Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

Pros and Cons

If p is a positive integer and q is a negative integer, which of these expressions is the greatest?

Snowman

Age 14 to 16Challenge Level
 All the words in the Snowman language consist of exactly seven letters formed from the letters {s, no, wm, an} arranged in some order where the paired letters cannot be separated. For example snonono'' and sssanwm'' are words in the language but sssmwan'' and sssawmn'' are not. How many words are there in the Snowman language?