You have two pieces of string.
If you ignite one string, it'll take exactly one hour to burn from one end to the other end.
The fire does not burn the string with consistent speed.
Answer
Light both ends of string A and one end of string B.
When string A is completely burned, exactly 30 minutes will have passed. At this point, you have only half of string B left. Now light the other end of string B too. When string B is fully burned, exactly 15 more minutes will have passed.
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Comments
Where's the question?- Amekne (26 Mar 2013)
The question is to accurately calculate the passage of 45 minutes.
- Glaive Lord (8 Aug 2013)
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