sol1.py

"""
Problem 15: https://projecteuler.net/problem=15

Starting in the top left corner of a 2x2 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 20x20 grid?
"""

frommathimportfactorial


defsolution(n: int=20) ->int:
"""
 Returns the number of paths possible in a n x n grid starting at top left
 corner going to bottom right corner and being able to move right and down
 only.
 >>> solution(25)
 126410606437752
 >>> solution(23)
 8233430727600
 >>> solution(20)
 137846528820
 >>> solution(15)
 155117520
 >>> solution(1)
 2
 """
n=2*n# middle entry of odd rows starting at row 3 is the solution for n = 1,
# 2, 3,...
k=n//2

returnint(factorial(n) / (factorial(k) *factorial(n-k)))


if__name__=="__main__":
importsys

iflen(sys.argv) ==1:
print(solution(20))
else:
try:
n=int(sys.argv[1])
print(solution(n))
exceptValueError:
print("Invalid entry - please enter a number.")