wu :: forums
« wu :: forums - Logicians and stamps »

Welcome, Guest. Please Login or Register.
Mar 29th, 2024, 6:41am

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: Icarus, SMQ, towr, ThudnBlunder, Eigenray, william wu, Grimbal)
   Logicians and stamps
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Logicians and stamps  (Read 6177 times)
Altamira_64
Junior Member
**





   


Posts: 116
Logicians and stamps  
« on: Apr 3rd, 2013, 11:53am »
Quote Quote Modify Modify

N logicians are about to play the following game:
A moderator sticks two stamps on each logicians' forehead. He tells everyone that in the beginning of the game he had n+1 red stamps and n+1 black stamps. They do not know, however, that the moderator has stuck one red and one black stamp on the forehead of each logician, except for one to whom he has stuck two red stamps.
The logicians are sitting on a circle so that anyone can see everyone else's stamps. The moderator asks them in turn, starting from the logician who is sitting in the position Nr 1, "what color are your stamps?" The logician with the two red stamps on his forehead is sitting in the position Nr x (unknown to us).
For which values of n and x the logician with the two red stamps can guess the color of his own stamps?
 
IP Logged
rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2872
Re: Logicians and stamps  
« Reply #1 on: Apr 4th, 2013, 7:39am »
Quote Quote Modify Modify

It depends how the logicians answer when they have incomplete knowledge of their own stamps - if they simply say they don't know, then no-one gains any new information from anyone's answer.
 
If the logicians say what they do know about their stamps (that they don't have two red) then, unless x=1, as soon as #1 speaks, everyone else, including X, knows that #1 sees n red stamps (and n-2 black stamps) so can deduce their own stamps. When x=1, everyone else deduces their own stamps as soon as #2 speaks. In both cases, the person to give partial information about their own stamps gains no information thereafter (since everyone else knows what he sees, they can deduce their stamps without considering his, meaning their deductions tell him nothing)
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Logicians and stamps  
« Reply #2 on: Apr 4th, 2013, 11:55am »
Quote Quote Modify Modify

on Apr 4th, 2013, 7:39am, rmsgrey wrote:
It depends how the logicians answer when they have incomplete knowledge of their own stamps - if they simply say they don't know, then no-one gains any new information from anyone's answer.
They do gain some information; for example for N=3, if x=2, player 1 and 3 will know by their second turn that they have a red and black stamp; if x=1 or 3, blue will know by his second turn that he has a red and black stamp. (Assuming I worked it out correctly.)
« Last Edit: Apr 4th, 2013, 11:56am by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Altamira_64
Junior Member
**





   


Posts: 116
Re: Logicians and stamps  
« Reply #3 on: Apr 4th, 2013, 4:12pm »
Quote Quote Modify Modify

on Apr 4th, 2013, 11:55am, towr wrote:

They do gain some information; for example for N=3, if x=2, player 1 and 3 will know by their second turn that they have a red and black stamp; if x=1 or 3, blue will know by his second turn that he has a red and black stamp. (Assuming I worked it out correctly.)

 
Blue??
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Logicians and stamps  
« Reply #4 on: Apr 4th, 2013, 10:18pm »
Quote Quote Modify Modify

Whoops.. That should be player 2
I work with a graph representation using colored edged to denote which worlds/states are indistinguishable to a user. So for me 1=red, 2=blue, 3=green.
You might have guessed by the fact player 1 and 3 were already mentioned and 2 was the only one left. Wink
« Last Edit: Apr 4th, 2013, 10:47pm by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
rmsgrey
Uberpuzzler
*****





134688278 134688278   rmsgrey   rmsgrey


Gender: male
Posts: 2872
Re: Logicians and stamps  
« Reply #5 on: Apr 5th, 2013, 5:50am »
Quote Quote Modify Modify

Ah, yeah, the old red-eyed monks thing of what they know about what each other knows about...
 
So, with 3 people, and 4 stamps of each colour:
 
if x=1:
 
#2 and #3 both know they don't have a red pair.
 
#1's statement shows he doesn't see two black pairs. #2s statement shows #3 doesn't have a black pair, so #3 knows what colours he has, from which #1 can deduce that he has a pair, but not which colour. From that, #2 can deduce he's not a black pair (otherwise #1 could deduce his own colour) and knows his pair. #1 is stuck with no way to break the colour symmetry.
 
If x=2:
 
#1's statement doesn't help #3, but from there it's as above, one turn later - and X (#2) is still stuck due to symmetry.
 
If x=3:
 
#1 and #2 tell each other nothing, #3 tells them they're not both black pairs, so #2 gets there on his second turn and #1 on his third.
 
 
In general, it looks like X can never know his own stamps because he has no way of telling red from black
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Logicians and stamps  
« Reply #6 on: Apr 5th, 2013, 6:19am »
Quote Quote Modify Modify

Yeah, considering the situation is completely symmetric if you change colors, the person stuck with the pair of one color can never find out which it is. Nothing he sees is different, and nothing that happens is different.
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Student2013
Newbie
*





   


Posts: 1
Re: Logicians and stamps  
« Reply #7 on: Jun 19th, 2013, 7:02am »
Quote Quote Modify Modify

Hey Guys, i hope that i can get some help from you. I really hope i can pass my logic exam tomorrow, so that i can take a break from school, and i dont know who to ask for help.  
 
Would you please help me?  It would mean the world to me, because i am really having a hard time now.  
 
Problem:  
 
Assuming that Lxy is a means "x loves y" and Rx "x is rich" write logical formulas for  
 
a) It is enough to love someone to be rich  
b) being rich doesn't mean loving someone
c) you are not rich i you love no one.  
d) Love is not always a symmetrical relation  
 
and  
 
 
Problem 2)  
 
Imagine you are married and wish to open a joint credit account. Which of the following would you prefer to have printed on your checks: "John and Jane Dole" or "John or Jane Dole"? Explain your decision.  
 
Again, if there is a good soul out there that wish to help me out, i am going to be forever thankful.  
 
yours sincerely,  
 
psychology student year 4.
IP Logged
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13730
Re: Logicians and stamps  
« Reply #8 on: Jun 19th, 2013, 10:35am »
Quote Quote Modify Modify

It might have been better to start your own topic rather than append it to this one...
 
As for 1d, (x,y: Lxy Lyx)
IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Grimbal
wu::riddles Moderator
Uberpuzzler
*****






   


Gender: male
Posts: 7526
Re: Logicians and stamps  
« Reply #9 on: Jun 20th, 2013, 9:46am »
Quote Quote Modify Modify

You should tell us what you think the answers are.  We would be happy to tell you where you are wrong.
 
But it is probably too late already.
IP Logged
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board