Measuring Time with Hourglasses 1

You’re making the perfect soft-boiled eggs: all you have to do is boil eggs in a pot of water for exactly 9 minutes. However, your kitchen timer is broken, and all you have are two hourglasses: one measures 4 minutes, the other measures 7 minutes. Using only these two hourglasses, how can you measure exactly 9 minutes?

Hint

You don’t have to wait for one hourglass to finish before starting the other.

Hint

You can flip an hourglass before all its sand has run out.

Hint

When the 7-minute hourglass finishes, the 4-minute hourglass has some sand remaining. How much time is left in it?

Solution

Start both hourglasses at the same time.

4-min hourglass: 4 minutes left
7-min hourglass: 7 minutes left
Elapsed: 0 min

At 4 minutes, the 4-minute hourglass runs out. Flip it.

4-min hourglass: 4 minutes left
7-min hourglass: 3 minutes left
Elapsed: 4 min

At 7 minutes, the 7-minute hourglass runs out. Flip it.

4-min hourglass: 1 minute left
7-min hourglass: 7 minutes left
Elapsed: 7 min

At 8 minutes, the 4-minute hourglass runs out. Flip the 7-minute hourglass.

4-min hourglass: done
7-min hourglass: 1 minute left
Elapsed: 8 min

The 7-minute hourglass runs its remaining 1 minute of sand, leaving us with 9 minutes measured.