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Mock AIME 2 2006-2007 Problems/Problem 11

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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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