If you move every guest from n to 2n, all of the odd rooms will open up, and you have room for a countably infinite number of new guests. I believe David Hilbe

If you move every guest from n to 2n, all of the odd rooms will open up, and you have room for a countably infinite number of new guests. I believe David Hilbert was the first to describe this paradox. Source: http://en.m.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel http://en.m.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gr...