You have two hourglasses: one measures 7 minutes and the other measures 11 minutes. You have no other instrument to measure time. How can you measure exactly 15 minutes?
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The hourglasses
With two clocks that do not measure the desired time, the solution is to create a useful difference. The key is to take advantage of a clock when it becomes partially empty.
Hints
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- Start both clocks at the same time.
- When the of 7 minutes it empty, puedes girarlo.
- When the 11-minute is empty, the 7-minute has a useful amount of sand left.
Solution
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Answer: start the 7 and 11 minute clocks at the same time. The procedure is: 1. In $t=0$, start both clocks.
- At $t=7$, the 7-minute clock is cleared. Turn it.
- At $t=11$, the 11-minute clock is cleared. At that point, the 7's clock has been running for 4 minutes since you turned it, so it has 3 minutes left.
- When the 7 clock clears again, we will be at $t=14$. Turn it again.
- When one more minute passes, we will be in $t=15$. This way you can measure exactly 15 minutes from the start.
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