You have two string-like fuses. Each burns in exactly one minute. The fuses are inhomogeneous, and may burn slowly at first, then quickly, then slowly, and so on. You have a match, and no watch. How do you measure exactly 45 seconds?
Light Fuse 1 at both ends and simultaneously light Fuse 2 at one end. As soon as Fuse 1 is burned out (i.e., after 30 seconds), light the other end of Fuse 2.
Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews.