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# Sand-glass I.

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Hourglass I. - Back to the Water and Weighing Puzzles

Having 2 sand-glasses: one 7-minute and the second one 4-minute, how can you correctly time 9 minutes?

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Sand-Glass I. - solution

Turn both sand-glasses. After 4 minutes turn upside down the 4-min sand-glass. When the 7-min sand-glass spills the last grain, turn the 7-min upside down. Then you have 1 minute in the 4-min sand-glass left and after spilling everything, in the 7-min sand-glass there will be 1 minute of sand down (already spilt). Turn the 7-min sand-glass upside down and let the 1 minute go back. And that's it. 4 + 3 + 1 + 1 = 9

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• 2 months later...

You can correctly time 9 minutes by repeatedly flipping over the two glasses in this order:

each 1 stands for a minute and ** stands for flip

1 1 1 1*1 1 1 1*1 1 1 1*1 1 1 1*1 1 1 1

*********1 1 1 1 1 1 1*1 1 1 1 1 1 1

once the one seven minute glass is done, there is only one minute left in the four minute glass. two more flips of the four minute glass will get you nine minutes. To make it easier, start the four minute glass and when it's half full flip the seven minute glass.

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• 2 weeks later...

I think there is a faster way to do this..

Start with both the hr glsses. At the end of 4 minutes keep the 4min glass inverted and wait for the 7min hr glass to get empty. When the 7min glass is empty keep it in inverted position. After 1 minute, totally 8 minutes have passed. Now invert the 7min hr glass. And u have 4 + 4 + 1 =9.

Tell me if its not right.

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I think I have something that could work...

Turn both glasses over and let them run. Once the 4 min is done, turn it over again and let it run until the 7 minute glass is done. Once the 7 minute glass is done, there is one minute left on the 4 minute glass, so turn it over to let the one minute run through and this begins the 9 minutes you are timing. Then just turn the 4 minute over two more times to gain the 8 more minutes you need to get a total of 9 minutes.

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Although, peachykeen, yours is the only answer anyone can understand, nine min. could be timed a bit faster using a similar method.

-Start both timers

1. When the 4 min. glass is done, start it again. (The 7 min. glass now has 3 min. left to count)

2. When the 7 min. glass is done, start it again. (There will be one min. remaining on the 4 min. glass and the 7 min. glass will now be counting that one min.)

3. When the 4 min. glass is done, the 7 min. glass will now have just one min. worth of sand on the bottom, turn it over and that sand will count the remaining min.

1. 4min. (from the 4 min. glass)

2. 3min. (from the 7 min. glass)

3. 1min. + 1min. (the first from the 4 min. glass, the second from the 7 min. glass)

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• 4 weeks later...

there is a much simpler meathod.

it says corectly time 9 mins with the two glasses, it never says you have to use them at the same time.

so start the 4 min glass, when that is half gone, start the 7 min glass

2+7=9

much faster and much less hassle then to stand there and flip the glasses several times.

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there is a much simpler meathod.

it says corectly time 9 mins with the two glasses, it never says you have to use them at the same time.

so start the 4 min glass, when that is half gone, start the 7 min glass

2+7=9

much faster and much less hassle then to stand there and flip the glasses several times.

It would be easier, but there is no way to tell that you are timing exactly 9 minutes because you cant, by sight, get the exact half way point of the 4 minute glass.

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Several people, so far, have commented on having "faster" ways to solve this problem.

I'd just like to point out, that ALL these methods take 9 minutes. None of them are "faster".

pedantic, but true

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• 2 weeks later...

4min---|--7min|Time

---------------------

down-4|down-7|0

up-4---|down-3|4

up-1---|up-7---|7

down-4|up-6---|8mins

In sand glasses we can count to the minute mentioned or for each inversion. So I don't think

4+3+1+1 =9 will work because we can't measure the last minute.Please point out if I'm wrong in this regard.

A probable solution will be

4min---|--7min| Time

---------------------------

down-4|*****| 0

up-4 --|down-7| 4

down-4|down-3| 8

up-1---|down-0| 9mins

4+4+1=9 .

P.S: Note that in both the tables the time is taken into account only if there is an inversion (down-up or up-down) of either of the sand glass in use.And ***** is used to indicate not needed, | is used as a separator....corrected one...

thanks,

firefox...

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• 4 weeks later...

a b

4/0 7/0

0/4 3/4 flip a

4/0 3/4 time begin

3min

1/3 0/7 flip a b

3/1 7/0

3min

0/4 4/3 flip b

3/4

3min

3+3+3=9 min

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Although, peachykeen, yours is the only answer anyone can understand, nine min. could be timed a bit faster using a similar method.

-Start both timers

1. When the 4 min. glass is done, start it again. (The 7 min. glass now has 3 min. left to count)

2. When the 7 min. glass is done, start it again. (There will be one min. remaining on the 4 min. glass and the 7 min. glass will now be counting that one min.)

3. When the 4 min. glass is done, the 7 min. glass will now have just one min. worth of sand on the bottom, turn it over and that sand will count the remaining min.

1. 4min. (from the 4 min. glass)

2. 3min. (from the 7 min. glass)

3. 1min. + 1min. (the first from the 4 min. glass, the second from the 7 min. glass)

We're trying to time 9 minutes! How can that ever be done faster than in exactly 9 minutes, huh? None of the methods could ever claim to be faster than any of the others. They could at best be simpler to use, simpler to understand even.

In that respect, b.t.w., your method wins by all means. Very clear, and easy to understand. Even for me

BoilingOil

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We're trying to time 9 minutes! How can that ever be done faster than in exactly 9 minutes, huh? None of the methods could ever claim to be faster than any of the others. They could at best be simpler to use, simpler to understand even.

In that respect, b.t.w., your method wins by all means. Very clear, and easy to understand. Even for me

BoilingOil

Several people, so far, have commented on having "faster" ways to solve this problem.

I'd just like to point out, that ALL these methods take 9 minutes. None of them are "faster".

pedantic, but true

There are faster ways of timing 9 minutes. The 9 minutes alone obviously take the same amount of time. But rookie's answer takes only 9 minutes. peachykeen's answer adds 7 minutes to the front of that for a total of 16 minutes.

Again, pedantic, but right <!-- s;) --><!-- s;) -->

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• 1 month later...

First.... You get a stop watch, press start wait for 9 minutes then press stop...

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• 2 weeks later...

I ve an easier answer to this...first you turn both the glasses upside down...wen 4 minutes r over then turn d glasses....we'll b left with 1 minute of sand in 4 minutes glass....now keep d 7 minutes glass aside and let d 1 minute of sand flow...wen the last grain is left turn the glass upside down nd repeat the same process ftr 4 min. of turning it again....we get 9 minutes...1+4+4...i hope it's right?

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• 3 weeks later...

Start both glasses at the same time.

turn 4 min glass over when it stops, giving you 8 mins.

When the 7 min glass stops, turn it over.

Then turn 7 min. glass over once again after 4 min. glass is finished with 8 mins., giving you 1 more minute.

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• 1 month later...
Sand-glass I. - Back to the Water and Weighing Puzzles

Having 2 sand-glasses: one 7-minute and the second one 4-minute. How can you correctly time 9 minutes.

Sand-Glass I. - solution

Turn both sand-glasses. After 4 minutes turn upside down the 4-min sand-glass. When the 7-min sand-glass spills the last grain, turn the 7-min upside down. Then you have 1 minute in the 4-min sand-glass left and after spilling everything, in the 7-min sand-glass there will be 1 minute of sand down (already spilt). Turn the 7-min sand-glass upside down and let the 1 minute go back. And that's it. 4 + 3 + 1 + 1 = 9

Start both the 7 and 4 minute at the same time.

Stop both when the 4 is complete. You will have 3 left in the 7 glass.

Start the now 3 and 4 at the same time.

Stop when the 3 is complete. You will have 1 left in the 4 glass.

Start the 7 and now 1 at the same time.

Stop whe the one is complete. You will have 6 in the 7 glass.

Start the now 6 and 4 at the same time.

Stop when 4 is complete. You will have 2 in the 7 glass.

Start the now 2 and 4 at the same time.

Stop when the 2 is complete.

You now have a full 7 and a half 4 equaling 9.

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• 2 weeks later...

Sand-glass I. - Back to the Water and Weighing Puzzles

Having 2 sand-glasses: one 7-minute and the second one 4-minute. How can you correctly time 9 minutes.

you let the 7 min go past all the way and let the 4 min go half way

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• 4 weeks later...

So will all these solutions work if the sand is nonlinear? They have been timed to complete the whole time, but not when they are flipped over mid way. For example if you start the 4 and 7 at the same time and at the end of the 4 min, you turn the 7 over it may not take 4 min for the 7 to run back out. If so what type of relationship might hold? I have no idea.

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Several people, so far, have commented on having "faster" ways to solve this problem.

I'd just like to point out, that ALL these methods take 9 minutes. None of them are "faster".

pedantic, but true

Well, since we're going to be pedantic, I will point out that none of them IS faster.

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Turn the 7 min glass over, let sand run to bottom.

Turn the 4 min glass over, when there's an equal amount of sand on top or bottom, 9 minutes have passed.

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• 4 weeks later...
there is a much simpler meathod.

it says corectly time 9 mins with the two glasses, it never says you have to use them at the same time.

so start the 4 min glass, when that is half gone, start the 7 min glass

2+7=9

much faster and much less hassle then to stand there and flip the glasses several times.

Aseatha85 is correct. Never did it mention that you were to time 9 minutes on EACH glass.

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• 4 weeks later...

For those who claim to turn over the hour glass half way through, have you ever tried to guess the halfway point an hourglass? I find it extremely hard to compare the estimated the volume of sand in the top and the bottom. If you are not skilled at "guessing" the halfway point of the 4 minute hourglass than you could be as much as a minute off.

T = 0min ---- Turn over the 4 and 7 minutes glasses.

T = 4min ---- The 4 runs out, Flip it. (3 minutes in 7 glass)

T = 7min ---- The 7 runs out, Flip it. (1 minute in the 4 glass)

T = 8min ---- The 4 runs out. 1 minute in bottom of 7 glass, Flip 7 glass.

T = 9min ---- The 7 runs out, 9 minutes reached +/- about 5 seconds to allow for flipping time.

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T-0 = Start both hourglasses

T-4 = 4 runs out, restart it (3 minutes left in the 7m HG)

T-7 = 7 runs out, restart it (1 minute left in the 4m HG)

T-8 = 4 runs out, restart it (6 minutes left in the 7m HG)

T-12 = 4 runs out, restart it (2 minutes left in the 7m HG)

T-14 = 7 runs out, restart it

Steps T-12 and T-14 give you the nine minutes - and yes, you have to wait 12 minutes to start timing for the 9. It beats playing with the idea the you can accurately measure when half of the time is measured. If your solution is to say flip it at the half way mark, then you might as well say flip the 4m HG three times and then stop when 1/4 of the sand is in the bottom after the third flip.

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• 2 months later...
Several people, so far, have commented on having "faster" ways to solve this problem.

I'd just like to point out, that ALL these methods take 9 minutes. None of them are "faster".

pedantic, but true

Cpotting,

I read your post and had to explain why I was laughing hysterically at my desk. My reply of "9 minutes takes 9 minutes" didn't seem to quell the worrying looks I was getting. But I don't care, that was funny.

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I think there is a faster way to do this..

Start with both the hr glsses. At the end of 4 minutes keep the 4min glass inverted and wait for the 7min hr glass to get empty. When the 7min glass is empty keep it in inverted position. After 1 minute, totally 8 minutes have passed. Now invert the 7min hr glass. And u have 4 + 4 + 1 =9.

Tell me if its not right.

I'm pretty sure that there is no faster way of measuring time...

Edit: Just read the comment above...

Edited by Trogdor
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