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        riddles >> easy >> HOURGLASSES
        
(Message started by: singh181 on Jun 5th, 2007, 8:25am)
Title: HOURGLASSES
Post by singh181 on Jun 5th, 2007, 8:25am
Q: You have two hourglasses: a 7 minute one and an 11 minute one. Using just these hourglasses, accurately time 15 minutes.

A:
Start 7 min and 11 min hourglasses together. When 7 min Hourglass is over we have 4 min remaining in 11 min Hourglass.
Now,  again start 7 min hourglass, now 4 min which was remaining in 11 min hourglass gets over.

Now, we have 3 min left in 7 min Hourglass. again start 11 min hourglass. when 3 min left in 7 min Hourglass gets over we have 8 min left in 11 min hourglass.

Now, start 8 min left in 11 min hourglass. when 8 min gets over then start 7 min hourglass. when 7 min gets over, we have successfully measured 15 mins.
Title: Re: HOURGLASSES
Post by towr on Jun 5th, 2007, 8:42am
You can do it much faster. [hide]2 x 11 - 7=15[/hide]
Title: Re: HOURGLASSES
Post by RedCrest on Jun 6th, 2007, 9:57pm
How about this?

[hideb]Set both hourglasses running, but when the 7-minute one runs out, flip the 11-minute one back over immediately, and it will measure out 4 minutes for you (because 11-7 = 4). After the four minutes in the 11-minute hourglass runs out, flip the 11-minute one back over and it will measure out 11 minutes for you. 4 + 11 = 15, so you have your 15 minutes exactly. [/hideb]

~Red
Title: Re: HOURGLASSES
Post by Grimbal on Jun 7th, 2007, 12:38am

on 06/06/07 at 21:57:33, RedCrest wrote:
How about this?

[hideb]...[/hideb]

~Red


[hide]You should NOT flip the 11-minute hourglass to measure the remaining 4 minutes.  This comes to determine the start at 7 minutes with one hourglass, and determine the end at 22 minutes (2x11) with the other hourglass.[/hide]
Title: Re: HOURGLASSES
Post by Grimbal on Jun 7th, 2007, 1:50am
Damn! I found a better way:
[hideb]
time 0: start both hourglasses.
time 7: 7 runs out, flip 7
time 11: 11 runs out, flip both.  7 now has 4 minutes.
time 15: 7 runs out.
[/hideb]
Title: Re: HOURGLASSES
Post by sitai on Jun 7th, 2007, 4:23pm
i guess you got it...  you took the scenic route though
Title: Re: HOURGLASSES
Post by srn347 on Aug 26th, 2007, 9:12pm
I don't know how or why to hide stuff but the answer is as stated at top except when the 7 minute one has 3 left turn it upside down.
Title: Re: HOURGLASSES
Post by maha on Jul 23rd, 2008, 9:37am
allow 7 min and 11 min hourglass simultaneusly to start...when 7 min hourglass is over, there ll be 4 mins remainig in 11 hourglass.invert tat to count 4 mins .again invert it to count 11 mins..tat totals to 15 mins... :)
Title: Re: HOURGLASSES
Post by rmsgrey on Jul 24th, 2008, 7:23am

on 07/23/08 at 09:37:54, maha wrote:
allow 7 min and 11 min hourglass simultaneusly to start...when 7 min hourglass is over, there ll be 4 mins remainig in 11 hourglass.invert tat to count 4 mins .again invert it to count 11 mins..tat totals to 15 mins... :)


If you invert the 11 minute hourglass after it's run for 7 minutes, it will take another 7 minutes for the 7 minutes worth of sand to run back out...
Title: Re: HOURGLASSES
Post by Grimbal on Jul 25th, 2008, 8:38am

on 06/07/07 at 00:38:39, Grimbal wrote:
You should NOT flip the 11-minute hourglass to measure the remaining 4 minutes. ...
::)
Title: Re: HOURGLASSES
Post by pasta12 on Jun 18th, 2012, 8:32am
How about this. Flip the 11 minute hourglass. When it runs out, immediately flip the 11 minute hourglass again. When the 11 minute hourglass has the same amount of sand remaining as the 7 minute hourglass has, 4 minutes has passed. 11 minutes and 4 minutes makes 15.
Title: Re: HOURGLASSES
Post by rmsgrey on Jun 19th, 2012, 5:12am

on 06/18/12 at 08:32:46, pasta12 wrote:
How about this. Flip the 11 minute hourglass. When it runs out, immediately flip the 11 minute hourglass again. When the 11 minute hourglass has the same amount of sand remaining as the 7 minute hourglass has, 4 minutes has passed. 11 minutes and 4 minutes makes 15.


Or you could flip the 11 minute glass, let it run out then flip it again. When the sand in the top and the sand in the bottom are in a 7:4 ratio, 4 minutes have passed.
Title: Re: HOURGLASSES
Post by sanhas on Sep 11th, 2012, 4:20am
Wow this one is pretty hard  :'(
Title: Re: HOURGLASSES
Post by Forest on Dec 1st, 2012, 10:28pm
How about this;
[hide]
Start both hourglasses at the same time.
When the 7min hourglass runs out, your 15 minute period starts. (There is 4 min remaining on the 11 min hourglass)
When the 11 min hourglass runs out, flip it
When it runs out again, 15 minutes has passed.[/hide]
Title: Re: HOURGLASSES
Post by Grimbal on Dec 3rd, 2012, 1:21am
It works.  But you are loosing 7 minutes for nothing.
Title: Re: HOURGLASSES
Post by marlonmark on Jan 2nd, 2013, 2:26am

A:
Start 7 min and 11 min hourglasses together. When 7 min Hourglass is over we have 4 min remaining in 11 min Hourglass.  
Now,  again start 7 min hourglass, now 4 min which was remaining in 11 min hourglass gets over.

Now, we have 3 min left in 7 min Hourglass. again start 11 min hourglass. when 3 min left in 7 min Hourglass gets over we have 8 min left in 11 min hourglass.

Now, start 8 min left in 11 min hourglass. when 8 min gets over then start 7 min hourglass. when 7 min gets over, we have successfully measured 15 mins.
Title: Re: HOURGLASSES
Post by towr on Jan 2nd, 2013, 10:13am

on 01/02/13 at 02:26:38, marlonmark wrote:
A:
Start 7 min and 11 min hourglasses together. When 7 min Hourglass is over we have 4 min remaining in 11 min Hourglass.  
Now,  again start 7 min hourglass, now 4 min which was remaining in 11 min hourglass gets over.

Now, we have 3 min left in 7 min Hourglass.
And 4 if you turn it over. 11+4=15
Title: Re: HOURGLASSES
Post by rmsgrey on Jan 3rd, 2013, 5:07am
Note that the "best" solution here relies on the property of hourglasses that the rate of flow of sand is independent of the amount of sand remaining (true except possibly for the very last bit of sand that requires a jolt to nudge out of its initial, stable, configuration)
Title: Re: HOURGLASSES
Post by jbcrowley on Jan 8th, 2013, 6:43am

on 12/01/12 at 22:28:39, Forest wrote:
How about this;
[hide]Start both hourglasses at the same time.
When the 7min hourglass runs out, your 15 minute period starts. (There is 4 min remaining on the 11 min hourglass)
When the 11 min hourglass runs out, flip it
When it runs out again, 15 minutes has passed.[/hide]

This is correct and the most efficient way to do this.
Title: Re: HOURGLASSES
Post by rmsgrey on Jan 10th, 2013, 6:13am

on 01/08/13 at 06:43:55, jbcrowley wrote:
This is correct and the most efficient way to do this.


It requires 22 minutes to time 15. It's possible, by invoking the "uniform flow rate" property of hourglasses, to time 15 minutes in just 15 minutes, though with 4 turns of the glasses rather than just 3
Title: Re: HOURGLASSES
Post by jbcrowley on Jan 10th, 2013, 10:41am

on 01/10/13 at 06:13:55, rmsgrey wrote:
It requires 22 minutes to time 15. It's possible, by invoking the "uniform flow rate" property of hourglasses, to time 15 minutes in just 15 minutes, though with 4 turns of the glasses rather than just 3

Heh... you are correct sir!  My daughter (12) actually figured this out using the method (I believe) you are referring to.  I should have known better to come on a forum like this with ravenous ambiguity-eating piranhas lurking about and make an ambiguous statement! ;)  What I meant to say was that this method is the most efficient in that it takes the least amount of flips. :P

*hides and waits to see if that was unambiguous enough*
Title: Re: HOURGLASSES
Post by whize on May 29th, 2013, 5:40pm

on 06/19/12 at 05:12:23, rmsgrey wrote:
Or you could flip the 11 minute glass, let it run out then flip it again. When the sand in the top and the sand in the bottom are in a 7:4 ratio, 4 minutes have passed.


Or you can take out your cell phone and start a 15 minute timer at the moment you flip the hourglasses, cause its cool to see the sand flowing and you can calibrate your hourglasses at the same time. This method takes just 2 flips and exactly 15 minutes.


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