sol1.py

"""
Problem 28
Url: https://projecteuler.net/problem=28
Statement:
Starting with the number 1 and moving to the right in a clockwise direction a 5
by 5 spiral is formed as follows:

 21 22 23 24 25
 20 7 8 9 10
 19 6 1 2 11
 18 5 4 3 12
 17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed
in the same way?
"""

frommathimportceil


defsolution(n: int=1001) ->int:
"""Returns the sum of the numbers on the diagonals in a n by n spiral
 formed in the same way.

 >>> solution(1001)
 669171001
 >>> solution(500)
 82959497
 >>> solution(100)
 651897
 >>> solution(50)
 79697
 >>> solution(10)
 537
 """
total=1

foriinrange(1, ceil(n/2.0)):
odd=2*i+1
even=2*i
total=total+4*odd**2-6*even

returntotal


if__name__=="__main__":
importsys

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