A knockout tournament starts with 50 teams. Every match knocks exactly one team out, and in any round with an odd number of teams left one team is given a bye and goes through without playing. How many matches are played altogether before a single winner remains?

Count knock-outs rather than rounds. Exactly one team wins, so the other 49 must be knocked out, and each match knocks out exactly one team. So there are 49 matches — and it makes no difference how the byes fall, because a bye knocks nobody out. The traps: 25 is the number of matches in the first round alone; 50 gives one match per team, which double-counts because a match needs two; 63 is the answer for 64 teams, the nearest tidy power of 2, and comes from assuming a tournament must start with such a number.