Analysis of xx-mith-te3-00073339-base.sdk

Contents

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

Original Sudoku

level: hard

position: 12.4.6.894.6.......982...6.....4..37...1....564....2.8.629.48..8.4..19..9..8..... initial

Autosolve

position: 12.4.6.894.6.......9821..6.....4..37...1....564....2.8.629.48..8.4..19..9..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: 0:00:07.070115

The following important HDP chains were detected:

* DIS # E5: 2,3,6,7 # B2: 3,7 => CTR => B2: 5
* PRF # E5: 2,3,6,7 + B2: 5 => SOL
* STA E5: 2,3,6,7
* CNT   2 HDP CHAINS /  35 HYP OPENED

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

Details

Positions

`12.4.6.894.6.......982...6.....4..37...1....564....2.8.629.48..8.4..19..9..8.....`	initial
`12.4.6.894.6.......9821..6.....4..37...1....564....2.8.629.48..8.4..19..9..8.....`	autosolve
`123456789456789123798213564219548637387162495645397218562934871834671952971825346`	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (10)
E2: 8,9
F2: 8,9
I3: 3,4
A4: 2,5
D4: 5,6
G4: 1,6
G5: 4,6
H5: 4,9
H6: 1,9
I7: 1,3

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G4,H6: 1.. / G4 = 1  => 13 pairs (_) / H6 = 1  =>  9 pairs (_)
B9,C9: 1.. / B9 = 1  => 11 pairs (_) / C9 = 1  =>  9 pairs (_)
H7,I7: 1.. / H7 = 1  => 14 pairs (_) / I7 = 1  => 11 pairs (_)
C6,H6: 1.. / C6 = 1  => 13 pairs (_) / H6 = 1  =>  9 pairs (_)
B4,B9: 1.. / B4 = 1  =>  9 pairs (_) / B9 = 1  => 11 pairs (_)
G2,G4: 1.. / G2 = 1  =>  9 pairs (_) / G4 = 1  => 13 pairs (_)
I2,I7: 1.. / I2 = 1  => 14 pairs (_) / I7 = 1  => 11 pairs (_)
H2,I2: 2.. / H2 = 2  => 14 pairs (_) / I2 = 2  => 11 pairs (_)
A4,A5: 2.. / A4 = 2  => 10 pairs (_) / A5 = 2  => 15 pairs (_)
A4,F4: 2.. / A4 = 2  => 10 pairs (_) / F4 = 2  => 15 pairs (_)
G3,I3: 4.. / G3 = 4  => 16 pairs (_) / I3 = 4  =>  9 pairs (_)
G5,H5: 4.. / G5 = 4  =>  9 pairs (_) / H5 = 4  => 13 pairs (_)
H5,H9: 4.. / H5 = 4  => 13 pairs (_) / H9 = 4  =>  9 pairs (_)
I3,I9: 4.. / I3 = 4  =>  9 pairs (_) / I9 = 4  => 16 pairs (_)
D4,E5: 6.. / D4 = 6  => 13 pairs (_) / E5 = 6  =>  9 pairs (_)
G4,G5: 6.. / G4 = 6  =>  9 pairs (_) / G5 = 6  => 13 pairs (_)
I8,I9: 6.. / I8 = 6  => 12 pairs (_) / I9 = 6  => 10 pairs (_)
D4,G4: 6.. / D4 = 6  => 13 pairs (_) / G4 = 6  =>  9 pairs (_)
E5,G5: 6.. / E5 = 6  =>  9 pairs (_) / G5 = 6  => 13 pairs (_)
E9,I9: 6.. / E9 = 6  => 12 pairs (_) / I9 = 6  => 10 pairs (_)
D4,D8: 6.. / D4 = 6  => 13 pairs (_) / D8 = 6  =>  9 pairs (_)
E2,F2: 8.. / E2 = 8  => 13 pairs (_) / F2 = 8  => 12 pairs (_)
B4,B5: 8.. / B4 = 8  => 11 pairs (_) / B5 = 8  => 12 pairs (_)
B4,F4: 8.. / B4 = 8  => 11 pairs (_) / F4 = 8  => 12 pairs (_)
E2,E5: 8.. / E2 = 8  => 13 pairs (_) / E5 = 8  => 12 pairs (_)
E2,F2: 9.. / E2 = 9  => 12 pairs (_) / F2 = 9  => 13 pairs (_)
H5,H6: 9.. / H5 = 9  =>  9 pairs (_) / H6 = 9  => 13 pairs (_)
C4,F4: 9.. / C4 = 9  => 11 pairs (_) / F4 = 9  => 11 pairs (_)
* DURATION: 0:00:08.988650  START: 19:14:26.029681  END: 19:14:35.018331 2025-04-04
* CP COUNT: (28)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:06.930120  START: 19:14:40.491075  END: 19:14:47.421195 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00073339-base-pr-002.dot
* REASONING
* DIS # E5: 2,3,6,7 # B2: 3,7 => CTR => B2: 5
* PRF # E5: 2,3,6,7 + B2: 5 => SOL
* STA E5: 2,3,6,7
* CNT   2 HDP CHAINS /  35 HYP OPENED

Header Info

rating: 16579; r2: 464933; index: 73339

Solution

position: 123456789456789123798213564219548637387162495645397218562934871834671952971825346 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 # E5: 8,9 => UNS
* INC # E5: 2,3,6,7 => UNS
* INC # F4: 8,9 => UNS
* INC # F5: 8,9 => UNS
* INC # G3: 3,4 => UNS
* INC # G3: 5,7 => UNS
* INC # I9: 3,4 => UNS
* INC # I9: 2,6 => UNS
* INC # F4: 2,5 => UNS
* INC # F4: 8,9 => UNS
* INC # D8: 5,6 => UNS
* INC # D8: 3,7 => UNS
* INC # C6: 1,9 => UNS
* INC # C6: 3,5,7 => UNS
* INC # I2: 1,3 => UNS
* INC # I2: 2 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E5: 8,9 => UNS
* INC # E5: 2,3,6,7 => UNS
* INC # F4: 8,9 => UNS
* INC # F5: 8,9 => UNS
* INC # G3: 3,4 => UNS
* INC # G3: 5,7 => UNS
* INC # I9: 3,4 => UNS
* INC # I9: 2,6 => UNS
* INC # F4: 2,5 => UNS
* INC # F4: 8,9 => UNS
* INC # D8: 5,6 => UNS
* INC # D8: 3,7 => UNS
* INC # C6: 1,9 => UNS
* INC # C6: 3,5,7 => UNS
* INC # I2: 1,3 => UNS
* INC # I2: 2 => UNS
* CNT  16 HDP CHAINS /  16 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E5: 8,9 => UNS
* INC # E5: 2,3,6,7 => UNS
* INC # F4: 8,9 => UNS
* INC # F5: 8,9 => UNS
* INC # G3: 3,4 => UNS
* INC # G3: 5,7 => UNS
* INC # I9: 3,4 => UNS
* INC # I9: 2,6 => UNS
* INC # F4: 2,5 => UNS
* INC # F4: 8,9 => UNS
* INC # D8: 5,6 => UNS
* INC # D8: 3,7 => UNS
* INC # C6: 1,9 => UNS
* INC # C6: 3,5,7 => UNS
* INC # I2: 1,3 => UNS
* INC # I2: 2 => UNS
* INC # E5: 8,9 # F4: 8,9 => UNS
* INC # E5: 8,9 # F5: 8,9 => UNS
* INC # E5: 8,9 # G3: 3,4 => UNS
* INC # E5: 8,9 # G3: 5,7 => UNS
* INC # E5: 8,9 # I9: 3,4 => UNS
* INC # E5: 8,9 # I9: 2,6 => UNS
* INC # E5: 8,9 # F4: 8,9 => UNS
* INC # E5: 8,9 # F5: 8,9 => UNS
* INC # E5: 8,9 # I8: 2,6 => UNS
* INC # E5: 8,9 # I8: 3 => UNS
* INC # E5: 8,9 # I9: 2,6 => UNS
* INC # E5: 8,9 # I9: 3,4 => UNS
* INC # E5: 8,9 # I9: 3,4 => UNS
* INC # E5: 8,9 # I9: 2,6 => UNS
* INC # E5: 8,9 # G3: 3,4 => UNS
* INC # E5: 8,9 # G3: 5,7 => UNS
* INC # E5: 8,9 => UNS
* DIS # E5: 2,3,6,7 # B2: 3,7 => CTR => B2: 5
* PRF # E5: 2,3,6,7 + B2: 5 => SOL
* STA E5: 2,3,6,7
* CNT  35 HDP CHAINS /  35 HYP OPENED