This depends on if you count "information propagation" time or not. For example, if you inform every guest about the pairing function when they check in, and mo

This depends on if you count "information propagation" time or not. For example, if you inform every guest about the pairing function when they check in, and moving from one room to any other takes finite time, all you need is a single "please move now" bit and each guest can move simultaneously. (If you don't assume you have instantaneous transmission and finite travel time, our unintuition about this also collides with unintuitive, unrelated, and very physically-real concepts like light cones - so I think it's within the spirit of the problem to assume we have them.)