[Retric]

I was not clear in my wording. They need to enter the room and know box one is this and thus I should treat that as box 22. But again without seeing the boxes they need a system to unambiguously order the boxes. That's not strictly a math problem as they are not say given exact x,y,z locations or precise measuring tools etc.

[danbruc]

Or what if it is dark inside the room and they can not read the numbers in the drawers? Or what if there is no gravity in the room and they can not determine which drawers are at the top? Or what if the director used a script or number system none of the prisoners can read or understand? Or what if the numbers are only 100 nm tall inscribed with electron-beam lithography on small pieces of metal? Or what if there is no oxygen in the room? Or what if the room is 10,000 km long, wide, and high?

[Retric]

A Revolving Filing Cabinet or even just a two sided one is a not exactly a 10,000 km long room. But, I think your getting the argument.

If you assume something not explicitly as part of the puzzle it's not necessarily the correct solution.