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"""This module contains a code example related to

Think Python, 2nd Edition

by Allen Downey

http://thinkpython2.com

Copyright 2015 Allen Downey

License: http://creativecommons.org/licenses/by/4.0/

"""

from __future__ import print_function, division

def str_fill(i, n):

"""Returns i as a string with at least n digits.

i: int

n: int length

returns: string

"""

return str(i).zfill(n)

def are_reversed(i, j):

"""Checks if i and j are the reverse of each other.

i: int

j: int

returns:bool

"""

return str_fill(i, 2) == str_fill(j, 2)[::-1]

def num_instances(diff, flag=False):

"""Counts the number of palindromic ages.

Returns the number of times the mother and daughter have

palindromic ages in their lives, given the difference in age.

diff: int difference in ages

flag: bool, if True, prints the details

"""

daughter = 0

count = 0

while True:

mother = daughter + diff

# assuming that mother and daughter don't have the same birthday,

# they have two chances per year to have palindromic ages.

if are_reversed(daughter, mother) or are_reversed(daughter, mother+1):

count = count + 1

if flag:

print(daughter, mother)

if mother > 120:

break

daughter = daughter + 1

return count

def check_diffs():

"""Finds age differences that satisfy the problem.

Enumerates the possible differences in age between mother

and daughter, and for each difference, counts the number of times

over their lives they will have ages that are the reverse of

each other.

"""

diff = 10

while diff < 70:

n = num_instances(diff)

if n > 0:

print(diff, n)

diff = diff + 1

print('diff #instances')

check_diffs()

print()

print('daughter mother')

num_instances(18, True)