wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> putnam exam (pure math) >> Number of balls in a bag
        
(Message started by: archau on Dec 30^th, 2007, 1:10pm)

Title: Number of balls in a bag
Post by archau on Dec 30^th, 2007, 1:10pm

We have balls numbered 1,2,3,4,5,..... and a bag

At time 0.9 secs we put ball 1 in the bag
At time 0.99 secs we remove ball 1 and push in balls 2,3

At time 0.999 sec we remove ball 2 and push in balls 4,5,6

....

How many balls are in the bag at time 1.0s?

Title: Re: Number of balls in a bag
Post by towr on Dec 30^th, 2007, 1:33pm

[hide]I dare you to name the lowest numbered ball that you didn't remove.[/hide]

Title: Re: Number of balls in a bag
Post by ThudanBlunder on Dec 30^th, 2007, 4:40pm

http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1117490596

Title: Re: Number of balls in a bag
Post by temporary on Jan 22^nd, 2008, 9:46pm

[hide]Countably infinite.[/hide]

Title: Re: Number of balls in a bag
Post by towr on Jan 23^rd, 2008, 12:52am

on 01/22/08 at 21:46:03, temporary wrote:

[hide]Countably infinite.[/hide]

[hide]Ok, then tell me which balls weren't taken out? All balls have a number, so give the lowest numbered ball that isn't in the bag.[/hide]

Title: Re: Number of balls in a bag
Post by temporary on Jan 23^rd, 2008, 6:19pm

The lowest number ball that wasn't removed is

Title: Re: Number of balls in a bag
Post by towr on Jan 24^th, 2008, 12:16am

on 01/23/08 at 18:19:37, temporary wrote:

The lowest number ball that wasn't removed is

Indeed, it's non-existent; hence all balls must have been removed; hence none remain.