Limits On Multiple RFID Tags / Sensors

I'm currently in the design & planning phase of creating a complex electronic puzzle box. Ultimately, there will be multiple puzzles and solutions involved in the process of a user completing it, and my question today is regarding just one of those puzzle solutions.

At some point, I would like to have the user extract 7 different cylindrical objects, and then have them insert those cylindrical objects into 7 cylindrical sockets. The objects themselves will each have a PASSIVE RFID tag or chip embedded in the bottom. Likewise, the 7 sockets will each have a sensor embedded in the bottom. Each of these sockets will only be separated by a couple of inches at the very most. To complete the puzzle, the 7 objects will each have to go into a specific, pre-determined socket in order for the next step to be unlocked. Now for my question:

I have a full understanding of the requirements for the hardware, the wiring, and the coding, but my concern is with the functionality of the RFID chips and sensors themselves. My research has indicated that there are opposing opinions on the feasibility of such an arrangement. Some say that this will work just fine, and others say that you can't have more than 2 sensors that close to one another (due to radio contamination in the sensors/chips/wires).

I have not yet invested in tags or sensors yet because I want to ensure I've worked out a proper setup. Is there a particular product that would be better suited for a setup like this? Or can a simple shielding method be implemented to protect against radio contamination between devices and wires? Or is the idea doomed for failure regardless?

As a follow-up, if the idea is in fact a bad one, would anyone have an idea for a substitute for the RFID chips/sensors so that the same type of puzzle solution could be implemented?

Thank you for your time!

Those inexpensive RFID-readers I've got for Arduino use, have a very short distance for readability. My guess is 2" apart will work just fine