You are a cook in a remote area with no clocks or other way of keeping time other than a four minute hourglass and a seven minute hourglass. You do have a stove however with water in a pot already boiling. Somebody asks you for a nine-minute egg, and you know this person is a perfectionist and will be able to tell if you undercook or overcook the eggs by even a few seconds. What is the least amount of time it will take to prepare the egg?
Solution
The least amount of time required is nine minutes.
Let’s name H4 the four minute hourglass and H7 the seven minute one. Here are the steps for the solution:
Flip H4 and H7 and put the egg into the boiling water.
When H4 runs out, H7 has 3 minutes to go and the egg has been boiling for 4 minutes. Flip H4.
When H7 runs out, H4 has 1 minute to go and the egg has been boiling for 7 minutes. Flip H7.
When H4 runs out again, H7 has been running for 1 minute and has 6 minutes to go, and the egg has been boiling for 8 minutes. Flip H7 again.
When H7 runs out, remove the egg. It had been boiling for 9 minutes.