[kristina0812]

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?

[ebaines]

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.