We are not allowed to used rng or pseudo code but are we allowed to use predefined numbers that are rearranged randomly?
Only if they are pre-generated they are no longer random they are a pre-defined sequence or non-random so any plays through a game relying on them would be the same each time.
Assuming you start using them at the same index point.
Could be beneficial as your game would be identical each play through and allow you to find bugs and even tweak gameplay by changing the numbers in the list/array.
Could limit your number of levels depending on the size of your data pool.