Maximum path sum I

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is \( 23 \).

\[ \color{red}{3}\\\\ 2\ \color{red}{4}\ 6\\\\ 8\ 5\ \color{red}{9}\ 3 \]

That is, \( 3+7+4+9=23 \).

Find the maximum total from top to bottom of the triangle below:

\[ 75\\\\ 95\ 64\\\\ 17\ 47\ 82\\\\ 18\ 35\ 87\ 10\\\\ 20\ 04\ 82\ 47\ 65\\\\ 19\ 01\ 23\ 75\ 03\ 34\\\\ 88\ 02\ 77\ 73\ 07\ 63\ 67\\\\ 99\ 65\ 04\ 28\ 06\ 16\ 70\ 92\\\\ 41\ 41\ 26\ 56\ 83\ 40\ 80\ 70\ 33\\\\ 41\ 48\ 72\ 33\ 47\ 32\ 37\ 16\ 94\ 29\\\\ 53\ 71\ 44\ 65\ 25\ 43\ 91\ 52\ 97\ 51\ 14\\\\ 70\ 11\ 33\ 28\ 77\ 73\ 17\ 78\ 39\ 68\ 17\ 57\\\\ 91\ 71\ 52\ 38\ 17\ 14\ 91\ 43\ 58\ 50\ 27\ 29\ 48\\\\ 63\ 66\ 04\ 68\ 89\ 53\ 67\ 30\ 73\ 16\ 69\ 87\ 40\ 31\\\\ 04\ 62\ 98\ 27\ 23\ 09\ 70\ 98\ 73\ 93\ 38\ 53\ 60\ 04\ 23 \]

NOTE: As there are only \( 16384 \) routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)