- This article is about the hotel. For the RIS Bouteina episode, see Hilbert Hotel (Bouteina episode).
Also, it had same-day dry cleaning, a sauna, a spa, a gymnasium, an ice machine at every floor, a business center complete with office equipment, a luxury lounge, two olympic-sized indoor pools, baby-sitting, as well as an astrometrics lab. (RIS Bouteina: "Hilbert Hotel")
Rooms came in several layouts: some came with two queen beds, others with one king bed. These rooms were considered to be non-suite rooms and were by far the most common rooms at Hilbert Hotel. Plus it had a conference room that could hold at least minor diplomatic conferences. (Star Trek: False Vacuum: "Wagon Train to the Stars")
In order to get to the artifact the Hydran Keepership sought after, adventurers had to answer several riddles. Each riddle was activated after resolving one of 40 trials, randomly assigned when one attempts to solve the riddle. The trials are activated by one's hotel key. While the trials have the safety protocols activated, the consequences for failure in solving the riddle were lethal. Also, one cannot activate the next riddle without solving the previous one first.
Holodeck 1 (10th floor)Edit
The hotel is full of customers. There is another customer willing to book a room in the hotel: would you be able to accomodate it? If so, how?
Holodeck 2 (20th floor)Edit
The hotel is still full of customers. This time around, there is a countably infinite number of new customers willing to book a room in the hotel: would you be able to If so, how?
Holodeck 3 (30th floor)Edit
Once again, the hotel is full of customers. But the situation is a little different this time: there is a countably infinite number of buses, all containing a countably infinite number of passengers. Will you be able to accommodate them? If so, how?
Holodeck 4 (40th floor)Edit
It is the 4th day in the Hilbert Hotel: the hotel has been emptied. An infinite number of aliens with unpronounceable names (to Romulans) would like to book hotel rooms. They all carry ID cards with a binary number on it, issued by the tourism board. Will you be able to accommodate them? If so, how?
This riddle activates in the event one solves the first four riddles successfully.
This riddle is as follows: somehow, even after trying to accommodate all the aliens of the previous riddle, there is now a countably infinite number of customers. However, even if the premises are supposed to be smoke free, the guest in room 1 goes to room 2 to get 2 cigars. Also, the guest in room 2 goes to room 3 to take 3 cigars. How could that be?