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: 0:00:02.897049

The following important HDP chains were detected:

* PRF # D1: 4,5 # D6: 2,3 => SOL
* STA # D1: 4,5 + D6: 2,3
* CNT   1 HDP CHAINS /  11 HYP OPENED

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

Positions

.23..6...456.89...7.9.....4...96.8.76...1.49.9......16..18.4.......91.48....7....	initial
.23..6...456.89...7.9.....4...96.8.76...1.49.9......16..18.4.......91.48....7....	autosolve
123456789456789123789132564214963857638517492975248316391824675567391248842675931	solved

Classification

level: hard

Pairing Analysis

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* PAIRS (5)
A1: 1,8
B3: 1,8
E1: 4,5
F5: 7,8
F6: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,B3: 1.. / A1 = 1  => 12 pairs (_) / B3 = 1  => 10 pairs (_)
A4,B4: 1.. / A4 = 1  => 10 pairs (_) / B4 = 1  => 12 pairs (_)
G9,I9: 1.. / G9 = 1  =>  5 pairs (_) / I9 = 1  =>  7 pairs (_)
A1,A4: 1.. / A1 = 1  => 12 pairs (_) / A4 = 1  => 10 pairs (_)
B3,B4: 1.. / B3 = 1  => 10 pairs (_) / B4 = 1  => 12 pairs (_)
D1,E1: 4.. / D1 = 4  => 13 pairs (_) / E1 = 4  =>  4 pairs (_)
B4,C4: 4.. / B4 = 4  => 10 pairs (_) / C4 = 4  => 10 pairs (_)
D6,E6: 4.. / D6 = 4  =>  4 pairs (_) / E6 = 4  => 13 pairs (_)
B9,C9: 4.. / B9 = 4  => 10 pairs (_) / C9 = 4  => 10 pairs (_)
B4,B9: 4.. / B4 = 4  => 10 pairs (_) / B9 = 4  => 10 pairs (_)
C4,C9: 4.. / C4 = 4  => 10 pairs (_) / C9 = 4  => 10 pairs (_)
D1,D6: 4.. / D1 = 4  => 13 pairs (_) / D6 = 4  =>  4 pairs (_)
E1,E6: 4.. / E1 = 4  =>  4 pairs (_) / E6 = 4  => 13 pairs (_)
G3,H3: 6.. / G3 = 6  =>  5 pairs (_) / H3 = 6  => 11 pairs (_)
D8,D9: 6.. / D8 = 6  =>  0 pairs (X) / D9 = 6  =>  5 pairs (_)
D1,D2: 7.. / D1 = 7  =>  5 pairs (_) / D2 = 7  =>  8 pairs (_)
F5,F6: 7.. / F5 = 7  =>  5 pairs (_) / F6 = 7  =>  5 pairs (_)
A1,B3: 8.. / A1 = 8  => 10 pairs (_) / B3 = 8  => 12 pairs (_)
H1,H3: 8.. / H1 = 8  => 12 pairs (_) / H3 = 8  => 10 pairs (_)
F5,F6: 8.. / F5 = 8  =>  5 pairs (_) / F6 = 8  =>  5 pairs (_)
A1,H1: 8.. / A1 = 8  => 10 pairs (_) / H1 = 8  => 12 pairs (_)
B3,H3: 8.. / B3 = 8  => 12 pairs (_) / H3 = 8  => 10 pairs (_)
A1,A9: 8.. / A1 = 8  => 10 pairs (_) / A9 = 8  => 12 pairs (_)
G1,I1: 9.. / G1 = 9  =>  6 pairs (_) / I1 = 9  =>  6 pairs (_)
B7,B9: 9.. / B7 = 9  =>  9 pairs (_) / B9 = 9  =>  0 pairs (X)
* DURATION: 0:00:07.485945  START: 19:05:39.128669  END: 19:05:46.614614 2025-04-06
* CP COUNT: (25)
* CLUE FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:02.783369  START: 19:05:49.153451  END: 19:05:51.936820 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00119878-base-pr-002.dot
* REASONING
* PRF # D1: 4,5 # D6: 2,3 => SOL
* STA # D1: 4,5 + D6: 2,3
* CNT   1 HDP CHAINS /  11 HYP OPENED

Header Info

rating: 31245; r2: 831165; index: 119878

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # D1: 4,5 => UNS
* INC # D1: 1,7 => UNS
* INC # E6: 4,5 => UNS
* INC # E6: 2,3 => UNS
* INC # B5: 7,8 => UNS
* INC # C5: 7,8 => UNS
* INC # B6: 7,8 => UNS
* INC # C6: 7,8 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 4,5 => UNS
* INC # D1: 1,7 => UNS
* INC # E6: 4,5 => UNS
* INC # E6: 2,3 => UNS
* INC # B5: 7,8 => UNS
* INC # C5: 7,8 => UNS
* INC # B6: 7,8 => UNS
* INC # C6: 7,8 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # D1: 4,5 => UNS
* INC # D1: 1,7 => UNS
* INC # E6: 4,5 => UNS
* INC # E6: 2,3 => UNS
* INC # B5: 7,8 => UNS
* INC # C5: 7,8 => UNS
* INC # B6: 7,8 => UNS
* INC # C6: 7,8 => UNS
* INC # D1: 4,5 # D6: 4,5 => UNS
* PRF # D1: 4,5 # D6: 2,3 => SOL
* STA # D1: 4,5 + D6: 2,3
* CNT  10 HDP CHAINS /  11 HYP OPENED