coverOn Friday I posted this puzzle….

I have 2 hourglasses.  One measures 7 minutes and the other measures 11 minutes.  What is the quickest way to use them to time the boiling of an egg for 15 minutes?
If you haven’t tried to solve it, have a go now.  For everyone else the answer is after the break.
Start the 2 hourglasses together.  When the 7 minute hourglass finishes, turn it over.  When the 11 minute hourglasses finishes, turn the 7 minute hourglass over again.  When the 7 minute hourglass finishes the 15 minutes will be up.
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle(UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

50 comments

    1. My solution was to start the 2 hourglass together after putting the water on the stove to boil. When the 7 minutes hourglass finishes turn the 11 minutes hourglass over and put the eggs into the boiling water. When it finishes, turn it over again. When it is finishes the eggs are ready.

    2. me too, but Richard’s answer is quicker.

      Some people suggested that you can’t use an hourglass that is calibrated for 7 minutes to measure three or four minutes though. I would like to know what answer they got.

    3. My solution was a bit different as well.
      Start the hourglasses together
      Start boling the eggs when the 7 min glass has finished.
      When the eleven min glass has finished, restart it.
      When it has finished again, quench, peel, salt and enjoy.

    4. Start the 7 minute timer. When it’s finished, turn it over, when it’s finished, butter a slice of bread to make soldiers. When you’ve finished, take the egg out.
      Simples. 🙂

    5. we need to boil the egg for 15 minutes… so by this… bloody’s answer goes wrong.

    1. Put the egg on a train traveling close to the speed of light (about 90% should be fine) from your frame of reference the 15 minutes the egg needs to cook will be done by the time the 7 minute timer runs out. Unfortunately your egg is now 70 million miles away 😦

  1. Start both at same time, When the 7 min glass finishes, put the eggs in boiling water.
    When the 11 min glass finishes, the eggs will have been boiling for 4 mins.
    Turn over the 11 min glass. When it finishes, the eggs will have been in for 15 mins. So 18 mins in total.

    1. I also got this solution.

      I think Richard’s solution is wrong. It makes the assumption that running the 7 minute timer for 4 minutes then turning it over will measure another 4 minutes. But that will only be true if the sand falls at a constant rate, and there’s no reason why it should.
      If approximate solutions like that are acceptable, why not just use the 7 minute timer twice to get approximately 15 minutes?

    1. That’s the answer I had, but it’s not 15 mins total it’s 22 minutes (the 15 minutes boiling time plus the 7 mins before you put the eggs in).

  2. This also depends on linear measurement, which was discounted by a comment on Friday.

    My solution also depends on linear measurement:
    – put the water on the heat
    – start both hourglasses at the same time
    – when the 7 minute hourglass finishes, lay the 11 minute hourglass on its side (4 minutes left)
    – put the egg in to the water
    – restart the 11 minute hourglass until it finishes
    – restart the 11 minute hourglass for the full 11 minutes
    – throw away the overcooked egg

  3. #####Start the 2 hourglasses together. When the 7 minute hourglass finishes, turn it over.

    7 minutes up, 4 minutes remaining in the 11 glass

    #####When the 11 minute hourglasses finishes, turn the 7 minute hourglass over again.

    11 minutes up, 3 minutes remaining in the 7 glass (only 4 minutes have passed since the previous turning over)

    ######When the 7 minute hourglass finishes the 15 minutes will be up.

    The remaining sand worth three minutes would have fallen by this time.

    11+3 = 14.

    Where am I going wrong, if indeed I’m wrong?

    1. #####Start the 2 hourglasses together. When the 7 minute hourglass finishes, turn it over.
      7 minutes up, 4 minutes remaining in the 11 glass
      #####When the 11 minute hourglasses finishes, turn the 7 minute hourglass over again.
      the 4 minutes of sand that has passed comes on top and flow back thus 4 minuts of sand left in the hourglass
      ######When the 7 minute hourglass finishes the 15 minutes will be up.
      11+4 = 15

  4. Isn’t the given answer wrong? It looks like this method would give 14 minutes, not 15. After 11 minutes, 4 minutes of the 7 minute hourglass sand will have flowed; turning this hourglass at this time will leave 3 more minutes before it is finished. 11 + 3 = 14.
    My method would be to start both hourglasses simultaneously, put the egg in the water when the 7 minute hourglass is finished, turn the 11 minute hourglass when it is finished and take the egg out when the 11 minute hourglass is finished for the second time.

    1. No, four minutes are in the bottom of the small hour glass when the big hour glass has finished. When you turn it over the four minutes ends up on _top_. Exactly what you need after 11 minutes have passed.

  5. 1. Turn over the 7-minute hourglass when you put the egg in the water.

    2. When the 7-minute hourglass is empty, turn it over again.

    3. When the 7-minute hourglass is empty a second time (totaling 14 minutes), count slowly from 1 to 60.

    4. Take overcooked egg off heat.

  6. Take both hourglasses. Knock on your neighbor’s door. Say “I will give you both of these lovely hourglasses if I can borrow your digital timer”.

  7. I thought you start the 7 hourglass and when it finishes turn it over. Then count the last minute on your own.

  8. It doesn’t take a minute to turn over an hour glass. This means that the answer given is wrong, unless you count the last minute on your own like my comment before. ^ (\(\
    ( =’;’=)
    (_(“)(“)

    1. Why would you need it to take a minute to turn over the hourglass? The answer is correct…
      7 + 4 + 4 = 15 minutes

  9. For those of you who get the water to boiling before putting in the egg–Be aware that you are very likely to break the egg! 🙂 Eggs should be started in cold water.

    1. I also started the hourglasses for 7 min. before putting the eggs on, but Richard’s answer is definitely quicker, because mine actually ended up taking 22 minutes. Oh, well.

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