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: 0:00:02.810328

The following important HDP chains were detected:

* PRF # I1: 7,9 # A4: 1,2 => SOL
* STA # I1: 7,9 + A4: 1,2
* CNT   1 HDP CHAINS /  12 HYP OPENED

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

Positions

...456...45....2..86.....1..8...437..34......7.63.58..34.5.8...6.8.47....7563....	initial
...456...45....2..86.....1..8..6437..34......7.63.58..34.5.8...6.8.47....7563....	autosolve
123456789457189236869723514281964375534872691796315842342598167618247953975631428	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (5)
G1: 7,9
G3: 4,5
I3: 4,5
D5: 7,8
E5: 7,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
F2,F3: 3.. / F2 = 3  => 12 pairs (_) / F3 = 3  =>  7 pairs (_)
H8,I8: 3.. / H8 = 3  =>  7 pairs (_) / I8 = 3  =>  5 pairs (_)
C3,F3: 3.. / C3 = 3  => 12 pairs (_) / F3 = 3  =>  7 pairs (_)
G3,I3: 4.. / G3 = 4  =>  6 pairs (_) / I3 = 4  =>  6 pairs (_)
H6,I6: 4.. / H6 = 4  =>  5 pairs (_) / I6 = 4  =>  5 pairs (_)
G3,G9: 4.. / G3 = 4  =>  6 pairs (_) / G9 = 4  =>  6 pairs (_)
H6,H9: 4.. / H6 = 4  =>  5 pairs (_) / H9 = 4  =>  5 pairs (_)
G3,I3: 5.. / G3 = 5  =>  6 pairs (_) / I3 = 5  =>  6 pairs (_)
A4,A5: 5.. / A4 = 5  =>  5 pairs (_) / A5 = 5  =>  4 pairs (_)
A4,I4: 5.. / A4 = 5  =>  5 pairs (_) / I4 = 5  =>  4 pairs (_)
H5,H8: 5.. / H5 = 5  =>  5 pairs (_) / H8 = 5  =>  6 pairs (_)
H2,I2: 6.. / H2 = 6  =>  8 pairs (_) / I2 = 6  =>  6 pairs (_)
G5,G7: 6.. / G5 = 6  =>  5 pairs (_) / G7 = 6  =>  5 pairs (_)
D5,E5: 7.. / D5 = 7  =>  4 pairs (_) / E5 = 7  =>  4 pairs (_)
G7,I7: 7.. / G7 = 7  => 13 pairs (_) / I7 = 7  =>  4 pairs (_)
G1,G7: 7.. / G1 = 7  =>  4 pairs (_) / G7 = 7  => 13 pairs (_)
D2,E2: 8.. / D2 = 8  =>  4 pairs (_) / E2 = 8  =>  4 pairs (_)
H1,I1: 8.. / H1 = 8  =>  5 pairs (_) / I1 = 8  =>  6 pairs (_)
D5,E5: 8.. / D5 = 8  =>  4 pairs (_) / E5 = 8  =>  4 pairs (_)
H9,I9: 8.. / H9 = 8  =>  6 pairs (_) / I9 = 8  =>  5 pairs (_)
D2,D5: 8.. / D2 = 8  =>  4 pairs (_) / D5 = 8  =>  4 pairs (_)
E2,E5: 8.. / E2 = 8  =>  4 pairs (_) / E5 = 8  =>  4 pairs (_)
H1,H9: 8.. / H1 = 8  =>  5 pairs (_) / H9 = 8  =>  6 pairs (_)
I1,I9: 8.. / I1 = 8  =>  6 pairs (_) / I9 = 8  =>  5 pairs (_)
* DURATION: 0:00:06.661799  START: 03:53:41.500474  END: 03:53:48.162273 2025-04-05
* CP COUNT: (24)
* INCONCLUSIVE

* DEEP PAIR REDUCTION
* DURATION: 0:00:02.697616  START: 03:53:51.486853  END: 03:53:54.184469 2025-04-05
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00112913-base-pr-002.dot
* REASONING
* PRF # I1: 7,9 # A4: 1,2 => SOL
* STA # I1: 7,9 + A4: 1,2
* CNT   1 HDP CHAINS /  12 HYP OPENED

Header Info

rating: 28802; r2: 567768; index: 112913

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # I1: 7,9 => UNS
* INC # I2: 7,9 => UNS
* INC # C1: 7,9 => UNS
* INC # C1: 1,2,3 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 1,6 => UNS
* INC # D2: 7,8 => UNS
* INC # D2: 1,9 => UNS
* INC # E2: 7,8 => UNS
* INC # E2: 1,9 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 7,9 => UNS
* INC # I2: 7,9 => UNS
* INC # C1: 7,9 => UNS
* INC # C1: 1,2,3 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 1,6 => UNS
* INC # D2: 7,8 => UNS
* INC # D2: 1,9 => UNS
* INC # E2: 7,8 => UNS
* INC # E2: 1,9 => UNS
* CNT  10 HDP CHAINS /  10 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # I1: 7,9 => UNS
* INC # I2: 7,9 => UNS
* INC # C1: 7,9 => UNS
* INC # C1: 1,2,3 => UNS
* INC # G7: 7,9 => UNS
* INC # G7: 1,6 => UNS
* INC # D2: 7,8 => UNS
* INC # D2: 1,9 => UNS
* INC # E2: 7,8 => UNS
* INC # E2: 1,9 => UNS
* PRF # I1: 7,9 # A4: 1,2 => SOL
* STA # I1: 7,9 + A4: 1,2
* CNT  11 HDP CHAINS /  12 HYP OPENED