sol1.py

"""
Problem 125: https://projecteuler.net/problem=125

The palindromic number 595 is interesting because it can be written as the sum
of consecutive squares: 6^2 + 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2.

There are exactly eleven palindromes below one-thousand that can be written as
consecutive square sums, and the sum of these palindromes is 4164. Note that
1 = 0^2 + 1^2 has not been included as this problem is concerned with the
squares of positive integers.

Find the sum of all the numbers less than 10^8 that are both palindromic and can
be written as the sum of consecutive squares.
"""

LIMIT=10**8


defis_palindrome(n: int) ->bool:
"""
 Check if an integer is palindromic.
 >>> is_palindrome(12521)
 True
 >>> is_palindrome(12522)
 False
 >>> is_palindrome(12210)
 False
 """
ifn%10==0:
returnFalse
s=str(n)
returns==s[::-1]


defsolution() ->int:
"""
 Returns the sum of all numbers less than 1e8 that are both palindromic and
 can be written as the sum of consecutive squares.
 """
answer=set()
first_square=1
sum_squares=5
whilesum_squares<LIMIT:
last_square=first_square+1
whilesum_squares<LIMIT:
ifis_palindrome(sum_squares):
answer.add(sum_squares)
last_square+=1
sum_squares+=last_square**2
first_square+=1
sum_squares=first_square**2+ (first_square+1) **2

returnsum(answer)


if__name__=="__main__":
print(solution())