Starting with any positive integernwe produce another numbermas follows.

- If
nis odd, thenm= 3n-1- If
nis even, thenm=n/2

By repeating this process,ngenerates a sequence called asnowstormthe numbers of which are calledsnowflakesofn

For example, the snowstorm of 4 is: 4, 2, 1, 2, 1, ... and so on. SOmetimes we arrange the snowflakes in a diagram to indicate cycles.

Here we have a cycle of length two

Questions:

1. show that starting with 12 also produces a length two and that starting with 13 produces a cycle of length five

2. Find a cycle with length greater than five

3. Explain why no cycle can coantin a number that is a multiple of three

4. Find all cycles of length five