This riddle begins with a classic intro…you have just been kidnapped (not again…)
Once again, the malevolent kindness of your captors provides you with a chance to escape, if you solve this puzzle.
You are given two hourglasses, one is an 11-minute hourglass and one is a 7-minute hourglass.
Your task? To measure exactly 15 minutes (give or take a second or two, it’s got to be doable, after all).
Of course, neither hourglass can measure 15 minutes, but you can combine both to measure it and there are actually two ways.
Needless to say, you can’t just count and say when the 15 minutes is up – you have to demonstrate it by using the hourglasses!
This is similar to the burning rope brainteaser.
Here is the more obvious (albeit less efficient solution):
1: Flip both hourglasses simultaneously, starting them both at the same time.
2: When the 7-minute hourglass expires, you begin to measure the 15 minute period. 4-minutes after the 7-minute hourglass runs out, the 11-minute hourglass will also run out (so you’ve measured 4 minutes thus far).
3: Since you know 4 minutes exactly have passed at this point, you can flip the 11-minute hourglass. Once that expires, you’ve measured 15-minutes.
However, there is a quicker way:
1: Flip the 11-minute and the 7-minute hourglasses simultaneously.
2: When the 7-minute hourglass expires, flip it again and restart it.
3: Once the 11-minute hourglass expires, flip the 7-minute again (it will only be partially finished).
4: After the 7-minute hourglass expires, 15 minutes have passed.
Here, you’re letting 7 minutes pass before restarting the 7-minute hourglass, but the 11-minute hourglass is still running at that point. After that 7 minutes, you have 4 minutes until the 11-minute hourglass expires. At this point, 11 minutes have elapsed in total, and the 7-minute hourglass has 3 minutes left to go UNTIL you flip it, at which point it will have 4 minutes to go, making 15 minutes in total.