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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?