Cubist logic problems

I’ve started messing with Perplex City. It’s an ARG, or ‘alternate reality game’, that has one fairly major hook: there’s a chance of winning 10 grand if you find a missing McGuffin (in this case, the ‘Receda Cube’).
It works on four levels. Firstly, there’s the grand mystery of the cube - whodunnit, whytheydunnit, and wheretheyleftit. Then, [...]