Question 18
For $n$ a positive integer, let $R(n)$ be the sum of remainders when $n$ is divided by $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, and $10$. For example, $R(15) = 1 + 0 + 3 + 0 + 3 + 1 + 7 + 6 + 5 = 26$. How many two-digit positive integers $n$ satisfy $R(n) = R(n + 1)$?