Mind Bender # 11 : Hour Glass Figures
You have just discovered your watch has broken, and that you only have two Hour Glasses in the house …
> one to measure 4 minutes; and
> another to measure 7 minutes.
Your dilemma is that you need to time something for 9 minutes!
How do you go about doing that?
10 October, 2007 at 3:09 pm
Start both at the same time. Upend the four minute timer at the completion of each of its cycles. Start timing when the seven minute timer runs out. Stop timing at the end of the fourth four minute cycle. (4×4)-7=9.
10 October, 2007 at 3:32 pm
Start them both together
When the 4 min runs out, turn it only
When the 7 min runs out, the 9 minutes starts
When the 4 min runs out (1 min later), flip it
When the 4 min runs out again, 5 minutes have gone, turn it again
When the 4 min runs out again, 9 minutes is up.
10 October, 2007 at 3:41 pm
Start the 4 minute timer when it is half way through start the 7 minute timer. The seven minute timer will finish 9 minutes after the start of the 4 minute time
10 October, 2007 at 3:44 pm
You start both hourglasses running simultaneously and each time the 4 minute glass finishes you turn it again.
At the time the 7 minute glass runs out you start the process that requires 9 minutes.
Once the 4 minute glass has run its course 4 times (ie 16 minutes) the timed process will have run for 9 minutes (4X4=16 - 7 = 9)
10 October, 2007 at 3:55 pm
Ok…this sounds complicated, but here goes:
*You would first flip both hourglasses over at the same time
*Once the 4min one is finished, flip it back over right away. You know that there’s 3 mins left on the 7min glass at this point
*The next one to end will be the 7min glass, which will end with a min to spare on the 4min glass. Flip the 7 back over.
*Now once the 4 min glass ends, flip it over again - at this point there’s 6 mins lift on the 7min glass.
*Get ready now…..as soon as the 4min glass ends, start timing. There is now 2 min left on the 7min glass.
*All you have to do now is let the 7min glass finish up its 2mins then flip it over to do a full 7mins again, equalling 9mins all up!
Phew….personally, I’d just probably call the ‘at the third stroke, the time will be 1:15’ people. Or even better, set the microwave!!
10 October, 2007 at 4:05 pm
start both hourglasses, at the end of 4 minute hourglass, restart the 4 minute one. when 7 minute one finishes, restart 7 minute hourglass. when the 4 minute one finishes, (at this stage 8 minutes elapsed), turn over the 7 minute one, (which has only run for 1 minute) and it will finish in one minute. 4 + $ + 1 = 9
10 October, 2007 at 4:06 pm
should read 4 + 4 + 1 = 9
10 October, 2007 at 4:34 pm
Set both hour glasses going at the same time. When the 4 minute one runs out, turn it over to start again. Now, when the 7 minute one runs out, there will still be one minute left on the 4 minute hour glass.
Start the process that needs 9 minutes at the point where the 7 minute one runs out. When the 4 minute one again runs out, turn it over. When it runs out again, you will have 5 minutes. Turn it over again and when it runs out for the fourth time in all, you will have your 9 minutes - being 1 minute + 4 minutes + 4 minutes. Or, 4 * 4 minutes less 7 minutes.
10 October, 2007 at 4:44 pm
Start them both at once.
Turn over the 4 min Hour Glass.
Start timing after the seven minute Hour Glass finishes
Turn over the 4 min Hour Glass three more times.
When the 4 min Hour Glass finishes for the fourth time (16 mins), then the nine minutes is up (16 mins - 7mins = 9 mins)
10 October, 2007 at 4:49 pm
flip both the 4 and 7 hourglass (hg) together. When the 4 runs out you have 3 mins in the 7 (hg). So now you have 4 and a 3mins (from the 7 hg). Immediately flip the 4 hg and 7 hg around. Since you had only 3 mins in the 7hg, when that runs out you have 1 min in the 4 hg. flip both around and when the 4 hg runs out (1 mins) you will have 6 mins in the 7hg. flip both around again, and when the 4 hg runs out you have 2 mins in the 7 hg. flip both around and when the 2 mins in the 7hg runs out, you have 2 mins in the 4hg. Now get ready to time the 9 minutes cos when you flip the 4 hg around, you get 2 minutes and when that runs out, you flip the 7hg around and you get another 7 mins totalling 9 mins.
Cheers,
dan
10 October, 2007 at 5:13 pm
lets call the 7 minute timer A and 4 minute timer B
Turn both together, when B runs out there is 3 minutes left in A, turn B over let A continue running when A runs out there is one minute left in B Turn A over let B continue running When B runs out there will be one minute of flow in A turn A over untill it runs out ,
Thats 4 minutes, and 3 minutes and 1 minute and 1 minute.
A total of nine minutes, and one very hard boiled egg
Paul.
10 October, 2007 at 5:20 pm
Upturn both hourglass at the same time, when the 4min hourglass runs out this will leave 3 mins left on the 7 min hourglass,
Up turn the 4 min hourglass, when the 7 min hourglass runs out (in 3 mins) you have 1 min left on the 4 min hourglass,
Upturn the 7 min hourglass, when the 4 min hourglass runs out you have 6 mins left on the 7 min hourglass,
Upturn the 4 min hourglass, when it runs out you will have 2 mins left on the 7 min hourglass.
Start timing your 9 min timing activity
When the 7 min hour galsss runs out (in two mins), up turn the 7 min hour glass and let it run for the full 7 mins.
Stop timing your 9 min activity.
10 October, 2007 at 5:46 pm
start with turning both 7min and 4min,
when 4min finished turn that, = 4min
when 7min finished turn that, = 7min
when 4min finished = 8min, turn the 7min which has only done 1min
when that finishes 8+1=9min.
10 October, 2007 at 5:46 pm
Start both timers simultaneously and continue reseting. When the 4 minute timer has completed three cycles start your timing period (12 minute timeline). When the 7 minute timer has completed three cycles finish your timing period (21 minute timeline). Your timing period has therefore been 9 minutes.
10 October, 2007 at 6:23 pm
Start of minute 1: Turn both hour glasses over.
After 4 minutes: 4 minute one will run out. Turn it over.
After 7 minutes: 7 minutes one will run out. Turn it over.
After 8 minutes: 4 minute one will run out again. Turn BOTH over (including the 7 minute one, which will have run down 1 minute).
After 9 minutes: 7 minute one will run out again.
A few seconds later: Go the the pub.
Chris, you’re gonna have to raise the bar a little mate!!!!
10 October, 2007 at 7:03 pm
I would do it this way….Call the 4 minute glass A and the 7 minute glass B. Turn both hour glasses over at the same time, and let them run for 4 minutes. This leaves glass A with 4 minutes on the bottom and glass B with 3 minutes on the top. Turn them both over again at the instant glass A runs out. Let them run until Glass B has run out. Glass A will have 1 minute on the top and 3 minutes on the bottom while glass B will have 7 minutes on the bottom and none on the top. At the instant glass B runs out, turn it over, but leave glass A running for the last minute. When glass A runs out lay them both on their sides. This will leave glass A with 0 on one side and 4 minutes on the other while glass B will have 6 minutes on 1 side and 1 on the other.
We are now ready to begin the 9 minute segment….Turn both glasses at the same time - glass A so the 4 minutes is on top and glass B so the 6 minutes is on top. When glass A runs out, glass B will now have 5 minutes on the bottom, so turn it over and your 9 minutes is up when glass B runs out.
10 October, 2007 at 8:15 pm
If I understand the puzzle correctly, this may be the solution.
Start both glasses. When 4-m finishes, there’s 3-minutes to go. Start 4-m again and when 3-m finishes, there’s 1 minute to go. Start 7-m and when 1-m finishes, there’s 6 minutes to go. Start 4-m again and when it finishes, there’s 2 minutes to go. Start 4-m again, and when 2-m finishes, there’s 2 minutes left. Start timing now. When the 2 minute’s up, start the 7-m and when that’s finished, total would be 9 minutes.
10 October, 2007 at 8:15 pm
Use the 7 minute timer, then use half the 4 minute timer. You can measure half with a ruler and make a mark.
10 October, 2007 at 8:32 pm
start timing both hour glasses, when the 4 min stops turn over again leaving 3 mins on the 7 min hour glass. when the seven minute hour glass stop’s there is now 1 min worth of sand remaining in the 4 min hour glass. repeat this so that when the seven minute hour glass stops next there is 2 mins worth of sand in the 4 min hour glass. the seven minute hour glass + the 2 mins worth of sand in the other hour glass now allows you to time for nine mins
10 October, 2007 at 10:07 pm
I’m sure there is more than one way to skin this cat but the method that came to mind first is as follows.
Start both the 7 and 4 min. timers.
When the 4m timer expires you still have 3 min left in the 7m timer.
Start the 4 min timer again quickly.
When the 7 min. timer expires you now have 1 min left in the 4m timer.
Start timing your 9 minutes at this point. This minute plus 2 times the 4 min timer will give you the 9 min. you need.
11 April, 2008 at 4:39 pm
I saw similar post three month ago. Topicality of this post sucks. Dude, you have to keep up to date.