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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?


Age 14 to 16
Challenge 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?