I saw this puzzle the other day.
You have two fuses. Each fuse is a piece of string, that burns for exactly 1 minute. However, the fuse doesn’t burn evenly, so cutting the fuse in half doesn’t give you two 30 second fuses.
The original puzzle is: using these two fuses, can you time exactly 45 seconds?
What times can you time exactly? What if you have three fuses?
If you have an infinite number of fuses, can you time any time at all as closely as you want?
Where does this puzzle stop being a puzzle and become a mathematical research question?