[jrm4]

For some reason this reminds me of the following teaser:

In a typical "tournament" -- say 64 teams, how many matches/games are played before declaring the final winner?

Not sure if there's a way to do spoilers here, but there's a very easy one sentence explanation that involves very close to "no math at all."

[dhosek]

A hint (bordering on solution): each game eliminates a player. Note that this will also give a solution to a tournament where there are not a power of two entrants (ignoring byes).

[gbacon]

Very close, as in one step of arithmetic.