Select a natural number between 1 to 50. Square the digits and add. Repeat this process until you see a pattern.
What other numbers end with one?
What happen if you do the process to number 37?
What conclusion can you give?

Interesting. Did you try it with 37? What series do you get? It seems that all starting numbers yield a pattern that either (a) goes to a series of 1's or (b) goes to a series that continuously cycles the same pattern - I'll leave it to you to see what that repeating pattern is, but here's a hint: it starts with 89. I find that there are 11 numbers that end up going to 1. Obviously 1 is one such starting number, and so is 10, but there are 9 others that are less obvious.