Hilbert's paradox of the Grand Hotel is a mathematical thought exercise in which is imagined a hotel with infinite rooms, thus capable of accommodating infinite guests. Even if the hotel is full to capacity, and an extra guest arrives, he or she can still be accommodated by putting them into room 1408, which nobody ever stays in because the television doesn't work and the bed smells a bit funny. Problems arise because only a finite number of the rooms have ocean view, and these rooms are usually filled by mathematicians, for whom the hotel is a popular conference venue. The hotel is also known for its annual Don Con, a popular convention where infinitely many Cambridge University dons visit the hotel for a week. These dons normally live in a (finite) cupboard in the university, which is po