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Rachel's Problem

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


Stage: 4 Challenge Level: Challenge Level:1
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?