# Problem 92: Square digit chains

![graphic](img092.gif)

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?