Problems 18 and 67 of Project Euler were the most interesting ones to me, as I almost brute forced them and yet without taking twenty billion years as claimed.
Here’s the problem
`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) ```

Here is my analogy to solve this problem, And here’s my solution in Python

```	n = []
for i in range(15):
n.append(map(int,raw_input().split()))
newresult = n.pop(0)
for i in range(14):
x = n.pop(0)
result = list(newresult)
#	print len(result)
newresult =[]
t = len(x)
for j in range(t):
if(j==0):
newresult.append(result+x.pop(0))
elif(j==t-1):
newresult.append(result+x.pop(0))
else:
newresult.append(max((result.pop(0)+x),result+x.pop(0)))
print newresult
print max(newresult)```

I essentially keep a list of all possible values by limiting to the max at each step, isn’t that amazing 😉