2007 Begets 2016 Begets 1008 Begets 504 Begets 252....
Step 1: Pick a whole number.
Step 2: If the number is even, divide by 2...but if it is odd, add 9.
Step 3: Repeat Step 2 using this new number.
Question 1: Investigate what happens for various starting numbers...how can you be systematic?
Question 2: What predictions can you make, given a particular starting number?
Hint: Try it......
Solution Commentary: What conjectures/predictions did you make?
Compare them with these conjectures posed by past students:
 For multiples of 3, you will always get back to the repeating pattern of 12, 6, 3,...
 For multiples of 9, you will always get back to the repeating pattern of 9, 18, 9,...
 10, 5, 14, 7, 16, 8, 4, 2, 1 cycles through all the numbers and you eventually get back to the starting number
 11 and its multiples cycles through all the numbers but you do not get back to the starting number (I think this is true for primes greater than 11 as well)
 Numbers that are doubles of each other have the same repeating sequence
 0 is not interesting
Can any of these conjectures be verified...or proven?
