Pair Reduction Analysis

Pair Reduction

Deep Pair Reduction

Time used: 0:00:00.129071

Deep Constraint Pair Analysis

Time used: 0:00:00.000011

List of important HDP chains detected for C3,G3: 2..:

* DIS # C3: 2 # G5: 4,7 => CTR => G5: 1,3,9
* DIS # C3: 2 + G5: 1,3,9 # C4: 1,9 => CTR => C4: 6,8
* DIS # C3: 2 + G5: 1,3,9 + C4: 6,8 # C5: 1,9 => CTR => C5: 8
* PRF # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 # C9: 1,5 => SOL
* STA # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 + C9: 1,5
* CNT   4 HDP CHAINS /  29 HYP OPENED

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

Positions

....2..3...3..1...18.9....5....4..2..5......67..6..8....4....1.8..7..6..96.......	initial
....2..3...3..1...18.9....5....4..2..5......67..6..8....4....1.8..7..6..96.......	autosolve

Classification

level: deep

Pairing Analysis

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* PAIRS (1)
A4: 3,6

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* CONSTRAINT PAIRS (AUTO SOLVE)
G1,I1: 1.. / G1 = 1  =>  1 pairs (_) / I1 = 1  =>  2 pairs (_)
C3,G3: 2.. / C3 = 2  =>  6 pairs (_) / G3 = 2  =>  2 pairs (_)
E3,F3: 3.. / E3 = 3  =>  1 pairs (_) / F3 = 3  =>  2 pairs (_)
A5,B6: 4.. / A5 = 4  =>  3 pairs (_) / B6 = 4  =>  4 pairs (_)
G4,H6: 5.. / G4 = 5  =>  2 pairs (_) / H6 = 5  =>  2 pairs (_)
H2,H3: 6.. / H2 = 6  =>  2 pairs (_) / H3 = 6  =>  3 pairs (_)
A4,C4: 6.. / A4 = 6  =>  1 pairs (_) / C4 = 6  =>  4 pairs (_)
E7,F7: 6.. / E7 = 6  =>  2 pairs (_) / F7 = 6  =>  2 pairs (_)
B7,C9: 7.. / B7 = 7  =>  2 pairs (_) / C9 = 7  =>  3 pairs (_)
C4,C5: 8.. / C4 = 8  =>  1 pairs (_) / C5 = 8  =>  1 pairs (_)
H2,H9: 8.. / H2 = 8  =>  4 pairs (_) / H9 = 8  =>  1 pairs (_)
* DURATION: 0:00:06.338223  START: 18:56:40.543348  END: 18:56:46.881571 2019-04-28
* CP COUNT: (11)
* INCONCLUSIVE

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* DEEP CONSTRAINT PAIRS (PAIR REDUCTION)
C3,G3: 2.. / C3 = 2 ==>  0 pairs (*) / G3 = 2  =>  0 pairs (X)
* DURATION: 0:00:20.378575  START: 18:56:47.475425  END: 18:57:07.854000 2019-04-28
* REASONING C3,G3: 2..
* DIS # C3: 2 # G5: 4,7 => CTR => G5: 1,3,9
* DIS # C3: 2 + G5: 1,3,9 # C4: 1,9 => CTR => C4: 6,8
* DIS # C3: 2 + G5: 1,3,9 + C4: 6,8 # C5: 1,9 => CTR => C5: 8
* PRF # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 # C9: 1,5 => SOL
* STA # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 + C9: 1,5
* CNT   4 HDP CHAINS /  29 HYP OPENED
* DCP COUNT: (1)
* SOLUTION FOUND

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=339

A1. Deep Constraint Pair Analysis

Full list of HDP chains traversed for C3,G3: 2..:

* INC # C3: 2 # G1: 4,7 => UNS
* INC # C3: 2 # I1: 4,7 => UNS
* INC # C3: 2 # G2: 4,7 => UNS
* INC # C3: 2 # H2: 4,7 => UNS
* INC # C3: 2 # I2: 4,7 => UNS
* INC # C3: 2 # H3: 4,7 => UNS
* INC # C3: 2 # F3: 4,7 => UNS
* INC # C3: 2 # F3: 3,6 => UNS
* DIS # C3: 2 # G5: 4,7 => CTR => G5: 1,3,9
* INC # C3: 2 + G5: 1,3,9 # G9: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # G9: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # G9: 2,3,5 => UNS
* INC # C3: 2 + G5: 1,3,9 # G1: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # I1: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # G2: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # H2: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # I2: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # H3: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # F3: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # F3: 3,6 => UNS
* INC # C3: 2 + G5: 1,3,9 # G9: 4,7 => UNS
* INC # C3: 2 + G5: 1,3,9 # G9: 2,3,5 => UNS
* INC # C3: 2 + G5: 1,3,9 # B4: 1,9 => UNS
* DIS # C3: 2 + G5: 1,3,9 # C4: 1,9 => CTR => C4: 6,8
* DIS # C3: 2 + G5: 1,3,9 + C4: 6,8 # C5: 1,9 => CTR => C5: 8
* INC # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 # E6: 1,9 => UNS
* INC # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 # I6: 1,9 => UNS
* PRF # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 # C9: 1,5 => SOL
* STA # C3: 2 + G5: 1,3,9 + C4: 6,8 + C5: 8 + C9: 1,5
* CNT  28 HDP CHAINS /  29 HYP OPENED