Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 11"
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| − | + | ==Problem== | |
| + | 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>. | ||
| + | ==Solution== | ||
| + | {{solution}} | ||
| − | [[Mock AIME 1 2006-2007]] | + | ---- |
| + | |||
| + | *[[Mock AIME 1 2006-2007/Problem 10 | Previous Problem]] | ||
| + | |||
| + | *[[Mock AIME 1 2006-2007/Problem 12 | Next Problem]] | ||
| + | |||
| + | *[[Mock AIME 1 2006-2007]] | ||
Revision as of 19:41, 22 August 2006
Problem
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 
.
Solution
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