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Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 8"

 
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== Problem ==
 
== Problem ==
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A regular polygon of <math>\displaystyle 2007</math> sides is inscribed in a circle. If three distinct vertices of the polygon are selected at random, the probability that the center of the circle lies in the interior of the triangle is <math>\displaystyle \frac ab.</math> Given that <math>\displaystyle a</math> and <math>\displaystyle b</math> are relatively prime positive integers, find <math>\displaystyle ab.</math>
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The positive integers <math>\displaystyle x_1, x_2, ... , x_7</math> satisfy <math>\displaystyle x_6 = 144</math> and <math>\displaystyle x_{n+3} = x_{n+2}(x_{n+1}+x_n)</math> for <math>\displaystyle n = 1, 2, 3, 4</math>. Find <math>\displaystyle \lfloor x_7 /10 \rfloor </math>.

Revision as of 18:13, 24 July 2006

Problem

The positive integers $\displaystyle x_1, x_2, ... , x_7$ satisfy $\displaystyle x_6 = 144$ and $\displaystyle x_{n+3} = x_{n+2}(x_{n+1}+x_n)$ for $\displaystyle n = 1, 2, 3, 4$. Find $\displaystyle \lfloor x_7 /10 \rfloor$.

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