Sunday 15 December 2013

Egg-ish puzzles

I had eggs this morning, so I figured some easy puzzles on eggs would fit the occasion...
  1. If it takes 10 minutes to hard-boil an egg, how long would it take to hard-boil 3 eggs?
  2. What happens if I continue cooking the egg for 20 minutes?
  3. Why can't I "roast" the egg directly on fire? (Or can I?)
  4. There are two pots, each containing water at boiling temperature. The second pot has twice the amount of water than the first. Now, I add in 3 eggs to each of the pots and start boiling them on the stove. Which set of eggs will be hard boiled first?
  5. A boy takes 5 minutes to finish an egg. How many boys are needed to finish 10 eggs in10 minutes?
  6. You have two eggs, one pot containing boiling water, and an access to a stove. You are tasked to find out what is the least amount of time needed to completely hard boil an egg. You test this by spinning the egg, and each test takes 1 minute. (Assume that the transition to hardness is stepwise, that is, the contents of the egg can either be in liquid form or solid form, but no "in-between", so test results are deterministic. Also assume that the eggs have "memory" - they remember how long they have been cooked, i.e. if it takes 2 minutes to hard-boil the egg, an egg that was cooked for 1 minute and sent for testing will need just another 1 minute.) You know from past experience that the eggs will definitely be hard boiled after 20 minutes. What strategy should you use so that the least amount of time is spent experimenting?
Good luck!

3 comments:

  1. 1) Based on experience, still 10 minutes if they are boiled together.
    2) You are just wasting electricity.
    3) By right you can. I steamed my hard-boiled eggs.
    4) Both, because the water is already at boiling temperature.
    5) 5 boys
    6) Take the median of 20 minutes = 10 minutes. Test the eggs after 10 minutes. If they are still liquid, boil for another 5 minutes, repeat test. If still liquid, boil for another 2.5 minutes. Repeat so that time value is getting close to 20 minutes. I guess you can call this the bracketing method? XD

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  2. Hahah you egg lover! You have rightfully earned yourself a silver egg-medal! Question 6 needs a little more mulling though :)

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  3. So what's the answer for question 6? You know I'm bad in this kind of thing XD

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