A number chain is created by continuously adding the square of the digits in a number to 
form a new number until it has been seen before.

For example,

44 ? 32 ? 13 ? 10 ? 1 ? 1
85 ? 89 ? 145 ? 42 ? 20 ? 4 ? 16 ? 37 ? 58 ? 89

Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. 
What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.

How many starting numbers below ten million will arrive at 89?