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: 0:00:04.554970

The following important HDP chains were detected:

* PRF # E3: 2,5 # I2: 1,6 => SOL
* STA # E3: 2,5 + I2: 1,6
* CNT   1 HDP CHAINS /  14 HYP OPENED

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

Positions

..34.........892...9...7...2.5......31...582..8.2.1.535...9..18..8.1.59.9.1...3.2	initial
..34.6.......892...9...7...2.5......31...582..8.2.1.535...9..18..8.1.59.9.1...3.2	autosolve
123456789457189236896327145275834961314965827689271453542793618738612594961548372	solved

Classification

level: hard

Pairing Analysis

--------------------------------------------------
* PAIRS (3)
E1: 2,5
H1: 7,8
F9: 4,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
D2,D3: 1.. / D2 = 1  =>  6 pairs (_) / D3 = 1  =>  5 pairs (_)
G4,I4: 1.. / G4 = 1  =>  5 pairs (_) / I4 = 1  =>  3 pairs (_)
B1,C3: 2.. / B1 = 2  =>  0 pairs (*) / C3 = 2  =>  0 pairs (X)
E1,E3: 2.. / E1 = 2  =>  6 pairs (_) / E3 = 2  =>  0 pairs (*)
F7,F8: 2.. / F7 = 2  =>  6 pairs (_) / F8 = 2  =>  4 pairs (_)
B1,E1: 2.. / B1 = 2  =>  0 pairs (*) / E1 = 2  =>  0 pairs (X)
C3,E3: 2.. / C3 = 2  =>  6 pairs (_) / E3 = 2  =>  0 pairs (*)
B8,F8: 2.. / B8 = 2  =>  6 pairs (_) / F8 = 2  =>  4 pairs (_)
C3,C7: 2.. / C3 = 2  =>  6 pairs (_) / C7 = 2  =>  0 pairs (*)
H2,H3: 3.. / H2 = 3  =>  4 pairs (_) / H3 = 3  =>  0 pairs (X)
B7,B8: 3.. / B7 = 3  =>  5 pairs (_) / B8 = 3  =>  5 pairs (_)
D2,H2: 3.. / D2 = 3  =>  0 pairs (X) / H2 = 3  =>  4 pairs (_)
E3,E4: 3.. / E3 = 3  => 11 pairs (_) / E4 = 3  => 23 pairs (_)
B1,B2: 5.. / B1 = 5  =>  5 pairs (_) / B2 = 5  =>  5 pairs (_)
D9,E9: 5.. / D9 = 5  => 23 pairs (_) / E9 = 5  => 11 pairs (_)
A1,A3: 8.. / A1 = 8  =>  9 pairs (_) / A3 = 8  =>  3 pairs (_)
H1,H3: 8.. / H1 = 8  =>  3 pairs (_) / H3 = 8  =>  9 pairs (_)
D4,F4: 8.. / D4 = 8  =>  6 pairs (_) / F4 = 8  => 14 pairs (_)
D9,F9: 8.. / D9 = 8  => 14 pairs (_) / F9 = 8  =>  6 pairs (_)
A1,H1: 8.. / A1 = 8  =>  9 pairs (_) / H1 = 8  =>  3 pairs (_)
A3,H3: 8.. / A3 = 8  =>  3 pairs (_) / H3 = 8  =>  9 pairs (_)
D4,D9: 8.. / D4 = 8  =>  6 pairs (_) / D9 = 8  => 14 pairs (_)
F4,F9: 8.. / F4 = 8  => 14 pairs (_) / F9 = 8  =>  6 pairs (_)
G1,I1: 9.. / G1 = 9  =>  3 pairs (_) / I1 = 9  =>  5 pairs (_)
C5,C6: 9.. / C5 = 9  =>  0 pairs (X) / C6 = 9  =>  3 pairs (_)
D4,D5: 9.. / D4 = 9  =>  0 pairs (X) / D5 = 9  =>  5 pairs (_)
C6,G6: 9.. / C6 = 9  =>  3 pairs (_) / G6 = 9  =>  0 pairs (X)
* DURATION: 0:00:06.731781  START: 17:35:45.420550  END: 17:35:52.152331 2025-04-06
* CP COUNT: (27)
* SOLUTION FOUND

* DEEP PAIR REDUCTION
* DURATION: 0:00:04.424964  START: 17:35:54.615144  END: 17:35:59.040108 2025-04-06
* SOLUTION FOUND
* SAVE PR GRAPH xx-mith-te3-00113812-base-pr-002.dot
* REASONING
* PRF # E3: 2,5 # I2: 1,6 => SOL
* STA # E3: 2,5 + I2: 1,6
* CNT   1 HDP CHAINS /  14 HYP OPENED

Header Info

rating: 28990; r2: 574347; index: 113812

A1. Pair Reduction Analysis

Full list of HDP chains traversed:

* INC # E3: 2,5 => UNS
* INC # E3: 3 => UNS
* INC # B1: 2,5 => UNS
* INC # B1: 7 => UNS
* INC # A1: 7,8 => UNS
* INC # A1: 1 => UNS
* INC # F4: 4,8 => UNS
* INC # F4: 3 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 2,5 => UNS
* INC # E3: 3 => UNS
* INC # B1: 2,5 => UNS
* INC # B1: 7 => UNS
* INC # A1: 7,8 => UNS
* INC # A1: 1 => UNS
* INC # F4: 4,8 => UNS
* INC # F4: 3 => UNS
* CNT   8 HDP CHAINS /   8 HYP OPENED

A3. Deep Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 2,5 => UNS
* INC # E3: 3 => UNS
* INC # B1: 2,5 => UNS
* INC # B1: 7 => UNS
* INC # A1: 7,8 => UNS
* INC # A1: 1 => UNS
* INC # F4: 4,8 => UNS
* INC # F4: 3 => UNS
* INC # E3: 2,5 # A2: 1,7 => UNS
* INC # E3: 2,5 # A2: 4,6 => UNS
* INC # E3: 2,5 # G1: 1,7 => UNS
* INC # E3: 2,5 # I1: 1,7 => UNS
* PRF # E3: 2,5 # I2: 1,6 => SOL
* STA # E3: 2,5 + I2: 1,6
* CNT  13 HDP CHAINS /  14 HYP OPENED