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55_LychrelNumbers.py
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55_LychrelNumbers.py
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'''
Created on Dec 31, 2016
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?
@author: mstackpo
'''
from datetime import datetime
start = datetime.now()
# list of numbers 0 - 9999, all zero
# check up to 50 iterations of permutation sums for palindrome
n = 10000
lychrel = [1]*n
lychrel[0] = 0
# start at 5 so don't get single digit palindromes
for i in range(1,n):
count = 0
s = str(i)
while( (lychrel[i]) & (count < 50) ):
total = str( int(s) + int(s[::-1]) )
count += 1
if (total == total[::-1]):
lychrel[i] = 0
#print(i, total, count)
s = total
#if(count == 50): print(i, total, count)
print(sum(lychrel))
end = datetime.now()
print( "runtime = %s" % (end - start) )