Maze Of Matrices
⎝ ⎜ ⎜ ⎜ ⎜ ⎛ 1 1 1 1 1 1 2 3 4 5 1 3 6 1 0 1 5 1 4 1 0 2 0 3 5 1 5 1 5 3 5 7 0 ⎠ ⎟ ⎟ ⎟ ⎟ ⎞ ⎝ ⎜ ⎜ ⎜ ⎜ ⎛ 2 2 2 2 2 2 4 6 8 1 0 2 6 1 2 2 0 3 0 2 8 2 0 4 0 7 0 2 1 0 3 0 7 0 1 4 0 ⎠ ⎟ ⎟ ⎟ ⎟ ⎞ = ⎝ ⎜ ⎜ ⎜ ⎜ ⎛ a b c d e b f g h i c g j k l d h k m n e i l n o ⎠ ⎟ ⎟ ⎟ ⎟ ⎞
Find a + f + j + m + o .
The answer is 17098.
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Upon observation, the second matrix is twice the first (call the first 5x5 symmetric matrix A ). We simply need to calculate t r a c e ( 2 A 2 ) , which is done by focusing on just the i − t h row & column ( i = 1 , 2 , 3 , 4 , 5 ):
a = 2 ( 1 2 + 1 2 + 1 2 + 1 2 + 1 2 ) = 1 0 ;
f = 2 ( 1 2 + 2 2 + 3 2 + 4 2 + 5 2 ) = 1 1 0 ;
j = 2 ( 1 2 + 3 2 + 6 2 + 1 0 2 + 1 5 2 ) = 7 4 2 ;
m = 2 ( 1 2 + 4 2 + 1 0 2 + 2 0 2 + 3 5 2 ) = 3 4 8 4 ;
o = 2 ( 1 2 + 5 2 + 1 5 2 + 3 5 2 + 7 0 2 = 1 2 7 5 2 .
and a + f + j + m + o = 1 7 , 0 9 8 .