Analysis of xx-mith-te3-00085723-base.sdk

Contents

Original Sudoku

level: hard

Original Sudoku

position: 1...56.8....18....6.82.7.5.2.6...9.3...7.25..5.....42.76.......8.2..16.5..16..8.. initial

Autosolve

position: 1...56.8....18....6.82.7.5.2.6...9.3...7.25..5.....42.76.......8.2..16.5..16..8.. 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: 0:00:06.348962

The following important HDP chains were detected:

* DIS # G7: 1,3 # B1: 3,4,9 => CTR => B1: 2,7
* DIS # G7: 1,3 + B1: 2,7 # H2: 4,9 => CTR => H2: 3,6
* PRF # G7: 1,3 + B1: 2,7 + H2: 3,6 # B2: 5 => SOL
* STA # G7: 1,3 + B1: 2,7 + H2: 3,6 + B2: 5
* CNT   3 HDP CHAINS /  26 HYP OPENED

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

Details

Positions

1...56.8....18....6.82.7.5.2.6...9.3...7.25..5.....42.76.......8.2..16.5..16..8.. initial
1...56.8....18....6.82.7.5.2.6...9.3...7.25..5.....42.76.......8.2..16.5..16..8.. autosolve
123456789457189236698237154286514973314792568579863421765948312842371695931625847 solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (4)
G3: 1,3
E4: 1,4
H4: 1,7
H5: 1,6

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
G3,I3: 1.. / G3 = 1  =>  5 pairs (_) / I3 = 1  => 10 pairs (_)
G3,G7: 1.. / G3 = 1  =>  5 pairs (_) / G7 = 1  => 10 pairs (_)
B1,B2: 2.. / B1 = 2  =>  6 pairs (_) / B2 = 2  =>  7 pairs (_)
E7,E9: 2.. / E7 = 2  =>  0 pairs (X) / E9 = 2  =>  4 pairs (_)
E9,I9: 2.. / E9 = 2  =>  4 pairs (_) / I9 = 2  =>  0 pairs (X)
B2,C2: 5.. / B2 = 5  =>  0 pairs (*) / C2 = 5  =>  0 pairs (X)
D4,F4: 5.. / D4 = 5  =>  5 pairs (_) / F4 = 5  =>  6 pairs (_)
C7,B9: 5.. / C7 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
B9,F9: 5.. / B9 = 5  =>  6 pairs (_) / F9 = 5  =>  0 pairs (*)
B2,B9: 5.. / B2 = 5  =>  0 pairs (*) / B9 = 5  =>  0 pairs (X)
C2,C7: 5.. / C2 = 5  =>  6 pairs (_) / C7 = 5  =>  0 pairs (*)
D4,D7: 5.. / D4 = 5  =>  5 pairs (_) / D7 = 5  =>  6 pairs (_)
H2,I2: 6.. / H2 = 6  =>  6 pairs (_) / I2 = 6  =>  6 pairs (_)
E5,E6: 6.. / E5 = 6  => 10 pairs (_) / E6 = 6  =>  4 pairs (_)
E6,I6: 6.. / E6 = 6  =>  4 pairs (_) / I6 = 6  => 10 pairs (_)
H2,H5: 6.. / H2 = 6  =>  6 pairs (_) / H5 = 6  =>  6 pairs (_)
G1,G2: 7.. / G1 = 7  =>  8 pairs (_) / G2 = 7  =>  5 pairs (_)
H4,I6: 7.. / H4 = 7  =>  3 pairs (_) / I6 = 7  =>  0 pairs (X)
E8,E9: 7.. / E8 = 7  =>  4 pairs (_) / E9 = 7  =>  0 pairs (X)
B4,H4: 7.. / B4 = 7  =>  0 pairs (X) / H4 = 7  =>  3 pairs (_)
E8,H8: 7.. / E8 = 7  =>  4 pairs (_) / H8 = 7  =>  0 pairs (X)
I6,I9: 7.. / I6 = 7  =>  0 pairs (X) / I9 = 7  =>  3 pairs (_)
I5,I6: 8.. / I5 = 8  =>  4 pairs (_) / I6 = 8  => 18 pairs (_)
D7,F7: 8.. / D7 = 8  =>  6 pairs (_) / F7 = 8  =>  6 pairs (_)
B5,I5: 8.. / B5 = 8  => 18 pairs (_) / I5 = 8  =>  4 pairs (_)
* DURATION: 0:00:05.893838  START: 22:07:52.280820  END: 22:07:58.174658 2025-04-04
* CP COUNT: (25)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:06.225336  START: 22:08:02.121503  END: 22:08:08.346839 2025-04-04
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00085723-base-pr-002.dot
* REASONING
* DIS # G7: 1,3 # B1: 3,4,9 => CTR => B1: 2,7
* DIS # G7: 1,3 + B1: 2,7 # H2: 4,9 => CTR => H2: 3,6
* PRF # G7: 1,3 + B1: 2,7 + H2: 3,6 # B2: 5 => SOL
* STA # G7: 1,3 + B1: 2,7 + H2: 3,6 + B2: 5
* CNT   3 HDP CHAINS /  26 HYP OPENED

Header Info

rating: 21474; r2: 470016; index: 85723

Solution

position: 123456789457189236698237154286514973314792568579863421765948312842371695931625847 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 # E5: 1,4 => UNS
* INC # E5: 3,6,9 => UNS
* INC # B4: 1,4 => UNS
* INC # B4: 7,8 => UNS
* INC # I6: 1,7 => UNS
* INC # I6: 6,8 => UNS
* INC # B4: 1,7 => UNS
* INC # B4: 4,8 => UNS
* INC # I5: 1,6 => UNS
* INC # I6: 1,6 => UNS
* INC # E5: 1,6 => UNS
* INC # E5: 3,4,9 => 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 # E5: 1,4 => UNS
* INC # E5: 3,6,9 => UNS
* INC # B4: 1,4 => UNS
* INC # B4: 7,8 => UNS
* INC # I6: 1,7 => UNS
* INC # I6: 6,8 => UNS
* INC # B4: 1,7 => UNS
* INC # B4: 4,8 => UNS
* INC # I5: 1,6 => UNS
* INC # I6: 1,6 => UNS
* INC # E5: 1,6 => UNS
* INC # E5: 3,4,9 => 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 # E5: 1,4 => UNS
* INC # E5: 3,6,9 => UNS
* INC # B4: 1,4 => UNS
* INC # B4: 7,8 => UNS
* INC # I6: 1,7 => UNS
* INC # I6: 6,8 => UNS
* INC # B4: 1,7 => UNS
* INC # B4: 4,8 => UNS
* INC # I5: 1,6 => UNS
* INC # I6: 1,6 => UNS
* INC # E5: 1,6 => UNS
* INC # E5: 3,4,9 => 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
* DIS # G7: 1,3 + B1: 2,7 # H2: 4,9 => CTR => H2: 3,6
* INC # G7: 1,3 + B1: 2,7 + H2: 3,6 # I2: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 + H2: 3,6 # I3: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 + H2: 3,6 # C1: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 + H2: 3,6 # D1: 4,9 => UNS
* INC # G7: 1,3 + B1: 2,7 + H2: 3,6 # B2: 2,7 => UNS
* PRF # G7: 1,3 + B1: 2,7 + H2: 3,6 # B2: 5 => SOL
* STA # G7: 1,3 + B1: 2,7 + H2: 3,6 + B2: 5
* CNT  25 HDP CHAINS /  26 HYP OPENED