Hourglass puzzle
July 16th, 2012 at 4:01:52 PM
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You have a 4-minute and a 7-minute hourglass. You need to mark off exactly nine minutes. How can you do it?
As usual, please put answers in spoiler tags.
As usual, please put answers in spoiler tags.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 16th, 2012 at 4:14:57 PM
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flip both over.
after four minutes, flip the four again.
after seven minutes the seven will be finished, the four will have a minute left.
flip the seven, after one minute the four will be empty, the seven will have one minute expired.
flip the seven and run out the last minute.
after four minutes, flip the four again.
after seven minutes the seven will be finished, the four will have a minute left.
flip the seven, after one minute the four will be empty, the seven will have one minute expired.
flip the seven and run out the last minute.
In a bet, there is a fool and a thief.
- Proverb.
July 16th, 2012 at 4:26:53 PM
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EDIT: I was beaten :(
July 16th, 2012 at 9:57:44 PM
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WongBo gets the prize for the first correct answer!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 17th, 2012 at 10:17:25 AM
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One better: how to get any integer number of minutes >= 7
7: start the 7
8: start the 4, then turn it over when it finishes
9: start both; when the 4 is done, turn it over; when the 7 is done, turn it over; when the 4 is done (1 minute later), turn the 7 over again
10: start both; when the 4 is done, turn it over; when the 7 is done (3 minutes later), turn the 4 over again
For any higher number, express it as 4N + K, where n is a positive integer and K is 7, 8, 9, or 10; run the 4-minute hourglass N times, then run the K-minute solution.
8: start the 4, then turn it over when it finishes
9: start both; when the 4 is done, turn it over; when the 7 is done, turn it over; when the 4 is done (1 minute later), turn the 7 over again
10: start both; when the 4 is done, turn it over; when the 7 is done (3 minutes later), turn the 4 over again
For any higher number, express it as 4N + K, where n is a positive integer and K is 7, 8, 9, or 10; run the 4-minute hourglass N times, then run the K-minute solution.
July 17th, 2012 at 11:11:16 AM
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Quote: Wizard (highlight mine)You have a 4-minute and a 7-minute hourglass. You need to mark off exactly nine minutes. How can you do it?
Some technical questions:
Is the time that an hourglass measures complete when the last grain of sand leaves the upper "bulb", or when it hits the pile in the lower bulb?
If you are trying to measure exactly nine minutes, how do you compensate for the time spent flipping the glasses?
Does the term "hourglass" apply to any timer that uses sand and is shaped like two connected bulbs, even if the amount of time measured is not an hour?
Simplicity is the ultimate sophistication - Leonardo da Vinci
July 17th, 2012 at 11:24:57 AM
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Quote: AyecarumbaSome technical questions:
Okay, "exactly" wasn't the best choice of words. Let's just say nine minutes give or take a few seconds due to hourglass flipping.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 17th, 2012 at 11:27:38 AM
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Quote: AyecarumbaQuote: Wizard (highlight mine)You have a 4-minute and a 7-minute hourglass. You need to mark off exactly nine minutes. How can you do it?
Some technical questions:
Is the time that an hourglass measures complete when the last grain of sand leaves the upper "bulb", or when it hits the pile in the lower bulb?
If you are trying to measure exactly nine minutes, how do you compensate for the time spent flipping the glasses?
Does the term "hourglass" apply to any timer that uses sand and is shaped like two connected bulbs, even if the amount of time measured is not an hour?
Come on. You know the answers here....
Vote for Nobody 2020!
July 17th, 2012 at 11:36:21 AM
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Quote: WizardOkay, "exactly" wasn't the best choice of words. Let's just say nine minutes give or take a few seconds due to hourglass flipping.
Hehe, thanks Wizard. I'm still curious about how hourglasses are actually supposed to work.. This calls for a poll.
Simplicity is the ultimate sophistication - Leonardo da Vinci
July 17th, 2012 at 11:48:08 AM
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This is similar to Jon McClain's water jug problem. (video contains swearing)
July 17th, 2012 at 1:17:21 PM
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I love that movie
July 17th, 2012 at 2:34:51 PM
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When does Dorothy die?
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
July 20th, 2012 at 6:48:58 PM
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Quote: WongBoflip both over.
after four minutes, flip the four again.
after seven minutes the seven will be finished, the four will have a minute left.
flip the seven, after one minute the four will be empty, the seven will have one minute expired.
flip the seven and run out the last minute.
I don't see where you are getting the nine minutes from?
July 20th, 2012 at 7:19:55 PM
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Quote: javedwahidI don't see where you are getting the nine minutes from?
flip both over.
after four minutes, flip the four again. total elapsed 4
after seven minutes the seven will be finished, the four will have a minute left. total elapsed 7.
flip the seven, after one minute the four will be empty, the seven will have one minute expired. total elapsed 8
flip the seven and run out the last minute.total elapsed 9
after four minutes, flip the four again. total elapsed 4
after seven minutes the seven will be finished, the four will have a minute left. total elapsed 7.
flip the seven, after one minute the four will be empty, the seven will have one minute expired. total elapsed 8
flip the seven and run out the last minute.total elapsed 9
In a bet, there is a fool and a thief.
- Proverb.
July 26th, 2012 at 3:40:48 PM
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Quote: AyecarumbaHehe, thanks Wizard. I'm still curious about how hourglasses are actually supposed to work.. This calls for a poll.
This depends on the calibration procedure during the fabrication process: After sealing the lower bulb, when the upper bulb is still open, you fill in a "good" amount of sand and start measuring time with a conventional clock. After the target time has elapsed you flip the hourglass, thus removing all excess sand. Then you seal the open bulb, and your hourglass is calibrated.
So you measure time with the hourglass from the moment you flip it to the moment the last sand particle *leaves* the upper bulb.
If you wait untill the last sand particle has dropped, you are too late :)
