7.5. There are 100 boxes numbered from 1 to 100. One of the boxes contains a prize, and the host knows where it is. The audience can send the host a batch of notes with questions that require a "yes" or "no" answer. The host shuffles the notes in the batch and, without reading the questions aloud, honestly answers all of them. What is the minimum number of notes that need to be sent to definitely find out where the prize is?
Answer: 99.

Solution: To be able to definitively determine which of the 100 boxes contains the prize, it is necessary to have the possibility of receiving at least 100 different answers to one set of questions. Since the host's answers for different prize positions can only differ by the number of "yes" responses, it is necessary to have the possibility of receiving at least 100 different counts of "yes." Therefore, at least 99 questions are required (from 0 to 99 "yes").

Example with 99 questions. Let the $k$-th question be: "Is the number of the box containing the prize less than or equal to $k$?" Then, if the number of "yes" answers is zero, the prize is in the hundredth box; if one, it is in the 99th box, and so on.

Criteria: Only the evaluation -3 points, only the example -3 points. Only the answer -0 points.