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

Home > Just Math
Get them up (Posted on 2014-10-01) Difficulty: 2 of 5
10 playing cards are placed face-down on a table, forming a circle.
Your are allowed to turn over simultaneously 4 cards that either:
a.)all 4 are consecutive,
or
b.) 2 are on the left and 2 on the right of any specific card chosen by you (i.e. out of 5 consecutive cards only the middle one remains unturned) .

By executing a final number of the above (a. or b.) procedures can you reach an "all face-up" state?

If yes, explain how.
Otherwise, prove why not.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Unsatisfying computer proof | Comment 3 of 5 |
(In reply to Unsatisfying computer proof by Charlie)

Errata:  Oh, by the way, the number of possible configurations is 2^10, not 2^12.  And it is not true that all of the configurations achieved by the computer program have a number of upturned cards equal to 2 mod 4; many of them equal 0 mod 4.



 

  Posted by Steve Herman on 2014-10-02 10:22:56
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