Originally posted by Nerevar:

you only need 5 cores to access everything by just destroyed and rebuilding and switching between the 3 devices that need the 5 cores currently. and you can find atleast 2 cores in each mine. most mines have more cores. my first mine had 6 in it. once a secret room right at the entrance contain FOUR cores and 2 chests. was barely guarded aswell.

This was not the case for me and my friends.. our first 2 mines had 0 cores.. then the third one had 1.. finally the 4th one had 7 in it.. So.. RNG can be an issue.. depending.