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        riddles >> easy >> 'Bug'gy Puzzle
        
(Message started by: u_think_u_succeed on Jul 31^st, 2007, 7:22am)

Title: 'Bug'gy Puzzle
Post by u_think_u_succeed on Jul 31^st, 2007, 7:22am

There are 4 bugs placed at the corners of a square of side 's'. Each bug, when moving. moves at a speed of 'b'.

Now, all four bugs start moving towards each other, and maintain their 'moving toward each other act' throughout, until they meet.

1. Where do they meet.
2. What is the distance covered by each bug.
3. Time when the bugs meet.

Now, try the above for

a) Three bugs on an equilateral triangle.
b) Five bugs on a regular pentagon.

Title: Re: 'Bug'gy Puzzle
Post by towr on Jul 31^st, 2007, 7:34am

I think it makes a bit of a difference how they move towards each other. You probably want something like "each bug moves to the one that started on the next corner clockwise" [hide]That way you get spiraling paths[/hide]
If the bugs (in the square, or another even-sided) case moved to the one in the opposite corner it wouldn't be very interesting.

Title: Re: 'Bug'gy Puzzle
Post by u_think_u_succeed on Jul 31^st, 2007, 7:39am

Quote:

You probably want something like "each bug moves to the one that started on the next corner clockwise"

Yup, sorry for not specifying it.

Title: Re: 'Bug'gy Puzzle
Post by jollytall on Jul 31^st, 2007, 11:12pm

They move exactly the same way as four missiles (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1142629557)move after the first period of their flight.

Title: Re: 'Bug'gy Puzzle
Post by nitinvashist on Sep 27^th, 2007, 6:56am

What about bugs at end of equilateral triangle and polygon?

Title: Re: 'Bug'gy Puzzle
Post by towr on Sep 27^th, 2007, 7:14am

There shouldn't be much of a qualitative difference in those cases. [hide]They'd still spiral inwards[/hide]

Title: Re: 'Bug'gy Puzzle
Post by nitinvashist on Sep 27^th, 2007, 7:58am

Surely, but it should be more spiral than say a square, and consequently the distance travelled should be more (I think).
I am looking for a general solution for n sided polygon of even/odd sides and the distance travelled before the bugs meet.
Is there a way to calculate the distance travelled using the relative motion of bugs?

Title: Re: 'Bug'gy Puzzle
Post by towr on Sep 27^th, 2007, 8:47am

on 09/27/07 at 07:58:49, nitinvashist wrote:

Surely, but it should be more spiral than say a square, and consequently the distance travelled should be more (I think).

That makes sense, as n goes to infinity, they should end up going in a circle.

Quote:

I am looking for a general solution for n sided polygon of even/odd sides and the distance travelled before the bugs meet.

A general solution is mentioned in the first post of the thread Jollytall linked to (i.e. here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1142629557)).