Question 77
Find the smallest integer $n \ge 10$ such that
$$
\left[ \frac{n}{1} \right] \left[ \frac{n}{2} \right] \cdots \left[ \frac{n}{10} \right] = \binom{n}{10}
$$
Here denote by $[r]$ the largest integer less than or equal to $r$ for a real number $r$. For example, $[3.14] = 3$ and $[5] = 5$.
$$
\left[ \frac{n}{1} \right] \left[ \frac{n}{2} \right] \cdots \left[ \frac{n}{10} \right] = \binom{n}{10}
$$
Here denote by $[r]$ the largest integer less than or equal to $r$ for a real number $r$. For example, $[3.14] = 3$ and $[5] = 5$.