Solution #28

To find the shortest path for the gecko, we unfold the room into a net, and then look for a short line path from gecko to fly. However, there is more than one way to unfold into a net, and different unfoldings will produce different straight line distances, so we must make sure we have found the most efficient route.

The optimum unfolding is as follows:

The gecko is one foot horizontally and vertically from the lower left corner of the upper 10 x 8 rectangle, and the fly is one foot horizontally and vertically from the upper right corner of the lower 8 x 10 rectangle.

The horizontal distance from G to F is thus 9 + 7 = 16, and the vertical distance is 1 + 12 + 1 = 14. The total distance is then √ 14² + 16²  = √ 452  = 2 √ 113  .