Difference between revisions of "2020 CIME I Problems/Problem 13"

 
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==See also==
 
==See also==
{{CIME box|year=2020|n=I|num-b=11|num-a=13}}
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{{CIME box|year=2020|n=I|num-b=12|num-a=14}}
  
 
[[Category:Intermediate Combinatorics Problems]]
 
[[Category:Intermediate Combinatorics Problems]]
 
{{MAC Notice}}
 
{{MAC Notice}}

Latest revision as of 10:54, 1 September 2020

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 $1000$.

Solution

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See also

2020 CIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 12
Followed by
Problem 14
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All CIME Problems and Solutions

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