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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>.
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==Problem==
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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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==Solution==
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{{solution}}
  
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[[Mock AIME 1 2006-2007]]
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----
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*[[Mock AIME 1 2006-2007/Problem 10 | Previous Problem]]
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*[[Mock AIME 1 2006-2007/Problem 12 | Next Problem]]
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*[[Mock AIME 1 2006-2007]]

Revision as of 18:41, 22 August 2006

Problem

Let $\mathcal{S}_{n}$ be the set of strings with only 0's or 1's with length $n$ such that any 3 adjacent place numbers sum to at least 1. For example, $00100$ works, but $10001$ does not. Find the number of elements in $\mathcal{S}_{11}$.

Solution

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