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

Home > Paradoxes
The Exclusive Club (Posted on 2013-07-01) Difficulty: 3 of 5
There is a club called the Exclusive Club. Somebody is a member of this club if and only if he has not shaved anybody who has shaved him. In other words, X is a member of the Exclusive Club if and only if there is no Y such that X shaves Y and Y shaves X.

A barber once claimed that he had shaved every member of the Exclusive Club and nobody else. Show that the barber's claim cannot be true.

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(3): solution | Comment 4 of 8 |
(In reply to re(2): solution by Steve Herman)

thank you Steve.  The key part is the use of "if and only if" in the second sentence describing membership requirements.


  Posted by Daniel on 2013-07-01 21:13:55
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 (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information