In a huge room lives a very hungry ant. The room is 4 meters wide, 4 meters high and 10 meters long. The ant is on one of the 4x4-meter walls, right in the middle (2 meters from each of the 4x10-meter walls), and 1 meter from the ceiling. Its food is on the opposite wall, also in the middle, but 1 meter from the floor. The poor ant is very hungry, and won't be able to walk more than 13.99 meters without dropping dead. Can it survive?
(The ant cannot fly, jump etc.)
My solution used the fact that the distance travelled by the ant, based on the ant's center of gravity, would be less than the linear distance of the walls it travels over, as it gains a little bit each time it changes directions perpendicularly (this gain would be roughly equal to twice the distance from the ants center of gravity to the travelling surface. As it makes this direction change twice, the ant essentiallly shortcuts 4 times its height, and since it only has to save 1 cm, the ant only has to be 2.5 mm high. Might cut it close depending on species, but I have definitely seen ants bigger than this.
As its probably unclear, think of the ant traveling around the inside of a circle, compared to traveling around the outside of the circle. The inside path is shorter.
different solution
