wu :: forums
« wu :: forums - TopSwops »

Welcome, Guest. Please Login or Register.
Aug 16th, 2018, 8:16pm

RIDDLES SITE WRITE MATH! Home Home Help Help Search Search Members Members Login Login Register Register
   wu :: forums
   riddles
   hard
(Moderators: ThudnBlunder, Eigenray, Grimbal, Icarus, william wu, towr, SMQ)
   TopSwops
« Previous topic | Next topic »
Pages: 1  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: TopSwops  (Read 6663 times)
nakli
Junior Member
**






   
WWW Email

Gender: male
Posts: 62
TopSwops  
« on: Oct 28th, 2010, 8:26am »
Quote Quote Modify Modify

Created by the mathematician John Conway and known as Topswops, the puzzle starts like this: Begin with a randomly ordered deck of cards numbered 1 to n, with n being however high a number you choose. Now count out the number of cards represented by whatever card is the top card, and turn that block of cards over on top of the remaining cards. Then count out the number of cards represented by the new top card and turn this whole block over on top of the remaining cards. Repeat until the card numbered 1 comes to the top (realizing that we know the card numbered 1 will always eventually come to the top).
 
Now here’s what needs to be done: Calculate the maximum and minimum number of steps required with n number of cards.
 
http://www.utdallas.edu/news/2010/10/28-6621_Computer-Scientists-Make-Pr ogress-on-Math-Puzzle_article.html
IP Logged

I was born naked on a bed with a lady.
towr
wu::riddles Moderator
Uberpuzzler
*****



Some people are average, some are just mean.

   


Gender: male
Posts: 13631
Re: TopSwops  
« Reply #1 on: Oct 28th, 2010, 9:06am »
Quote Quote Modify Modify

Isn't the minimum simply 0 steps, notably when 1 is randomly on top?
 
The first terms for the maximum can be found at http://www.research.att.com/~njas/sequences/A000375  
 
[edit]
Ah, the point rather seems to be to find upper and lower bounds to the maximum number of steps n cards might take.
[/edit]
« Last Edit: Oct 28th, 2010, 9:18am by towr » IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
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