## Square digit chains

### Problem 92

Published on Friday, 1st April 2005, 06:00 pm; Solved by 19600

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?