This problem asks you find the largest possible sum that can be achieved by adding together the numbers encountered on a path to the bottom of a triangle composed of random 2-digit numbers. It reads:

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

As this problem is a simplified clone of problem 67, the only difference being the size of the triangle, I'll save my explanation of my code for my next post (which will include a modified version of this code designed for #67). Rather than implementing a brute force solution (totally doable, according to the problem text, as there are "only" 16384 (or 215 / 2) routes down the triangle), I wrote something that could be used for triangles of any size. As soon as I learn file I/O in C#, I'll use the same code to tackle #67.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Problem018
{
    class Program
    {
        static void Main(string[] args)
        {
            List<int[]> triangle = new List<int[]>();
            triangle.Add(new int[]  {75});
            triangle.Add(new int[]  {95, 64 });
            triangle.Add(new int[]  {17, 47, 82});
            triangle.Add(new int[]  {18, 35, 87, 10});
            triangle.Add(new int[]  {20, 04, 82, 47, 65});
            triangle.Add(new int[]  {19, 01, 23, 75, 03, 34});
            triangle.Add(new int[]  {88, 02, 77, 73, 07, 63, 67});
            triangle.Add(new int[]  {99, 65, 04, 28, 06, 16, 70, 92});
            triangle.Add(new int[]  {41, 41, 26, 56, 83, 40, 80, 70, 33});
            triangle.Add(new int[]  {41, 48, 72, 33, 47, 32, 37, 16, 94, 29});
            triangle.Add(new int[]  {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14});
            triangle.Add(new int[]  {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57});
            triangle.Add(new int[]  {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48});
            triangle.Add(new int[]  {63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31});
            triangle.Add(new int[]  {04, 62, 98, 27, 23, 09, 70, 98, 73, 93, 38, 53, 60, 04, 23});

            for (int i = triangle.Count() - 2; i >= 0; i--)
            {
                for (int j = 0; j < triangle[i].Length; j++)
                {
                    triangle[i][j] += Math.Max(triangle[i + 1][j], triangle[i + 1][j + 1]);
                }
            }

            Console.WriteLine("The maximum total is {0}", triangle[0][0]);
        }
    }
}