Is It Possible for a Bug to Traverse Less Than 14 Meters in a Room?

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Discussion Overview

The discussion revolves around a problem involving a bug traversing a distance in a room with specific dimensions. Participants explore whether the bug can travel less than 14 meters from its starting position to a goal location, considering the constraints of the bug's movement and the room's geometry.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants calculate the distance between the starting point and the goal to be 10.2 meters, referencing the Pythagorean theorem.
  • Others suggest that the bug must walk the distance, implying that the path taken is crucial to the calculation.
  • One participant mentions that a bug of length 1 cm could theoretically traverse about 13.962 meters, but later revises this based on the bug's actual position.
  • Another participant proposes a distance of approximately 13.928 meters using a different calculation method.
  • Several participants suggest "unfolding" the room to visualize the problem, noting that there are multiple ways to do this, leading to different conclusions about the shortest path.
  • Some participants argue that no unfolding method can yield a path shorter than 14 meters given the configuration described.

Areas of Agreement / Disagreement

Participants express differing views on whether the bug can traverse less than 14 meters, with some calculations suggesting it is possible while others assert that it is not. The discussion remains unresolved with multiple competing perspectives on the problem.

Contextual Notes

There are limitations regarding the assumptions about the bug's movement and the specific configurations of the room that may affect the calculations. The discussion highlights the dependency on how the problem is visualized and approached mathematically.

moje_ime
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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?
(Sorry for my bad English).
 

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Sure. Those two points are only 10.2 metres apart.

Oops. Did I spill the beans?
 
Last edited:
DaveC426913 said:
Sure. Those two points are only 10.2 metres apart.

Oops. Did I spill the beans?
Could you explain how you arrived at 10.2 meters?
 
Hi,
My solution's also 10.2 meters.
The keyword is "Pythagorean theorem".
 
I suspect that there's a missing bit in the list of givens: the bug has to walk there.
 
Last edited:
the bug MUST walk there...
Any idea?
 
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:
the bug MUST walk there...
Any idea?

Yeah I think I can get there in sqrt(194) which is approx 13.928 meters.
 
Hint- try "unfolding" the room to make it flat.
 
  • #10
Hint- try "unfolding" the room to make it flat.
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
shmoe said:
Hint- try "unfolding" the room to make it flat.
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
DaveC426913 said:
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.

Is your path a straight line? (I don't want to give much more away)
 
  • #13
DaveC426913 said:
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.

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.
 

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