Okay Einsteins... riddle me this?

Question

Your mission is to accurately measure 9 minutes. You only have two hourglasses at your disposal. One hourglass measures 4 minutes and the other measures 7 minutes. There are two possible answers but I will reward the most elegant solution. You may begin.

Answer 1

Turn the 7 minute and 4 minute hourglasses.
When the 4 minute hourglass runs out, turn it over.
When the 7 minute hourglass runs out, turn it over.

When the 4 minute timer runs out this time the 7 minute hourglass has been running for one minute.

Now turn over the 7 minute timer back over and when it runs out you have 9 minutes

Answer 2

Start the hour glasses at the same time.

When the 4 minutes is up, flip the 7 minute hourglass and the 4 minute hour glass back over. At this point the 7m will have 3m left.

When the 3 minutes are up, flip over the 4m glass which will now have 1m remaining.

Now you can start timing and after the 1 minute, flip the 4m glass, wait for it to run out, then flip it again. This will measure the 9 minutes (1+4+4).

Bluedoggy: 7+3=9?

Answer 3

Start both hour glasses at the same time. Start timing when you have to flip the 4-minute hourglass for the third time and stop when you have to flip the 7-minute hourglass for the third time. The time between is 9 minutes

Answer 4

Is this the elegant answer?:

Start both.
When the 4-minute hourglass has expired, flip it over (keep the 7-minute hourglass going).
Flip both of them when the 7-minute hourglass expires.
Flip both of them again after the 4-minute hourglass expires, and when the 7-minute hourglass expires, 9 minutes is up!

Answer 5

I think I've figured out the two ways you were thinking of. One requires preparation of 7 minutes, the other requires no prep work.

METHOD 1:
Start them together.
After 4 minutes, flip the 4 minute timer
Stop when the 7 minute time runs out.
Put the 4 minute timer on its side.

This method takes 7 minutes to prepare and you have a timer with 1 minute of sand left.

Now to time 9 minutes all you need is the 4 minute timer.
Start the 1 minute of sand
1 minute later, flip it.
4 minutes later, flip it again.
4 minutes later, you are done.

RESULT: 7 minutes prep, 9 minutes timed.

METHOD 2 (Best)
Start them together.
After 4 minutes, flip the 4 minute timer
After 3 more minutes, flip them 7 minute timer.
After 1 more minute (from the 4 timer), flip the 7 minute timer *again*
After 1 more minute the 7 minute timer will be done.

RESULT: 0 minutes prep time, 9 minutes timed (Best)

Edit: Now that I reread the other answers, I think Louise had this second method, which is obviously the most elegant. Plus she has better looking legs than I do.

But to show that I did do some thinking on this, here is a *third* method you could use.

METHOD 3
Start them together.
After 4 minutes, put the 7 minute timer on its side.

Now to time 9 minutes, you start them again.
3 minutes later, you flip them both.
3 minutes later, you flip them both.
3 minutes later, you flip them both.

RESULT: 4 minutes prep time, 9 minutes timed

So there you have *three* methods!

METHOD 1: 7 minutes prep, 9 minutes timed.
METHOD 2: 0 minutes prep, 9 minutes timed. <-- IDEAL
METHOD 3: 4 minutes prep, 9 minutes timed.

Answer 6

Time being a man made concept in terms of minutes and hours is inconsequential. Hourglasses cannot be used as an accurate measure of time.

However as the other answers states start both timers together etc... To accurately time nine minutes the human judgement factor would have to be erradicated. This is impossible using hour glasses.

Answer 7

Start both.
When the 4 finishes flip it over until the 7 finishes.
When the 7 finishes stop both.

Start the countdown.
Restart 7 and when it finishes flip the 4 over because now it should have 3 minutes of sand left. 7+3 = 9

Yes 7+3 really does = 9, now you figure that out

Answer 8

Start both at the same time.
When the 4 minute runs out, there is only 3 minutes left on the 7
Turn the 4 over immediately and when the 7 runs out there is only one minute left.
START TIMIMG
When the remaining one minute runs out of the 4, run it twice more.
1+4+4=9

Answer 9

start both hourglasses at the same time.
when the 4 minute finishes flip it immediately.
When the 7 minute finishes flip it immediately.
when the 4 minute finishes again flip it again.
When the 7 minute finishes again turn the 4 minute on its side so that the sand stopps, but each side will have exactly two minutes left.
now you can measure the time.
now, start your 7 minute hourglass, when that is done start your half full 4 minute hourglass.

Answer 10

do them in parallel: turn glass of 7 minutes and turn the one of 4 minutes, as well.
after 4 minutes, stop the one of 7 minutes: this means you have 3 minutes left on it now.

now turn the 3 minutes with one of 4, in parallel again and stop the hourglass with 4 mintues after the other one runs out - this means you have now 1 minute left on it.

okay.

now turn the one with 7 again, from start, in parallel with the one minute. when the minute runs out, stop it - so you have a one minute separated on the hourglass of 7, right?

okay.
now you start measuring: u will use hourglass of 4 twice and the separated one minute once:

once 4
once 4
once 1

there you have it: 9 mintues!

:o)