1. 1 2 3 4 5 6 7 8 9

2. Add two numbers to get the next one in the sequence:
4,7
4+7 = 11 which is 1(mod 10)
4,7,1
7+1 = 8
4,7,1,8
8+1 = 9
4,7,1,8,9
8+9 = 17 which is 7(mod10)

3. 4,7,1,8,9,7,6,3,9,2,1,3,4,7,.....
cycle length 12

4. 0,0,0,0,0,...
cycle length 1

5. 5,5,0,5,5,0,5,5,0,....
cycle length 3

6. 2,6,8,4,2,6,8,4,....
cycle length 4

7. 2,2,4,6,0,6,6,2,8,0,8,8,6,4,0,4,4,8,2,0,2,2,...
cycle length 20

8. 1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,1,7,8,5,3,8,1,9,0,9,9,8,7,5,2,7,9,6,5,1,6,7,3,0,3,3,6,9,5,4,9,3,2,5,7,2,9,1,0,1,1,..... cycle length 60

10. Inviting Inquiry How will you know you’ve found them all?
How many distinct cycles are there?
How will you know you’ve found them all?
What if your clock has 7 numbers? 5? 12?
Is there a relationship between the number of cycles and the size of the clock?