Grex Paradox Conference

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Grex Paradox Item 15: Paradox of the Eggs
Entered by md on Tue Nov 7 15:04:13 UTC 1995:

A man sets 12 eggs in front of you.  He's numbered the eggs "1" 
through "12" with a marker pen.  He tells you that he has candled 
the eggs and knows for a fact that one, and only one, of them has 
a double yolk.  He says you must break open each egg, starting 
with #1 and proceeding in numeric order to #12.  He says that he 
will not tell you which egg has the double yolk, and promises 
that you won't know which one it is until you actually open it up 
and see the double yolk; that is, you'll never be able to hand 
him an unopened egg and say, "The double yolk is in this one."

You reason as follows:  

   "Obviously, he couldn't have put the double yolk egg in 
   position #12, because if I break open eggs #1 through #11 and 
   see all single yolks I'll know for sure that it must be #12 
   without opening it up.  So, the last egg that could have the 
   double yolk is #11.  

   "But the last egg that could have the double yolk can't be 
   #11, either, because if it is, and I break open eggs #1 
   through #10 and see all single yolks, then I'll know for sure 
   that it must be #11 without opening it up, since #11 is the 
   last one it could be.  So, the last egg that could have the 
   double yolk is #10.  

   "But if the last egg that could have the double yolk is #10, 
   then *that* wouldn't be a surprise, either, because if I break 
   open eggs #1 through #9 and see all single yolks I'll know 
   for sure that it must be #11 without opening it up.  So, the 
   last egg that could have the double yolk is #9." 


Using the same reasoning process, you go all the way back to egg 
#1, and conclude that *none* of the eggs can possibly have a 
double yolk.  You then start breaking open the eggs in sequence, 
and are stunned to see a double yolk when you break open #5!  

How can this be?

9 responses total.

#1 of 9 by md on Mon Nov 27 21:40:54 1995:

Give up, eh?  Too tough for you, eh?  Time to send back your Mensa pin, eh?

#2 of 9 by md on Mon Mar 18 13:43:01 1996:

Can't take the pressure, eh?  Not as smart as you thought you were, eh?

#3 of 9 by lucey on Wed May 29 02:33:58 1996:

 Fine, I'll dare to be the first person (besides md) to enter a response.

 It is true that if all of the yolks up to and including yolk #11 are single
youlks, then #12 must be a double yolk.  However, it does not follow that if
yolk #10 is a single yolk, that yolk #11 must be a double.  There is still
the possiblity that it is in #12 sa well as in #11.  This can not be known
fo rsure until #11 is opened up.  Thus, the whole line of logic dissolv. 
Paradox is resolved. :)

#4 of 9 by nephi on Sat Jun 8 08:23:25 1996:

Cool.  8^)

#5 of 9 by yo on Thu Aug 21 12:00:06 1997:

woooie

#6 of 9 by willow on Mon Oct 6 14:02:16 1997:

Isn't this the which day will they hang the guy argument all over again?

#7 of 9 by diznave on Thu Jan 8 16:26:57 1998:

No, this is the 'Guess how many eggs are in that veggie omlette' argument all
over again for the first time.      <what?>

#8 of 9 by eyenot on Sun Jun 20 07:12:36 1999:

there is no argument .
basically you can pretend there's an argument by ignoring the presence of all
the eggs besides those eggs that you've smashed already, except for one, and
then astonish yourself with the fact that besides eggs you've smashed and eggs
you've ignored save one, there happens to be one egg left to peruse.

i mean ocm eon. this isn't a paradox. it's like saying this :

out of three identical triplets one is timmy. you won't know until you call out
timmy's name and he responds , just which one is timmy. so you call out five
hundred other names but never call out timy.

...

timmy does not respond !! ...

...

so logic then would deduce that timmy is -not- in the line since you what,
named every name possible -except- for timmy's, so timmy cannot possibly be
there,  or else he would knwo that 'hey this person has said every name -but-
timmy,'' i bet they're using a roundabout way of saying timy ... indirectly.'
and then respond by saying 'my name is timmy!'

but then you defeat the entire purpose of what you're doing,

and say 'no, see you can't be timmmy becasuuuse

timmy isn't even here ! else he would have answered already!'

and sinc eyou defeated your own purpose by purposefully being ignorant,
in a situation where knowledge and awareness are called for,
it is not reality that is paradoxic

but your own warped perceptions that have crossed themselves

and made a totally sensible reality -appear- to be apradoxic.

in other words if the old man says to you 'you will not know which egg is
double yolked until you break it open' you just say 'that's f****in right' and
smash eggs until a double yolk falls out. there it is ! number wtfe !

and then you say 'yup you were right all along no way i coulda guessed
especially with one in twelve ofdds of being correct...'

but noooo you=could-  MAKE it paradoxic by only breaking ONE
egg and then saying 'hey man. this isn't a oduble yolk... NONE of these f'in
eggs are double yolks, you understand me ?! you freakin' GET IT, brah ?!?!'

and leave hmim maybe stunned except for to say 'but you've totally ignored the
other...'

'THEY DO NOT EXIST OKAY ? THOSE EGGS ARE NOT THERE AND I -INSIST-... THAT IF 
THEY --AAARREEE-- THERE... THAT THAT IS THEREFORE A PARADOX.'

BECAUSE I SAID SO !

        i mean come on have some common sense.

#9 of 9 by vectra on Thu Aug 19 04:19:26 1999:

you need to be clever to be clever duh

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