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Found problems: 26

2019 PUMaC Combinatorics A, 2
Tags: combinatorics , binary
Keith has $10$ coins labeled $1$ through $10$, where the $i$th coin has weight $2^i$. The coins are all fair, so the probability of flipping heads on any of the coins is $\tfrac{1}{2}$. After flipping all of the coins, Keith takes all of the coins which land heads and measures their total weight, $W$. If the probability that $137\le W\le 1061$ is $\tfrac{m}{n}$ for coprime positive integers $m,n$, determine $m+n$.