Question:
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?
Answer:
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.
{ 1 comment… read it below or add one }
This interview question is a great example of a clever problem designed to test a hapless, captive job applicant’s ‘critical thinking’ skills. Unfortunately, this type of problem only demonstrates one’s ability to ’solve’ hypothetical/philosophical puzzles which wouldn’t exist in real life…any number of which could be memorized by job applicants who know how the game is played.
Explanation: In real life, you could never light 2 fuses in 3 places simultaneously with one match…or even 2 matches. Thus ensuring that the ‘exactly 45 second’ goal is unattainable. The best you could do would probably be 46 – 47 seconds with one match. Further, someone with pyrotechnics experience would never buy a fuse from a manufacturer that burns inconsistently – too dangerous. They are typically rated in x-seconds per foot, for example, and are designed to burn evenly.
In the end, I hope I could answer the question above, in an interview setting, to get the job at which I knew I could excel. However, it wouldn’t make me feel bad if I didn’t get it right. I have years of successful real-world problem-solving under my belt. Another interview approach is to have an applicant brainstorm about a real problem currently facing the firm. This way, the interviewer has real context against which to gauge the answers, and, the firm may get a great, new solution from an applicant which is just what they need…in which case that applicant should be hired immediately!
Maybe I would agree to solve the puzzle, if the interviewer would agree to solve one of mine! By the way, I’d feel a little sheepish asking this type of question if I were an interviewer.