All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
The logician's favorite game (Posted on 2005-03-18) Difficulty: 3 of 5
A logician has a favorite game to play at parties. He shows a set of solidly colored stickers to all his logician friends. Each logician, without looking, puts a random sticker on his/her own back. Each logician can only see the stickers on other people's backs, and no one can look at the unused stickers. The logicians take turns announcing whether they can deduce their own color. The game ends when someone announces he/she can deduce his/her own color.

One time while playing this game, no one had yet ended the game even though everyone had a turn. Should they continue to take second turns, or should they just give up and start a new game? Prove that it is impossible for a game that hasn't ended after everyone's first turn to ever end, or provide a counterexample.

See The Solution Submitted by Tristan    
Rating: 3.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts maybe i'm just being silly | Comment 6 of 28 |
"The game ends when someone announces he/she can deduce his/her own color."

a terribly silly counterexample would be one where i just ask another person what color is on my back.  "i deduce by so-and-so's answer that the colour on my back is xxx."  but since it's their favourite game, i'm guessing they wouldn't do that ... it'd get boring if every game was played out like that.  any given game can be ended that way in a worst case scenario.

another silly counterexample would be one where there are x number of players and x+y number of stickers.  since you can see all the other players' stickers, you're only left with (x-1)+y guesses.  if we can assume that all players have perfect photographic memory, then it would depend on the number y.

if y is large, but variety is little (example: all blue, except for one, or a few, red), then it's possible to end the game in a few turns.  if y is large, and variety also (example: take one of those paint sample books and cut out all the colour in the spectrum), then it's probably impossible to begin with, except in the method above.  since it's their favourite game, it would probably mean they wouldn't mind playing it over and over, so they can probably name all the colours in play. 

if y is little, then it would not be hard to guess.

y would not be zero, as this is their favourite game (replay value), and it would be too simple for logicians to announce they can deduce it in the first turn.

since it's their favourite game, however, i would rule out large y with large variety.  also, these are logicians playing. they would probably not want to guess and just give the correct answer the first try.

my question with this problem is this:  what if you get it wrong?  the rules state that the game ends when someone announces he/she can deduce his/her own colour.  i mean, anyone can do that at any time;  it's just a matter of whether they are correct or not.  what if they are incorrect?  does the game end?  are they penalized?  does it keep going? 

pardon a rambling novice;  it's early and the coffee hasn't kicked in yet.


  Posted by starlitsky on 2005-03-19 14:20:54
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information