Analysis of xx-mith-te3-00085722-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1...56.8....18....6.87.2.5.2.....973...2.75.85.....42.76.......8.2.71..5..162.8.7 initial

Autosolve

position: 1...56.8....18....6.87.2.5.2.....973...2.75.85.....42.76.......8.2.71..5..162.8.7 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: 0:00:06.187806

The following important HDP chains were detected:

* DIS # G7: 1,3 # B1: 3,4,9 => CTR => B1: 2,7
* PRF # G7: 1,3 + B1: 2,7 # B2: 5 => SOL
* STA # G7: 1,3 + B1: 2,7 + B2: 5
* CNT   2 HDP CHAINS /  25 HYP OPENED

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

Details

Positions

1...56.8....18....6.87.2.5.2.....973...2.75.85.....42.76.......8.2.71..5..162.8.7 initial
1...56.8....18....6.87.2.5.2.....973...2.75.85.....42.76.......8.2.71..5..162.8.7 autosolve
123456789457189236698732154286514973314297568579863421765948312842371695931625847 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
G3: 1,3
C4: 4,6
H5: 1,6
I6: 1,6
G8: 3,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  6 pairs (_) / I3 = 1  => 14 pairs (_)
H5,I6: 1.. / H5 = 1  => 13 pairs (_) / I6 = 1  =>  5 pairs (_)
B4,E4: 1.. / B4 = 1  => 17 pairs (_) / E4 = 1  =>  5 pairs (_)
G3,G7: 1.. / G3 = 1  =>  6 pairs (_) / G7 = 1  => 14 pairs (_)
H5,H7: 1.. / H5 = 1  => 13 pairs (_) / H7 = 1  =>  5 pairs (_)
B1,B2: 2.. / B1 = 2  =>  7 pairs (_) / B2 = 2  =>  7 pairs (_)
G7,I7: 2.. / G7 = 2  =>  6 pairs (_) / I7 = 2  => 10 pairs (_)
B2,C2: 5.. / B2 = 5  =>  0 pairs (*) / C2 = 5  =>  0 pairs (X)
D4,F4: 5.. / D4 = 5  =>  6 pairs (_) / F4 = 5  =>  7 pairs (_)
C7,B9: 5.. / C7 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
B9,F9: 5.. / B9 = 5  =>  7 pairs (_) / F9 = 5  =>  0 pairs (*)
B2,B9: 5.. / B2 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
C2,C7: 5.. / C2 = 5  =>  7 pairs (_) / C7 = 5  =>  0 pairs (*)
D4,D7: 5.. / D4 = 5  =>  6 pairs (_) / D7 = 5  =>  7 pairs (_)
H5,I6: 6.. / H5 = 6  =>  5 pairs (_) / I6 = 6  => 13 pairs (_)
G8,H8: 6.. / G8 = 6  =>  4 pairs (_) / H8 = 6  => 14 pairs (_)
C4,E4: 6.. / C4 = 6  =>  5 pairs (_) / E4 = 6  => 20 pairs (_)
G2,G8: 6.. / G2 = 6  => 14 pairs (_) / G8 = 6  =>  4 pairs (_)
I2,I6: 6.. / I2 = 6  =>  5 pairs (_) / I6 = 6  => 13 pairs (_)
G1,G2: 7.. / G1 = 7  =>  8 pairs (_) / G2 = 7  =>  5 pairs (_)
B6,C6: 7.. / B6 = 7  =>  9 pairs (_) / C6 = 7  =>  9 pairs (_)
B4,B6: 8.. / B4 = 8  =>  6 pairs (_) / B6 = 8  => 17 pairs (_)
D7,F7: 8.. / D7 = 8  =>  7 pairs (_) / F7 = 8  =>  7 pairs (_)
* DURATION: 0:00:06.039848  START: 12:35:29.753012  END: 12:35:35.792860 2025-04-06
* CP COUNT: (23)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:06.065129  START: 12:35:39.691715  END: 12:35:45.756844 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00085722-base-pr-002.dot
* REASONING
* DIS # G7: 1,3 # B1: 3,4,9 => CTR => B1: 2,7
* PRF # G7: 1,3 + B1: 2,7 # B2: 5 => SOL
* STA # G7: 1,3 + B1: 2,7 + B2: 5
* CNT   2 HDP CHAINS /  25 HYP OPENED

Header Info

rating: 21473; r2: 448117; index: 85722

Solution

position: 123456789457189236698732154286514973314297568579863421765948312842371695931625847 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 # G7: 1,3 => UNS
* INC # G7: 2 => UNS
* INC # C5: 4,6 => UNS
* INC # C5: 3,9 => UNS
* INC # E4: 4,6 => UNS
* INC # E4: 1 => UNS
* INC # E5: 1,6 => UNS
* INC # E5: 3,4,9 => UNS
* INC # E6: 1,6 => UNS
* INC # E6: 3,9 => UNS
* INC # H8: 3,6 => UNS
* INC # H8: 4,9 => UNS
* INC # G2: 3,6 => UNS
* INC # G2: 2,7 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # G7: 1,3 => UNS
* INC # G7: 2 => UNS
* INC # C5: 4,6 => UNS
* INC # C5: 3,9 => UNS
* INC # E4: 4,6 => UNS
* INC # E4: 1 => UNS
* INC # E5: 1,6 => UNS
* INC # E5: 3,4,9 => UNS
* INC # E6: 1,6 => UNS
* INC # E6: 3,9 => UNS
* INC # H8: 3,6 => UNS
* INC # H8: 4,9 => UNS
* INC # G2: 3,6 => UNS
* INC # G2: 2,7 => UNS
* CNT  14 HDP CHAINS /  14 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # G7: 1,3 => UNS
* INC # G7: 2 => UNS
* INC # C5: 4,6 => UNS
* INC # C5: 3,9 => UNS
* INC # E4: 4,6 => UNS
* INC # E4: 1 => UNS
* INC # E5: 1,6 => UNS
* INC # E5: 3,4,9 => UNS
* INC # E6: 1,6 => UNS
* INC # E6: 3,9 => UNS
* INC # H8: 3,6 => UNS
* INC # H8: 4,9 => UNS
* INC # G2: 3,6 => UNS
* INC # G2: 2,7 => UNS
* INC # G7: 1,3 # B2: 5,7 => UNS
* INC # G7: 1,3 # B2: 2 => UNS
* INC # G7: 1,3 # B1: 2,7 => UNS
* DIS # G7: 1,3 # B1: 3,4,9 => CTR => B1: 2,7
* INC # G7: 1,3 + B1: 2,7 # I2: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 # I3: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 # C1: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 # D1: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 # B2: 2,7 => UNS
* PRF # G7: 1,3 + B1: 2,7 # B2: 5 => SOL
* STA # G7: 1,3 + B1: 2,7 + B2: 5
* CNT  24 HDP CHAINS /  25 HYP OPENED