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        riddles >> easy >> Hard-boiled eggs
        
(Message started by: Eigenray on Nov 16^th, 2005, 9:26am)

Title: Hard-boiled eggs
Post by Eigenray on Nov 16^th, 2005, 9:26am

Some idiot boiled 3 eggs and put them back in the carton with 3 raw eggs (actually I he boiled 6 but only put 3 back to use later, but that's irrelevant). Of course he didn't label them or anything because he just assumed he'd be able to remember which were which. The question is twofold.

1) How can he tell them apart?

2) If you randomly crack open eggs until you find all 3 cooked ones, what's the expected number you will go through?
a) More generally, what if there are M raw and N cooked?
b) What if you stop as soon as you are able to determine which eggs are which?

(One would expect this to have been asked before, but any regular can guess what happens if you try searching for "egg".)

Title: Re: Hard-boiled eggs
Post by Grimbal on Nov 16^th, 2005, 9:46am

1) if he is fast enough, the cooked ones should still be hot.
Or he can cook them all.
[hide] but the usual trick is to make them spin. Cooked eggs spin easily, raw eggs don't [/hide]

Title: Re: Hard-boiled eggs
Post by Three Hands on Nov 16^th, 2005, 11:09am

An addition to Grimbal's suggestion:
[hide]Spin the egg, then stop it and release it. If the egg starts to spin again, it is raw. If it stays stopped, it is cooked - at least, it works for hard-boiled eggs[/hide]

Title: Re: Hard-boiled eggs
Post by towr on Nov 16^th, 2005, 2:35pm

[hide]You can usually shake them to find out which are boiled and which aren't.
The boiled ones don't sound like anything much, the raw ones sound like they have liquid inside, which they do. [/hide]

Title: Re: Hard-boiled eggs
Post by beatsamurai on Nov 16^th, 2005, 3:32pm

I've never tried it but I bet this would work:
[hideb]Hold a bright light behind the egg. I imagine a raw egg would be slightly translucent and you'd be able to make out the yolk. The hard-boiled ones would likely not let the light through as easily.[/hideb]

Title: Re: Hard-boiled eggs
Post by Grimbal on Nov 17^th, 2005, 12:57am

If you wait enough, will they stink differently?

Title: Re: Hard-boiled eggs
Post by otter on Nov 17^th, 2005, 6:07am

on 11/16/05 at 15:32:14, beatsamurai wrote:

This is called "candling" an egg. You are correct. As light passes through a raw egg, the "white" of the egg will transmit light and the yolk will be clearly visible. A hard-boiled egg will not transmit light readily and the internal features will not be distinguishable.

Title: Re: Hard-boiled eggs
Post by Grimbal on Nov 20^th, 2005, 9:20am

A boiled egg in the morning is hard to beat.

Btw, why does it say "hard" and is in the easy forum?

Title: Re: Hard-boiled eggs
Post by towr on Nov 20^th, 2005, 11:03am

on 11/20/05 at 09:20:25, Grimbal wrote:

Btw, why does it say "hard" and is in the easy forum?

Because the egg is hard-boiled, rather than soft and snotty..

Title: Re: Hard-boiled eggs
Post by Dynasty on Nov 20^th, 2005, 12:25pm

if you're looking for a probability independent of the characteristics of raw and hard boiled eggs, i believe it would be....

[hideb]Wouldn't the number of expected eggs to go through be 5.5?

in terms of M and N.... where M = number of cooked eggs and N = number of raw eggs

M+N - (1- M/(M+N))

am I way off here? lol [/hideb]

Title: Re: Hard-boiled eggs
Post by Eigenray on Nov 24^th, 2005, 10:49am

Yeah. Are most people aware of this? It was something I'd always known somehow, but then I asked someone the other day and he hadn't heard it. Anyway, Three Hands's answer is the one I use in practice.

on 11/20/05 at 12:25:16, Dynasty wrote:

if you're looking for a probability independent of the characteristics of raw and hard boiled eggs, i believe it would be....

No... what's your reasoning?
For example, if N=M=2, there are 6 possibilities:
OOXX : 2
OXOX : 3
XOOX : 3
OXXO : 4
XOXO : 4
XXOO : 4,
for an expected value of 20/6 eggs checked.