Looping 2

For this looping trick you start with any two numbers from 0 to 9 and follow this rule: add the two numbers and write down just the digit that is in the ones place. 

For example, start with 8 and 9. Adding them gives you 17. Keep just the 7, which is in the ones place. Now you have 8-9-7. Add the last two numbers, the 9 and the 7. That gives 16; just keep the 6, then you have 8-9-7-6. Keep going, adding the last two numbers in the series each time, keeping only the digit in the ones place. Do this until you get 8 and 9 again. Then the loop starts all over. How many numbers are in the 8-9 loop before it repeats? 

What happens with 2 and 6?

Does the order of the numbers you choose make a difference?

Post your ideas and findings! Remember to write your name at the beginning of your post.