Analysis of xx-mith-te3-00094817-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: ...4.678...718.2....8.72...27..4186........4.8...6.1.753.......7.1.24...9.....6.. initial

Autosolve

position: ...4.678...718.2....8.72.1.27..4186........428..26.1.753.......7.1.24...9.....6.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

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

Pair Reduction

Pair Reduction

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

Deep Pair Reduction

Deep Pair Reduction

Time used: 0:00:05.509425

The following important HDP chains were detected:

* PRF # A5: 1,3 # I3: 3,5,9 => SOL
* STA # A5: 1,3 + I3: 3,5,9
* CNT   1 HDP CHAINS /  21 HYP OPENED

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

Details

Positions

...4.678...718.2....8.72...27..4186........4.8...6.1.753.......7.1.24...9.....6.. initial
...4.678...718.2....8.72.1.27..4186........428..26.1.753.......7.1.24...9.....6.. autosolve
123456789457189236698372415279541863316897542845263197532618974761924358984735621 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (9)
A1: 1,3
D5: 7,8
F5: 7,8
B8: 6,8
C9: 2,4
E7: 1,9
G7: 4,9
H7: 2,7
H9: 2,7

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B1: 1.. / A1 = 1  =>  9 pairs (_) / B1 = 1  => 13 pairs (_)
A5,B5: 1.. / A5 = 1  => 13 pairs (_) / B5 = 1  =>  9 pairs (_)
E7,E9: 1.. / E7 = 1  => 10 pairs (_) / E9 = 1  => 14 pairs (_)
I7,I9: 1.. / I7 = 1  => 14 pairs (_) / I9 = 1  => 10 pairs (_)
E7,I7: 1.. / E7 = 1  => 10 pairs (_) / I7 = 1  => 14 pairs (_)
E9,I9: 1.. / E9 = 1  => 14 pairs (_) / I9 = 1  => 10 pairs (_)
A1,A5: 1.. / A1 = 1  =>  9 pairs (_) / A5 = 1  => 13 pairs (_)
B1,B5: 1.. / B1 = 1  => 13 pairs (_) / B5 = 1  =>  9 pairs (_)
B1,C1: 2.. / B1 = 2  => 10 pairs (_) / C1 = 2  => 10 pairs (_)
H7,H9: 2.. / H7 = 2  =>  8 pairs (_) / H9 = 2  => 18 pairs (_)
C7,H7: 2.. / C7 = 2  => 18 pairs (_) / H7 = 2  =>  8 pairs (_)
B1,B9: 2.. / B1 = 2  => 10 pairs (_) / B9 = 2  => 10 pairs (_)
A2,A3: 4.. / A2 = 4  => 10 pairs (_) / A3 = 4  => 11 pairs (_)
B6,C6: 4.. / B6 = 4  => 10 pairs (_) / C6 = 4  => 11 pairs (_)
A2,I2: 4.. / A2 = 4  => 10 pairs (_) / I2 = 4  => 11 pairs (_)
B6,B9: 4.. / B6 = 4  => 10 pairs (_) / B9 = 4  => 11 pairs (_)
G3,G7: 4.. / G3 = 4  =>  0 pairs (*) / G7 = 4  =>  0 pairs (X)
I2,I3: 6.. / I2 = 6  => 11 pairs (_) / I3 = 6  => 11 pairs (_)
C7,B8: 6.. / C7 = 6  => 12 pairs (_) / B8 = 6  => 18 pairs (_)
D7,D8: 6.. / D7 = 6  => 18 pairs (_) / D8 = 6  => 12 pairs (_)
C7,D7: 6.. / C7 = 6  => 12 pairs (_) / D7 = 6  => 18 pairs (_)
B8,D8: 6.. / B8 = 6  => 18 pairs (_) / D8 = 6  => 12 pairs (_)
C5,C7: 6.. / C5 = 6  => 18 pairs (_) / C7 = 6  => 12 pairs (_)
D5,F5: 7.. / D5 = 7  =>  8 pairs (_) / F5 = 7  => 10 pairs (_)
H7,H9: 7.. / H7 = 7  => 18 pairs (_) / H9 = 7  =>  8 pairs (_)
D5,F5: 8.. / D5 = 8  => 10 pairs (_) / F5 = 8  =>  8 pairs (_)
B8,B9: 8.. / B8 = 8  => 12 pairs (_) / B9 = 8  => 18 pairs (_)
* DURATION: 0:00:09.155957  START: 14:45:09.931012  END: 14:45:19.086969 2025-04-06
* CP COUNT: (27)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:05.377292  START: 14:45:25.272452  END: 14:45:30.649744 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00094817-base-pr-002.dot
* REASONING
* PRF # A5: 1,3 # I3: 3,5,9 => SOL
* STA # A5: 1,3 + I3: 3,5,9
* CNT   1 HDP CHAINS /  21 HYP OPENED

Header Info

rating: 23974; r2: 754315; index: 94817

Solution

position: 123456789457189236698372415279541863316897542845263197532618974761924358984735621 solved
Solution

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 # A5: 1,3 => UNS
* INC # A5: 6 => UNS
* INC # D7: 7,8 => UNS
* INC # D9: 7,8 => UNS
* INC # F7: 7,8 => UNS
* INC # F9: 7,8 => UNS
* INC # D8: 6,8 => UNS
* INC # D8: 3,5,9 => UNS
* INC # C7: 2,4 => UNS
* INC # B9: 2,4 => UNS
* INC # I7: 1,9 => UNS
* INC # I7: 4,8 => UNS
* INC # I7: 4,9 => UNS
* INC # I7: 1,8 => UNS
* INC # G3: 4,9 => UNS
* INC # G3: 3,5 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 1,3 => UNS
* INC # A5: 6 => UNS
* INC # D7: 7,8 => UNS
* INC # D9: 7,8 => UNS
* INC # F7: 7,8 => UNS
* INC # F9: 7,8 => UNS
* INC # D8: 6,8 => UNS
* INC # D8: 3,5,9 => UNS
* INC # C7: 2,4 => UNS
* INC # B9: 2,4 => UNS
* INC # I7: 1,9 => UNS
* INC # I7: 4,8 => UNS
* INC # I7: 4,9 => UNS
* INC # I7: 1,8 => UNS
* INC # G3: 4,9 => UNS
* INC # G3: 3,5 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # A5: 1,3 => UNS
* INC # A5: 6 => UNS
* INC # D7: 7,8 => UNS
* INC # D9: 7,8 => UNS
* INC # F7: 7,8 => UNS
* INC # F9: 7,8 => UNS
* INC # D8: 6,8 => UNS
* INC # D8: 3,5,9 => UNS
* INC # C7: 2,4 => UNS
* INC # B9: 2,4 => UNS
* INC # I7: 1,9 => UNS
* INC # I7: 4,8 => UNS
* INC # I7: 4,9 => UNS
* INC # I7: 1,8 => UNS
* INC # G3: 4,9 => UNS
* INC # G3: 3,5 => UNS
* INC # A5: 1,3 # F2: 5,9 => UNS
* INC # A5: 1,3 # H2: 5,9 => UNS
* INC # A5: 1,3 # I3: 4,6 => UNS
* PRF # A5: 1,3 # I3: 3,5,9 => SOL
* STA # A5: 1,3 + I3: 3,5,9
* CNT  20 HDP CHAINS /  21 HYP OPENED