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Two Fuses

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Here is a fun puzzle a college room mate once gave to me:

You have two lengths of fuse, and a book of matches. You know that each fuse length has (somehow) been cut so that if the fuse is allowed to burn from end to end, it will take precisely 1 minute to burn down. However, the fuses will not necessarily burn at an even pace; all you know is the total combustion time of each fuse. Using nothing but the two lengths of fuse and the matches to ignite them with, how can you measure an interval of 45 seconds?

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Call the two fuses A and B. The strategy is as follows

1) Light A from both ends and simultaneously light 1 end of B

2) When A burns out after 30 sec, immediately light the other end of B.

3) B will burn out at the 45 sec mark.

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