perplexus.info :: Shapes : Four bugs

Four bugs (Posted on 2002-05-07)

Four bugs are located in the corners of a square, 10 inches on the side. They are arranged like this:

            A---B
            |   |
            D---C

As the clock starts, A begins crawling directly toward B, which goes to C, C goes to D and D to A.

Each bug will home in exactly on its target, reguardless of the target's motion, so their paths will be curves spiraling toward the center of the square where they will meet.

What distance will each of the bugs have covered by then?

Submitted by levik

Rating: 4.0000 (12 votes)

Solution: (Hide)

The answer is 10 inches.
First thing to notice is the symmetry. Each bug will home in on its target at exactly the same speed, and each will approach the center at exactly the same speed. This means that the four bugs will always form a square.
Since they form a square, their travel paths will always be at right angles to one another. That means that at any given instant, Bug B's motion does not take it any closer or any further away from Bug A. Hence, Bug B's motion does not increase or decrease the distance Bug A must travel.
So Bug A must travel the 10 inches that was separating the two bugs at the start. This applies for the other bugs as well.
(Solution submitted by friedlinguini)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Problem Solution With Explanation	K Sengupta	2007-05-16 05:45:54
answer	K Sengupta	2007-04-15 13:55:31
re: response to Jason	Gamer	2003-10-26 21:16:31
Solution	Antonio	2003-08-23 08:35:52
four bugs	terry	2003-01-19 21:19:09
Spiral	Half-Mad	2002-05-08 18:53:37
response to Jason	jim	2002-05-08 05:00:49
HALF MIND REBUT	JASON	2002-05-08 02:07:21
Jason's solution	Half-Mad	2002-05-08 00:13:38
SOLUTION	JASON	2002-05-08 00:02:03
Possible solution	Half-Mad	2002-05-07 21:39:51
solution	Aaron Seligman	2002-05-07 14:28:34
Solution	friedlinguini	2002-05-07 13:08:23

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