Easy one:
You have two pieces of fuse, each of which burns in 1 minute. Use these pieces of fuse to time 45 seconds. You may not use scissors, and the burn rate can vary along the fuse.

Question

asnaseer · Answer

1. light both ends of fuse 1 and one end of fuse 2
2. fuse 1 should completely burn out after 30s (since both its ends were lit). this means fuse 2 has also now burnt for 30s and has 30s remaining.
3. at this point, light the other end of fuse 2 so that it will now burn out after 15s.

this gives 30s+15s=45s

turingtest · Answer

Bingo! Medal for asnaseer!