Guesses needed to find a number up to 1000

A friend secretly chooses an integer from $1$ to $1000$. You make guesses, and after each wrong guess the friend tells you whether the secret number is above or below it. What is the smallest number $n$ of guesses that lets you be certain of identifying the number, whatever it is?

10. Use binary search, guessing the middle of the remaining range each time. With $k$ guesses you can distinguish at most $2^k-1$ numbers, and $2^9-1=511<1000\le 1023=2^{10}-1$, so $10$ guesses suffice and $9$ do not.