See All Cells

A friend sent me this puzzle.

The question is: Whether "No inmate should see the corpse more than once" means that no cell should be traversed more than once. For example, assume some cells have no inmates then the corpse could pass through the cell twice and still not violate the give constraint. To make the puzzle more interesting we will take my interpretation in bold above as the right one.

Now solve.

I think I know the answer.