tag:blogger.com,1999:blog-15628310.post1046941762627456782..comments2021-03-02T05:02:26.838-05:00Comments on Question of the day: Another Question About AliceAnonymoushttp://www.blogger.com/profile/18153935609499338685noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-15628310.post-71235666250378636792009-12-11T10:17:19.058-05:002009-12-11T10:17:19.058-05:00Here's Rich's solution:
After a minute th...Here's Rich's solution:<br /><br />After a minute there will always be an ant in the middle, regardless of how many we placed on there or how they were oriented. This can be visualised if we give Alice a baton to begin with and every time an ant meets another, as well as saying hello it passes the baton on, so the baton will move at a speed of one metre per second until it reaches the end of the stick and will come back the other way, thus the baton will be in the middle of the stick after a minute and will obviously be accompanied by an ant.<br /><br />The lucky ant holding the baton after a minute will be Alice if and only if there are an equal number of ants either side of her when we start. To prove this it is required to notice that after a minute the ants (as a collective) will have moved into positions that were a mirror image of how they started, so if Alice were in the middle after a minute and we started with L ants to the left and R ants to the right of her after a minute there would be R ants to the left of her and L ants to the right of her, but since ants cannot pass one another L must equal R for Alice to be the one in the middle.Anonymoushttps://www.blogger.com/profile/18153935609499338685noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-75103842228997869232009-12-11T09:17:26.862-05:002009-12-11T09:17:26.862-05:00So does this false choice of governance think the ...So does this false choice of governance think the ant will be back in the middle after a minute? Or would the ant be Obama instead of Alice?<br /><br />Oh, wait...that's a conspiracy too.USAF Pilothttps://www.blogger.com/profile/01326339691636594880noreply@blogger.comtag:blogger.com,1999:blog-15628310.post-90988823237553238362009-12-09T17:23:46.954-05:002009-12-09T17:23:46.954-05:00Apologies, forgot to include that Alice's stic...Apologies, forgot to include that Alice's stick is 1 metre long! Is quite fundamental to the question actually as well.Unknownhttps://www.blogger.com/profile/03189875170596849517noreply@blogger.com