You have two small, simple, unmarked hourglasses. One measures four minutes, and the other measures seven minutes. Using only these, how can you be sure nine minutes have passed?
Start by flipping both hourglasses at the same time. This begins the countdown on both the four-minute and seven-minute hourglasses.
When the four-minute hourglass runs out, flip it over immediately. At this point, four minutes have passed, and the seven-minute hourglass still has three minutes left.
When the seven-minute hourglass runs out, flip it over immediately. At this moment, you have a total of seven minutes passed. The four-minute hourglass has been running for three additional minutes since it was last flipped, leaving it with just one minute left.
When the four-minute hourglass runs out the second time, one minute has passed from the seven-minute hourglass that was flipped. Now, flip the seven-minute hourglass again immediately.
Let the seven-minute hourglass run for the final minute. When it runs out, a total of nine minutes will have passed: four minutes initially, plus the three minutes remaining from the seven-minute hourglass, plus the additional two minutes from the subsequent flips.