Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 5"
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| − | + | ==Problem== | |
| + | In Zuminglish, all words consist only of the letters <math>M, O,</math> and <math>P</math>. As in English, <math>O</math> is said to be a vowel and <math>M</math> and <math>P</math> are consonants. A string of <math>M's, O's,</math> and <math>P's</math> is a word in Zuminglish if and only if between any two <math>O's</math> there appear at least two consonants. Let <math>N</math> denote the number of <math>10</math>-letter Zuminglish words. Determine the remainder obtained when <math>N</math> is divided by <math>1000</math>. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
| + | |||
| + | ==See also== | ||
Revision as of 07:34, 14 February 2008
Problem
In Zuminglish, all words consist only of the letters 
and 
. As in English, 
is said to be a vowel and 
and are consonants. A string of 
and 
is a word in Zuminglish if and only if between any two 
there appear at least two consonants. Let 
denote the number of 
-letter Zuminglish words. Determine the remainder obtained when is divided by 
.
Solution
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