2020 CIME I Problems/Problem 13

Problem 13

Chris writes on a piece of paper the positive integers from $1$ to $8$ in that order. Then, he randomly writes either $+$ or $\times$ between every two adjacent numbers, each with equal probability. The expected value of the expression he writes can be expressed as $\frac{p}{q}$ for relatively prime positive integers $p$ and $q$. Find the remainder when $p+q$ is divided by $1000$.


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See also

2020 CIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
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All CIME Problems and Solutions

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