Here’s a gorgeous logic problem I heard recently:
You’re given two ropes and a lighter. These are your only tools.
Each of the two ropes, when lit on one end, will take exactly one hour to burn all the way through to the other end. However, neither of the ropes burn at a constant rate. For instance, it may take 59 minutes to burn through the first half of a rope, and then burn through the second half in the final minute. (Imagine that the ropes vary in thickness in density.) Also, the ropes are not identical, so Rope A does not necessarily burn at the same rate of Rope B.
Your mission, should you choose to accept it:
Measure a period of 45 minutes.