Here is a classic puzzle. Say that you have two hourglasses of different sizes. The bigger hourglass runs for 11 minutes while the smaller one runs for 7 minutes. Using these two hourglasses, how can you measure 15 minutes exactly.?

## Solution

**Step 1:** Start the two hourglasses at the same time.

**Step 2:** When the 7-minute hourglass finishes, quickly turn it over without wasting a millisecond. At this point, 7 minutes had gone by.

**Step 3:** When the 11-minute hourglass runs out, the bottom part of the 7-minute hourglass has 4 minutes worth of sand. Now, quickly turn over the 4-minute hourglass. At this point, 11 minutes had gone by.

**Step 4:** Just wait for the turned over 7-minute hourglass to finish its 4 minutes worth of sand. Once it runs out, exactly 15 minutes will have gone by assuming that you turned over the hourglasses at a nigh-superhuman speed.

This is the only optimal solution for solving this puzzle. Well, you could always buy a clock or a watch I suppose.

That’s so cool I didn’t really realize how to solve it until I read this.You have a very interesting blog.

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Thanks for reading. I’m glad that you liked it.

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Math can be so much fun. No matter what, the answers are always practical. I enjoy your posts.

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Thank you.

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flip both hourglasses at the same time and start dropping sand. when all the sand of the smaller hourglass has fallen out, begin to measure the time. and then the remaining sand of the bigger one has fallen out, flip it immediately. and when all of the sand in the bigger hourglass has fallen out, stop measuring the time… is this correct?

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Yes :)

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thank you for replying! interesting blog.

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Fun. I love being right.

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Turn over both together. When the 7 minute timer is over, begin counting. The 11 minute timer will have 4 minutes left; when it is finished, turn over the 7 minute timer.

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This was my solution too :)

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Although I think you mean the 11 minute timer gets turned again at the end, not the 7?

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Sorry, my answer makes no sense. Don’t know what I was smoking.

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After the 4 minutes worth of sand run out, turn over the 11-minute hourglass. 4+11=15.

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clue for another solution: 22 -7 = 15

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That’s the formal solution, though it takes a few more turns and requires more time…. Unless if you have a 7-minute hourglass that can cause time to go backward 😃

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Yes, requires more time, 22 mins to be precise. But one turn only, of the bigger hourglass.

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Oh, I see. I was thinking about the formal solution which requires 5 turns.

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