You have 2 hourglasses, a 7-minute timer and a 11-minute timer.
How do you use these to time 15 minutes?
Follow these steps:
| Time (minutes) | Action |
|---|---|
| 0 | Start both timers. |
| 7 | When the 7-minute timer finishes turn it upside-down. |
| 11 | When the 11-minute timer finishes turn, turn the 7-minute timer upside-down. At this point it has 4 minutes of sand at the top. |
| 15 | When the 7-minute timer finishes, you are done. |
Note, that this assumes that a half-finished timer will measure the same time when turned upside-down. This may not be true in physical systems. (For real hourglasses with sand, this is going to be accurate enough).
To solve the puzzle without this assumption, set-up 7 minutes before you need to start timing:
| Time (minutes) | Action |
|---|---|
| -7 | Start both timers. |
| 0 | When the 7-minute timer finishes, your time starts. |
| 4 | When the 11-minute timer finishes, turn it upside-down. |
| 15 | When the 11-minute timer finishes again, you are done. |