# Help to a bug (or me?)

1. Jun 12, 2006

### moje_ime

I need a help.
Here is the question:
There is a bug in a room. The room is 4 meters high, 4 meters wide and 10 meters long.
The bug is sitting on the left (4x4) wall, one meter up from the ground, in the middle.
The bug must come to the goal which is on the totally right side, in the middle of the right wall (4x4), three meters up from the ground.
Can the bug pass the distance less than 14 meters?

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2. Jun 12, 2006

### DaveC426913

Sure. Those two points are only 10.2 metres apart.

Oops. Did I spill the beans?

Last edited: Jun 12, 2006
3. Jun 13, 2006

### HallsofIvy

Could you explain how you arrived at 10.2 meters?

4. Jun 13, 2006

### lonesome-dreamer

Hi,
My solution's also 10.2 meters.
The keyword is "Pythagorean theorem".

5. Jun 13, 2006

### DaveC426913

I suspect that there's a missing bit in the list of givens: the bug has to walk there.

Last edited: Jun 13, 2006
6. Jun 13, 2006

### moje_ime

the bug MUST walk there....
Any idea???

7. Jun 13, 2006

### heartless

Theoretically it's possible. Remember that bug is 3d, and not infinitely flexible. For bug of length of 1cm It comes out to be about 13.962m. Anyway less than 14.
//edit Wait, sorry, I thought it said that bug, is in the middle and walks to the middle. Let me do my calculations again... BRB

Ok, since here it seems like he's one down, three up/double walls, my calculations show that it's again ~ 13.962m for bug of length of 1cm.

Last edited: Jun 13, 2006
8. Jun 13, 2006

### uart

Yeah I think I can get there in sqrt(194) which is approx 13.928 meters.

9. Jun 13, 2006

### shmoe

Hint- try "unfolding" the room to make it flat.

10. Jun 13, 2006

### uart

It's a good problems though. Note that there are two different ways of "unfolding" it, one way that works and one way that doesn't.

11. Jun 13, 2006

### DaveC426913

This was, of course, the first thing I thought of as well. But it does not solve the problem, not with the configuration given. No matter how I unfold it and construct a path, I cannot get a shorter path than 14m.

12. Jun 13, 2006

### shmoe

Is your path a straight line? (I don't want to give much more away)

13. Jun 14, 2006

### uart

See my post above Dave, there are two different ways of unfolding it. One that gives the distance as the hypotenuse of a triangle 14cm by 2cm (obviously no good) and another that gives a 13cm by 5cm triangle, which is where I got the sqrt(194) from.