B4 = 1  => 11 pairs (_) / C4 = 1  => 11 pairs (_)
B8,C8: 1.. / B8 = 1  => 11 pairs (_) / C8 = 1  => 11 pairs (_)
D2,I2: 1.. / D2 = 1  =>  9 pairs (_) / I2 = 1  => 10 pairs (_)
D3,I3: 1.. / D3 = 1  => 10 pairs (_) / I3 = 1  =>  9 pairs (_)
B4,B8: 1.. / B4 = 1  => 11 pairs (_) / B8 = 1  => 11 pairs (_)
C4,C8: 1.. / C4 = 1  => 11 pairs (_) / C8 = 1  => 11 pairs (_)
C1,A2: 3.. / C1 = 3  =>  8 pairs (_) / A2 = 3  => 14 pairs (_)
D3,F3: 3.. / D3 = 3  => 10 pairs (_) / F3 = 3  => 11 pairs (_)
H1,H2: 3.. / H1 = 3  => 14 pairs (_) / H2 = 3  =>  8 pairs (_)
D5,F5: 3.. / D5 = 3  => 11 pairs (_) / F5 = 3  => 10 pairs (_)
A7,C7: 3.. / A7 = 3  =>  8 pairs (_) / C7 = 3  => 14 pairs (_)
C1,H1: 3.. / C1 = 3  =>  8 pairs (_) / H1 = 3  => 14 pairs (_)
A2,H2: 3.. / A2 = 3  => 14 pairs (_) / H2 = 3  =>  8 pairs (_)
A2,A7: 3.. / A2 = 3  => 14 pairs (_) / A7 = 3  =>  8 pairs (_)
C1,C7: 3.. / C1 = 3  =>  8 pairs (_) / C7 = 3  => 14 pairs (_)
D3,D5: 3.. / D3 = 3  => 10 pairs (_) / D5 = 3  => 11 pairs (_)
F3,F5: 3.. / F3 = 3  => 11 pairs (_) / F5 = 3  => 10 pairs (_)
A2,B2: 4.. / A2 = 4  =>  8 pairs (_) / B2 = 4  => 11 pairs (_)
G1,G3: 4.. / G1 = 4  => 15 pairs (_) / G3 = 4  =>  8 pairs (_)
E1,E2: 5.. / E1 = 5  =>  8 pairs (_) / E2 = 5  => 14 pairs (_)
G5,G6: 5.. / G5 = 5  => 14 pairs (_) / G6 = 5  =>  8 pairs (_)
C1,E1: 5.. / C1 = 5  => 14 pairs (_) / E1 = 5  =>  8 pairs (_)
E1,E3: 7.. / E1 = 7  => 15 pairs (_) / E3 = 7  =>  8 pairs (_)
G1,G3: 7.. / G1 = 7  =>  8 pairs (_) / G3 = 7  => 15 pairs (_)
A5,B5: 7.. / A5 = 7  =>  9 pairs (_) / B5 = 7  => 15 pairs (_)
A7,B7: 7.. / A7 = 7  => 15 pairs (_) / B7 = 7  =>  9 pairs (_)
E1,G1: 7.. / E1 = 7  => 15 pairs (_) / G1 = 7  =>  8 pairs (_)
E3,G3: 7.. / E3 = 7  =>  8 pairs (_) / G3 = 7  => 15 pairs (_)
A5,A7: 7.. / A5 = 7  =>  9 pairs (_) / A7 = 7  => 15 pairs (_)
B5,B7: 7.. / B5 = 7  => 15 pairs (_) / B7 = 7  =>  9 pairs (_)
G5,G6: 9.. / G5 = 9  =>  8 pairs (_) / G6 = 9  => 14 pairs (_)
A9,B9: 9.. / A9 = 9  => 12 pairs (_) / B9 = 9  => 10 pairs (_)
A6,G6: 9.. / A6 = 9  =>  8 pairs (_) / G6 = 9  => 14 pairs (_)
B5,B9: 9.. / B5 = 9  => 12 pairs (_) / B9 = 9  => 10 pairs (_)
* DURATION: 0:00:10.408543  START: 13:40:54.346512  END: 13:41:04.755055 2025-04-05
* CP COUNT: (36)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:11.299460  START: 13:41:10.512601  END: 13:41:21.812061 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00144227-base-pr-002.dot
* REASONING
* PRF # A2: 4 # C4: 2,8 => SOL
* STA # A2: 4 + C4: 2,8
* CNT   1 HDP CHAINS /  51 HYP OPENED

Header Info

rating: 38444; r2: 749214; index: 144227

Solution

position: 123456789457189236689372451218594673745623918936817524372961845561748392894235167 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 # A2: 3,5 => UNS
* INC # A2: 4 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 3 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 6,7,9 => UNS
* INC # I2: 1,2 => UNS
* INC # I2: 6,8 => UNS
* INC # D3: 1,2 => UNS
* INC # D3: 3,4 => UNS
* INC # A5: 5,9 => UNS
* INC # B5: 5,9 => UNS
* INC # A6: 5,9 => UNS
* INC # A6: 2,8 => UNS
* INC # B5: 6,7 => UNS
* INC # B5: 4,5,9 => UNS
* INC # B5: 6,9 => UNS
* INC # B5: 4,5,7 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 3,5 => UNS
* INC # A2: 4 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 3 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 6,7,9 => UNS
* INC # I2: 1,2 => UNS
* INC # I2: 6,8 => UNS
* INC # D3: 1,2 => UNS
* INC # D3: 3,4 => UNS
* INC # A5: 5,9 => UNS
* INC # B5: 5,9 => UNS
* INC # A6: 5,9 => UNS
* INC # A6: 2,8 => UNS
* INC # B5: 6,7 => UNS
* INC # B5: 4,5,9 => UNS
* INC # B5: 6,9 => UNS
* INC # B5: 4,5,7 => UNS
* CNT  18 HDP CHAINS /  18 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A2: 3,5 => UNS
* INC # A2: 4 => UNS
* INC # A2: 4,5 => UNS
* INC # A2: 3 => UNS
* INC # B5: 4,5 => UNS
* INC # B5: 6,7,9 => UNS
* INC # I2: 1,2 => UNS
* INC # I2: 6,8 => UNS
* INC # D3: 1,2 => UNS
* INC # D3: 3,4 => UNS
* INC # A5: 5,9 => UNS
* INC # B5: 5,9 => UNS
* INC # A6: 5,9 => UNS
* INC # A6: 2,8 => UNS
* INC # B5: 6,7 => UNS
* INC # B5: 4,5,9 => UNS
* INC # B5: 6,9 => UNS
* INC # B5: 4,5,7 => UNS
* INC # A2: 3,5 # I2: 1,2 => UNS
* INC # A2: 3,5 # I2: 6,8 => UNS
* INC # A2: 3,5 # D3: 1,2 => UNS
* INC # A2: 3,5 # D3: 3,4 => UNS
* INC # A2: 3,5 # C4: 1,6 => UNS
* INC # A2: 3,5 # C4: 2,8 => UNS
* INC # A2: 3,5 # B8: 1,6 => UNS
* INC # A2: 3,5 # B8: 5 => UNS
* INC # A2: 3,5 # A5: 5,9 => UNS
* INC # A2: 3,5 # B5: 5,9 => UNS
* INC # A2: 3,5 # A6: 5,9 => UNS
* INC # A2: 3,5 # A6: 2,8 => UNS
* INC # A2: 3,5 # B5: 6,7 => UNS
* INC # A2: 3,5 # B5: 5,9 => UNS
* INC # A2: 3,5 # B5: 6,9 => UNS
* INC # A2: 3,5 # B5: 5,7 => UNS
* INC # A2: 3,5 => UNS
* INC # A2: 4 # D3: 2,3 => UNS
* INC # A2: 4 # D3: 1 => UNS
* INC # A2: 4 # F5: 2,3 => UNS
* INC # A2: 4 # F5: 4,6,8 => UNS
* INC # A2: 4 # G2: 6,8 => UNS
* INC # A2: 4 # I2: 6,8 => UNS
* INC # A2: 4 # D1: 6,8 => UNS
* INC # A2: 4 # F1: 6,8 => UNS
* INC # A2: 4 # H6: 6,8 => UNS
* INC # A2: 4 # H9: 6,8 => UNS
* INC # A2: 4 # I2: 1,2 => UNS
* INC # A2: 4 # I2: 6,8 => UNS
* INC # A2: 4 # D3: 1,2 => UNS
* INC # A2: 4 # D3: 3 => UNS
* PRF # A2: 4 # C4: 2,8 => SOL
* STA # A2: 4 + C4: 2,8
* CNT  50 HDP CHAINS /  51 HYP OPENED