Euler15.cs

/*
Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
How many such routes are there through a 20×20 grid?
*/

using System;

class Program
{
    static void Main()
    {
        var size = 20;
            var grid = new long[size + 1, size + 1];
            
            for (int i = 0; i < size + 1; i++)
            {
                grid[i, 0] = 1;
                grid[0, i] = 1;
            }

            for (int i = 1; i < grid.GetLength(0); i++)
                for (int k = 1; k < grid.GetLength(1); k++)
                    grid[i, k] = grid[i, k - 1] + grid[i - 1, k];
            
            Console.WriteLine(grid[grid.GetLength(0) - 1, grid.GetLength(1) - 1]);
    }
}