Problem:
Define a good word as a sequence of letters that consists only of the letters , , and - some of these letters may not appear in the sequence - and in which is never immediately followed by is never immediately followed by , and is never immediately followed by . How many seven-letter good words are there?
Solution:
There are three choices for the first letter and two choices for each subsequent letter, so there are -letter good words. Substitute to find there are seven-letter good words.
The problems on this page are the property of the MAA's American Mathematics Competitions