"""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
        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)