Below is the solution to Project Euler problem 92. Its written in python and takes about 10 minutes to reach the solution depending on your hardware. There are some comments in the code to know what the program is doing.

#!/usr/bin/env python

number_89 = 0

for z in range(10000000, 1, -1):

        def chain(z):
                var = z
                chaindigit = 0
                while (chaindigit != 1 or chaindigit != 89):
                        # Transform the number into a string
                        list =  [int(i) for i in str(var)]
                        # Multiply each list member 
                        chain = [x * y for x, y in zip(list, list)]
                        # Add the remaining list members
                        chaindigit = sum(chain)
                        var = chaindigit
                        # Check whether it ends in 89 or 1 
                        if (chaindigit == 1 or chaindigit == 89):
                                # If it ends in 89 increment the value of number_89
                                if (chaindigit == 89):
                                        global number_89
                                        number_89 = number_89 + 1
                                break
        chain(z)

print "There are", number_89,"chain numbers that end in 89."