You are given two fuses and a lighter. When lit, each fuse takes exactly 1 hour to burn from one end to the other. The fuses do not burn at a constant rate, though, and they are not identical. In other words, you may make no assumptions about the relationship between the length of a section of fuse and the time it has taken or will take to burn. Two equal lengths of fuse will not necessarily take the same time to burn. Using only the fuses and the lighter, measure a period of exactly 45 minutes?

Here is a clue:

If you light both ends of a fuse, it would burn completely in half the time.

Light both ends of first fuse and only one of the second. When the first fuse burns off completely, light the other end of the second.

[Hat tip to PIE]

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