[Guest]

Imagine a room with dimensions 12x12x30 feet. A spider clings to the top of one of the 12x12 walls, exactly one foot from the ceiling and exactly 6 feet from either wall (i.e., in the middle side to side). A fly clings to the opposite 12x12 wall, exactly one foot from the floor and exactly 6 feet from either wall. What is the shortest path ALONG THE SURFACES that the spider can use to catch the fly? The fly will remain in the same place the entire time, and the spider cannot leave the surfaces of the room.

For example, an obviously incorrect answer is for the spider to walk to a wall (6 feet), walk across the length of the room (30 feet), walk to the middle of the fly's wall (6 feet), and then walk down to the fly (10 feet) for a total of 52 feet. The answer is shorter and more complicated than this.

[curr3nt]

42

1 foot up, 30 along ceiling, 11 down

edit - Trying to walk along the walls in a diagonal would be a bit over 43. sqrt(10² + 42²)

Edited March 29, 2011 by curr3nt

[curr3nt]

I can get about 40.7 ( sqrt((1+30+6)² + (6+11)²) ) going left along wall to ceiling, to left wall to fly's wall.

edit - changed 37² + 17² to the break out of measurements

Edited March 29, 2011 by curr3nt

[Guest]

curr3nt, you're correct!

For anyone who hasn't figured it out and hasn't looked at curr3nt's solution, I recommend taking some time to draw it and think it out. It's satisfying.

[Guest]

the problem with the third post is that is does not make a box because the ceiling and the floor are connected

[curr3nt]

the problem with the third post is that is does not make a box because the ceiling and the floor are connected

That is the ceiling and a wall, not floor.