2023 SSMO Relay Round 4 Problems/Problem 3

Problem

Let $T=$ TNYWR. $N+1$ numbers are chosen from the set $\{1,2,3,\dots,N+1\}$ with replacement. If the probability that the median of these $N+1$ numbers is greater than $\frac{N+2}{2}$ is $M,$ such that the decimal representation of $\frac{1}{M}$ has $a$ $0$ 's before the first nonzero digit of it, find $n$ rounded to nearest multiple of $5.$

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2023 SSMO Relay Round 4 Problems/Problem 3

Problem

Solution