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Two sand glasses – Brain Teaser

hour_glass_1What is the quickest way to time a 9 minute cooking session with two sand-glasses of 4 and 7 minutes respectively?

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A riddle to challenge your mind | Back – Next | Arrange the numbers 1-9

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Posted by Ken.Kabaki on May 17th, 2009 and filed under Discussions. You can follow any responses to this entry through the RSS 2.0. You can leave a response by filling following comment form or trackback to this entry from your site

9 Responses for “Two sand glasses – Brain Teaser”

  1. Eric J says:
    May 19, 2009 at 10:10 am

    Before cooking:
    Start both timers – run down 4-minute timer and flip it. Run down remaining 3 minutes of the 7-minute timer and flip it. Run down remaining 1 minute of the 4-minute timer and flip it. Run down 4-minute timer – 7-minute timer should now be have 2 minutes remaining. Total setup time = 12 minutes.
    Start cooking:
    Run down remaining 2 minutes on 7-minute timer, flip it and run down all 7 minutes. Total cooking time = 9 minutes.

    Reply
  2. Mike Sprayberry says:
    May 18, 2009 at 9:39 am

    T=0: Start both timers.
    T=4: When 4m empties, flip it to restart.
    T=7: When 7m empties, flip it to restart (there will 1 min left on 4m).
    T=8: When 4m empties, flip the 7m which has been running only 1 min.
    T=9: When the 7m empties, you have finished your 9 minute cooking session.

    Reply
  3. Allan Ropski says:
    May 18, 2009 at 9:37 am

    Start 1-4 min and 1-7 min at t=0
    When 4 minutes expires, begin 4 min timer again, (t=4), 3 minutes remain on 7 minute timer
    When 7 min timer expires, begin any timer(t=7); 1 minute remains on 4 minute timer.
    When this 4 minutes timer expires (t=8), one minutes has been drawn out of other timer(began at t=7), flip this and when expires in 1 minute, 9 minutes has elapsed in first 9 minutes.

    Reply
  4. KevinM says:
    May 18, 2009 at 9:22 am

    Flip both 4 and 7 timers over.
    When 4 finishes, there is 3 left in 7 timer. Flip 4 Again.
    When 7 finishes, 4 has 1 minute left.

    Now for the 9 minute timing …
    Now start with 1 minute left in 4 minute timer. Run to completion
    Flip 4 minute timer. Run to completion.
    Flip 4 minute timer. Run to completion.

    Total time = 7 + 9 = 16 minutes

    Seems easy, so there must be an optimization somewhere …

    Optimization:

    Flip 4 and 7.
    When 4 is done, flip again.
    When 7 is done — the 4 is divided into 1 and 3.
    Flip 4 (to run for 1 minute) and flip 7.
    When 4 is done, 7 has 1 minute … flip 7 minute and run to completion to get to 9 minutes time.

    Minimum time = 7 + 1 + 1 = 9 minutes

    Reply
  5. J Rowlands says:
    May 18, 2009 at 9:11 am

    Start both timers. When the 4 minute timer runs out, turn it over. When the 7 minute timer runs out start the cooking session. There will be 1 minute remaining in the 4 minute timer. When the last minute runs out of the four minute timer, turn it over. When it runs out (5 minutes into cooking session) turn it over and let it run out again. Cooking session complete.

    Total elapsed time is 16 minutes.

    Reply
  6. lee says:
    May 17, 2009 at 11:46 pm

    turn 4minute sand glass and 7 minute sandglass at same time. When 4 minute runs out, turn it again. When 7 minute runs out, there is one minute left in the 4 min sandglass, two more lots of 4 minutes = 9 minutes!
    Total time = 16 minutes

    Reply
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