Difference between revisions of "2003 AIME II Problems/Problem 3"
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== Problem == | == Problem == | ||
| + | Define a <math>good~word</math> as a sequence of letters that consists only of the letters <math>A</math>, <math>B</math>, and <math>C</math> - some of these letters may not appear in the sequence - and in which <math>A</math> is never immediately followed by <math>B</math>, <math>B</math> is never immediately followed by <math>C</math>, and <math>C</math> is never immediately followed by <math>A</math>. How many seven-letter good words are there? | ||
== Solution == | == Solution == | ||
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== See also == | == See also == | ||
| − | + | {{AIME box|year=2003|n=II|num-b=2|num-a=4}} | |
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Revision as of 14:36, 21 November 2007
Problem
Define a 
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
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See also
| 2003 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
