Two hourglasses are nearby: one takes 7 minutes to empty, the other takes 11. How can you measure exactly 15 minutes using only the two hourglasses and no other timing device?
Hints
Watch the moments when each glass finishes and reset carefully.
Answer
Start both hourglasses together. When the 7-minute glass empties, flip it (7 minutes elapsed). When the 11-minute glass empties (after 11 minutes), the 7-minute glass has been running for 4 minutes since its last flip, leaving 3 minutes of sand, so flip it again and let it run for 3 minutes. At that point 14 minutes have passed, so start the 7-minute glass once more and stop after 1 minute (when its sand has run for 1 minute), reaching exactly 15 minutes.