Find the Shortest Route for an Ant in a Cube Shaped Room | Brainteaser

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In summary, the conversation is about a brainteaser involving an ant in a cube shaped room. The ant needs to go from one corner of the floor to the opposite corner on the ceiling, but cannot fly. The shortest route is the body diagonal, but the ant is tired and wants to take the shortest possible route. The solution involves walking diagonally to the corner directly below the desired end point, and then going up for a total walking distance of approximately 2.1415 times the length of the cube.
  • #1
tanujkush
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Ok so here is a brainteaser, you should get it in your second attempt at the max., else consider yourself poor at math :biggrin:

An ant is in one corner of a cube shaped room. (say one of the bottom corners on the floor). The ant decides to go to the opposite corner on the roof, which would fall on the diagonal of the cube. Unfortunately, the ant cannot fly, else it would have taken the body diagonal route of the cube to reach there. But the ant is most tired, and it wants to take the shortest route possible. Help the ant out!
 

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  • #2
walk diagonally (at 22.5°) along the floor to the middle of the opposite face and then walk diagonally (at 22.5°) up to the opposite corner. A total walking distance of approximately 2.16 times the length of the cube face.
 
  • #3
redargon said:
walk diagonally (at 22.5°) along the floor to the middle of the opposite face and then walk diagonally (at 22.5°) up to the opposite corner. A total walking distance of approximately 2.16 times the length of the cube face.

spot on!
 
  • #4
Have I misunderstood the question? Why not walk diagonally to the corner directly below the End, and then go up. Walking distance is sqrt 2 + 1 times the cube length, approx 2.1415 times the length.
 
  • #5
Gib Z said:
Have I misunderstood the question? Why not walk diagonally to the corner directly below the End, and then go up. Walking distance is sqrt 2 + 1 times the cube length, approx 2.1415 times the length.

walking till the midpoint of the opposite face and then straight to the point end gives you a total distance of sqrt((2a)^2+a^2) = sqrt(5)*a = 2.23606a

walking on the bottom diagonal and then straight up to End is a distance of (sqrt(2)+1)*a = 2.414a>2.3606a
 
  • #6
My bad, something exploded in my brain as I used digits of pi for sqrt 2.
 
  • #7
If the sides of the cube are unfolded to a flat surface, the ant's shortest path will be a straight line
 
  • #8
bpet said:
If the sides of the cube are unfolded to a flat surface, the ant's shortest path will be a straight line

thats exactly the logic! i was asked this question as a part of my mathematics aptitude some time before undergrad, and I was stumped at the time
 

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