Square Digit Chains

October 19, 2018

Today’s task appears on Project Euler, Rosetta Code, and Sloane’s, so it is well worth a look; we even did a version of this task in a previous exercise. Here is the Project Euler version of the problem:

A number chain is created by continuously added the square of the digits of 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?

Your task is to write a program to find the count of starting numbers below ten million that arrive at 89, following the usual Project Euler rule that your computation may take no more than a minute of computation on a recent-vintage personal computer. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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