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Problem euler #55

If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
Not all numbers produce palindromes so quickly. For example,

349 + 943 = 1292,
1292 + 2921 = 4213
4213 + 3124 = 7337

That is, 349 took three iterations to arrive at a palindrome.

Although no one has proved it yet, it is thought that some numbers, like 196,
never produce a palindrome. A number that never forms a palindrome through the
reverse and add process is called a Lychrel number. Due to the theoretical
nature of these numbers, and for the purpose of this problem, we shall assume
that a number is Lychrel until proven otherwise. In addition you are given that
for every number below ten-thousand, it will either (i) become a palindrome in
less than fifty iterations, or, (ii) no one, with all the computing power that
exists, has managed so far to map it to a palindrome. In fact, 10677 is the
first number to be shown to require over fifty iterations before producing a
palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).

Surprisingly, there are palindromic numbers that are themselves Lychrel
numbers; the first example is 4994.

How many Lychrel numbers are there below ten-thousand?

NOTE: Wording was modified slightly on 24 April 2007 to emphasise the
theoretical nature of Lychrel numbers.



import time

ts = time.time()

def is_palindromic(n):
    return str(n) == str(n)[::-1]

def is_lychrel(n):
    sn = n
    count = 0
    while True:
        if is_palindromic(n) and count > 0:
            return False
            count += 1
            n += int(str(n)[::-1])
        if count > 50:
            return True

res = 0
for n in range(10, 10000):
    if is_lychrel(n):
        res += 1

print "problem euler 55: {} \nelapsed time: {}sec".format(res, time.time() - ts)
Categorie:Project Euler, python
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