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?
Look at the picture! How many lines do pass through specific box with number inside. The result would be the sum of all boxes and 1 which did not pass through box but upper sides.
Here is the code.
n = 20 li =  temp =  for i in range(n): temp +=  li += [temp] for j in range(n-1): temp =  for i in range(n, 0, -1): temp += [sum(li[j][:i])] temp.reverse() li += [temp] tot = 0 for i in range(n): tot += sum(li[i]) print(tot + 1)
The output is: 137846528820.
This run:~ 0.017461299896240234.