2 Candles puzzle

[CraigD]

This puzzle was described to me in 2001 by a colleague, who heard it from her son, who heard it from his calculus teacher. According to the teacher, this was asked in a job interview, with a correct answer winning the job.

 

You have 2 candles, each of which burns completely in exactly 1 hour. They do not burn at a constant rate - e.g. one inch may take 15 minutes to burn, another only 10. How can you use these candles to tell when exactly 15 minutes have passed?

 

I wasn’t initially given the following, important clue (highlight to reveal): The candles can be burned on either or both ends.

 

Answer (highlight to reveal): Simultaneously light one candle on both ends, the other on one end; When the 1st candle burns completely (after 30 minutes), light the remaining end of the other candle (which now has 30 minutes left to burn), and begin timing; When the last candle burns completely, 15 minutes have passed since you began timing.

[Tormod]

I had to cheat. Good one. :confused:

[Qfwfq]

I heard it a few years ago with fuses rather than candles, so the hint is something one can suppose if they happen to think of it, and the hint my friend gave me was only like: "You either think of the right idea or there's no way of reaching it by deduction." I spent some tten or twenty minutes to think of what "the right idea" might be and I got it.

 

Actually, I was told one had to mark an interval of 45 minutes but 15 is essentially the same thing.

[rockytriton]

I saw this same riddle before but it used ropes instead of candles. I figured it out after a while but I probably wouldn't have figured it out if they used candles in the example, since they didn't give the hint that you gave.