bug on the box problem A bug walks on the surface of a box ($L=B=1$, $H=2$), starting at a corner, $A$. You want to feed the bug but you also want the bug to walk the longest distance.  The bug takes the shortest path possible.  Where do you put the food to make it walk the longest?
The box floats in the air and the bug can walk on any face of box it wants.
Hint: its not $B$ Refer the image

Given that the 2D topology of the 3D box is as shown in the figures in this answer and previous answers, there is a simple geometric solution that clearly shows the max distance is the distance to B if you can only put food in one location of the box. If you draw a circle centered at A that completely encloses the 2D topology of the box, the only place that circle touches the box is at B. The radius is the longest straight line distance within the circle and that radius is the $sqrt{10}$Box inscribe in a circle
