Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 11"
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11. Let <math>\mathcal{S}_{n}</math> be the set of strings with only 0's or 1's with length <math>n</math> such that any 3 adjacent place numbers sum to at least 1. For example, <math>00100</math> works, but <math>10001</math> does not. Find the number of elements in <math>\mathcal{S}_{11}</math>. | 11. Let <math>\mathcal{S}_{n}</math> be the set of strings with only 0's or 1's with length <math>n</math> such that any 3 adjacent place numbers sum to at least 1. For example, <math>00100</math> works, but <math>10001</math> does not. Find the number of elements in <math>\mathcal{S}_{11}</math>. | ||
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Revision as of 14:58, 24 July 2006
11. Let 
be the set of strings with only 0's or 1's with length 
such that any 3 adjacent place numbers sum to at least 1. For example, 
works, but 
does not. Find the number of elements in 
.
