mersenneforum.org  

Go Back   mersenneforum.org > Fun Stuff > Puzzles

Reply
 
Thread Tools
Old 2005-03-30, 20:22   #1
JHansen
 
JHansen's Avatar
 
Apr 2004
Copenhagen, Denmark

22×29 Posts
Default Poker puzzle

It's by birthday today, and one of my gifts was a poker set. Sweeeet

Of course we couldn't resist trying to see if we could handle the chips like the pros on TV. More specific we tried to take two stacks of chips of equal height, and then "fold" them together into one stack using only one hand. We were'nt that good...

But, we found an interesting problem in the process:

Find (is possible) a closed form for the Poker Number P(n).

The Poker Number is defined as follows:

Take two differently coloured stacks (here: Red(R) and Blue(B)) of chips of equal height, n, and apply the following shuffle procedure:

1) Place the R stack in your left hand and the B in your right hand.

2) Take one chip from the left stack and place it on the table in fromt of you.
3) Take one chip from the right stack and place it on top of the stack in front of you.
4) repeat 2) and 3) until all chips are in the stack in front of you.
5) Take the top n chips and make that your new right stack and let the bottom n chips be your new left stack.

Steps 2)-5) is defined to be one operation.

The Poker Number P(n) > 0 is defined as the minimum number of operations needed for all the chips in the left stack to be red again and all the chips in the right stack to be blue.

Here are the first few values: P(n)= 1,2,4,3,6,10,12,4,8,....

Is there a simple formula for the Poker Number? Is seems that P(2^n)=n+1.

--
Cheers,
Jes
JHansen is offline   Reply With Quote
Old 2005-03-31, 09:57   #2
cheesehead
 
cheesehead's Avatar
 
"Richard B. Woods"
Aug 2002
Wisconsin USA

22×3×599 Posts
Default

See the similar sequence A002326, "Number of riffle shuffles of 2n+2 cards required to return a deck to initial state", in the OEIS at http://www.research.att.com/cgi-bin/...i?Anum=A002326


A002326 starts with a first term of 0 instead of 1 as your sequence begins.

Last fiddled with by cheesehead on 2005-03-31 at 10:01
cheesehead is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Some puzzle Harrywill Puzzles 4 2017-05-03 05:10
Video Poker Unregistered Information & Answers 7 2010-06-23 02:42
4 4s puzzle henryzz Puzzles 4 2007-09-23 07:31
Dot puzzle nibble4bits Puzzles 37 2006-02-27 09:35
now HERE'S a puzzle. Orgasmic Troll Puzzles 6 2005-12-08 07:19

All times are UTC. The time now is 03:09.

Sat Nov 28 03:09:18 UTC 2020 up 79 days, 20 mins, 3 users, load averages: 1.53, 1.36, 1.20

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.