A 64-player binary tournament bracket is about to start. You plan to free up your schedule in advance to watch some of the matchups (meaning, you can plan to watch the second semifinal, for example, but you cannot decide to watch one game or another based on the results of previous matches and teams seen). What is the minimum number of matches you must plan to see in order to confidently answer any (well-posed) question of the form, "Who won in the match between Team X and Team Y?"
Example logic/tiny hints:
If it were only a 4-player tournament, merely watching the final would give you all the information you need. If it were an 8-player tournament, watching the final and the semifinals would give you all the information you need. Similarly, watching every round of games after the first in the 64-player tournament consists of $16+8+4+2+1=31$ games, but the actual solution is more efficient than this. The answer can be deduced with only pencil and paper (no computer assistance).