Candle Problem

I suddenly remembered this problem. It's one of those "think outside the box" dealies. I like the solution, it's elegant and this is a puzzle that can be solved without any outrageous tricks.

Math Problem: Burning Candles

Placed in an enclosed room with only two candles--one which burns for exactly 30 minutes and one that burns for exactly 45 minutes--and a method of lighting the candles, how can one tell when one hour has passed?

Note: The burn times of the candles is not necessarily related to their lengths, so breaking a candle in half, for example, would not ensure that the burn time is halved.

Note: There are not clocks or any other hidden or secret objects in the room--this problem can be solved by only thinking and lighting candles.

Hint: Candles may be lit upside-down, etc with no change in burn time.



Solution

Since there is a candle that will burn for 45 minutes, we can try to make the 30 minute candle burn for 15 minutes instead. Breaking the 30-minute candle isn't helpful, however, lighting it from both sides simultaneously will result in a halved burn time.

Light the 30-minute candle from both sides simultaneously. When it is burnt out, light the 45-minute candle. When that one goes out, one hour will have passed.