We claim the answer is $n-1$. This is achievable, as we can ask the following questions: $1$. Is the number $n-1$? $2$. Is the number $n-1$ or $n-2$? ... $n-1$. Is the number $n-1$, $n-2$, ..., or $1$? If we get $x$ yes answers, $0<x\le n-1$, then we know the wizard's number is $x$, because exactly $x$ questions will give a response of yes. If the wizard answers no to each of the questions, then his number is $n$. Now, assume for contradiction that it is possible to use less than $n-1$ questions to determine the wizard's number. This means that if the wizard gives $x$ yes responses, $0\le x\le n-2$, then we can determine his number, so each $x$ corresponds to at most one number between $1$ and $n$. However, there are $n$ possible numbers and at most $n-1$ possible values of $x$, so we have our contradiction and the least number of questions is indeed $n-1$.