NL-NWO 2018 Problem 5

At a quiz show there are three doors. Behind exactly one of the doors, a prize is hidden. You may ask the quizmaster whether the prize is behind the left-hand door. You may also ask whether the prize is behind the right-hand door. You may ask each of these two questions multiple times, in any order that you like. Each time, the quizmaster will answer 'yes' or 'no'. The quizmaster is allowed to lie at most $10$ times. You have to announce in advance how many questions you will be asking (but which questions you will ask may depend on the answers of the quizmaster). What is the smallest number you can announce, such that you can still determine with absolute certainty the door behind which the prize is hidden?