A room is 30 feet long, 12 feet wide and 12 feet high.

geometry/spider.and.fly New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

A room is 30 feet long, 12 feet wide and 12 feet high.  A spider is on
one end wall, midway across it and 1 foot below the ceiling; a fly is on
the opposite end wall, midway across it and 1 foot above the floor.
What is the shortest distance the spider must crawl along the walls,
ceiling and floor to reach the fly?  (Down the wall, across the floor and
up the other wall is 11 + 30 + 1 = 42 feet; it can be done in less.)

[ Editor: problem statement reconstructed from the postings; the room's
dimensions are inferred from the figures in the solution. ]

Show solution

How about 40 ft.

Method:

This is easiest to see if you envision laying the walls of the room out flat
as follows:

Draw the ceiling rectangle with the long lines horizontal.

Connected to it on the bottom, draw the side wall, and the floor connected
below that.

Draw the starting wall on the left side, connected to the ceiling.

Draw the ending wall on the right side, connected to the floor.

This gives a diagram that looks something like this:

x---x---------x
|  s|  ceil   |
x---x---------x
    |         |   |
     x---------x---x
    |  floor  |e  |
     x---------x---x

The starting point (s) centered vertically within the left square, 1 foot
from the right side of it.

The ending point (e) is centered vertically within the right square, 1 foot
from the left side of it.

If you draw a line between those two points, it is 40 feet.  It covers 32
feet horizontally (1 foot on starting wall, 1 foot on ending wall, and 30
feet in between). It covers 24 feet vertically (6 feet until it gets to the
side wall, 12 feet on the side wall, and 6 feet more till it gets to the
end).  This is the sides of a 3-4-5 triangle, scaled up by 8.  QED.

-- Dave Blackburn <daveb@net.shi.com>, March 1998
   (puzzle posted by Shalabh Mohan)