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Monday, July 28, 2008

Fun with Fuses...

Assume that you have a number of long fuses, of which you only know that they burn for exactly one hour after you lighted them at one end. However, you don't know whether they burn with constant speed, so the first half of the fuse can be burnt in only ten minutes while the rest takes the other fifty minutes to burn completely. Also assume that you have a lighter.

The Question: How can you measure exactly three quarters of an hour with these fuses?

Hint: Two fuses are sufficient to measure three quarters of an hour!. A fuse can be lighted from both ends at the same time (which reduces its burning time significantly!).

Answer: With only two fuses that burn exactly one hour, one can measure three quarters of an hour accurately, by lighting the first fuse at both ends and the other fuse at one end simultaneously. When the first fuse is burnt out after exactly half an hour (!) you know that the second fuse still has exactly half an hour to go before it will be burnt completely, but we won't wait for that. We will now also light the other end of the second fuse. This means that the second fuse will now be burnt completely after another quarter of an hour, which adds up to exactly three quarters of an hour since we started lighting the first fuse!

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