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www.mikescher.com/www/statics/euler/Euler_Problem-092_description.md

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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?