Q. You are given two 60 minute long fuse ropes (i.e. the kind that you would find on the end of a bomb) and a lighter. The fuses do not necessarily burn at a fixed rate. For example, given an 8 foot rope, it may take 5 minutes for the first 4 feet of the fuse to burn, while the last 4 feet could take 55 minutes to burn (a much slower rate) (5+55=60 minutes). Using these two fuses and the lighter, how can you determine 45 minutes?
HINT: You can use the lighter any number of times
Solution :
Light the first fuse at both ends and the other fuse at one end simultaneously. When the first fuse is burned out, you know that exactly half an hour has passed. You also know that the second fuse still has exactly half an hour to go before it will be burned completely, but we won't wait for that. Now also light the other end of the second fuse. This means that the second fuse will be burned completely after another quarter of an hour, which adds up to exactly 45 minutes since we started lighting the first fuse.
HINT: You can use the lighter any number of times
Solution :
Light the first fuse at both ends and the other fuse at one end simultaneously. When the first fuse is burned out, you know that exactly half an hour has passed. You also know that the second fuse still has exactly half an hour to go before it will be burned completely, but we won't wait for that. Now also light the other end of the second fuse. This means that the second fuse will be burned completely after another quarter of an hour, which adds up to exactly 45 minutes since we started lighting the first fuse.
