Two very simple mechanisms can be combined to achieve a precision that neither possesses on its own.
Exactly Fifteen Minutes
Riddle statement
You have two hourglasses: one takes 7 minutes to empty and the other takes 11 minutes.
You may start and turn them over as many times as you like, but you have no other way to measure time.
How can you measure exactly 15 minutes from the moment you begin?
Show solution
Solution
Answer: start both hourglasses at the same time.
- At 7 minutes, the 7-minute hourglass empties. Turn it over.
- At 11 minutes, the 11-minute hourglass empties. Four minutes have passed since the other hourglass was turned, so four minutes’ worth of sand has collected in its lower chamber.
- Turn the 7-minute hourglass over again. That sand is now in the upper chamber and takes exactly 4 minutes to fall.
The hourglass will therefore empty at:
$
11+4=15.
$
This measures exactly 15 minutes from the start.