[anigbrowl]

I guess it depends on how you interpret 'lined up'. What if the room is circular, the table runs around the circumference, and you enter the room through a trapdoor in the center? Then your entry point to the list is effectively randomized and on any given trial the algorithm will work no better than chance.

[bd]

Well, there are actually two unstated preconditions that need to hold for proposed strategy to work:

1) every prisoner uses the same entry (with the same reference frame in respect to boxes)

2) there are no changes in the arrangement of boxes between prisoner visits (this is extra requirement, as it includes wardens not doing any rearrangements in the meanwhile)

But otherwise, the strategy could be extended for arbitrary topologies - just state additional algorithm for defining starting point of labeling and then use a deterministic rule telling which box would be the next one.

For example, for circular arrangement - start at 12:00 and go clockwise.

Or, for arbitrary random arrangement - start at upper left box and then proceed in (axis-aligned) grid: leftmost->rightmost->down to next leftmost->repeat.

[req2]

I believe the standard interpretation of 'lined up' is 'in a line', as in a 'straight curve', which disallows your otherwise ingenious foil.

[anigbrowl]

True. But as soon as I thought of the circle, I said to myself 'ah, the idea that it's a straight line is exactly the sort of assumption that you gets you into trouble!' so I threw the whole solution out.

I figured a straight line would be equivalent to a random arrangement with each of the boxes being numbered, so I assumed the vagueness was designed to lead one into making a foolish assumption about their ordinal presentation. Maybe I'm paranoid :-)