18.py

# 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.

# 3
# 7 4
# 2 4 6
# 8 5 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)



a =[
    [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, 9,70,98,73,93,38,53,60,04,23]
]



for i in range(len(a) -2, -1, -1):
    for j, v in enumerate(a[i]):
        a[i][j] =  v + max(a[i+1][j], a[i+1][j+1])

print a[0][0]