My Math Forum probability problem in hexagon

 February 7th, 2014, 03:28 PM #1 Newbie   Joined: Feb 2014 Posts: 2 Thanks: 0 probability problem in hexagon So say I have 6 bugs standing on the 6 vertices of a hexagon, one per vertex. And say they each pick a vertex that they are not currently on, and starts moving in a straight line towards that vertex at the same speed. So my question is how many possibilities are there for the bugs to move to the vertices such that none of them are ever in the same place at the same time?
 February 7th, 2014, 03:51 PM #2 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 664 Thanks: 87 Re: probability problem in hexagon This seems like it should simply be 6! = 720 (719 other than the starting position).
 February 7th, 2014, 04:01 PM #3 Newbie   Joined: Feb 2014 Posts: 2 Thanks: 0 Re: probability problem in hexagon I don't think so. No lines can intersect with another line at a point that is the same distance away from both starting vertices, so I think there are less.
February 8th, 2014, 06:43 AM   #4
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: probability problem in hexagon

Hello, leuler!

Quote:
 I have 6 bugs standing on the 6 vertices of a hexagon, one per vertex. They each pick another vertex and start moving directly toward that vertex at the same speed. So my question is: how many possibilities are there for the bugs to move to the vertices such that [color=blue]none of them are ever in the same place at the same time[/color]?

The answer seems to be the number of derangements of 6 objects:$\;d(6) \:=\:265.$

But you remind us that the bugs must not collide . . . ack!

 Tags hexagon, probability, problem

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post gaussrelatz Algebra 3 April 14th, 2012 08:37 PM e81 Algebra 2 May 17th, 2011 10:15 PM Rekooo Algebra 1 December 19th, 2010 06:26 AM Hangman Algebra 3 April 8th, 2009 04:28 AM teixeira Algebra 7 September 27th, 2007 01:36 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top