i'm not sure if this is more a CS or math problem, but i'll try my luck here first:
- given a pool of unique 32 bit integers (the values are under my control)
- up to 8 integers are randomly taken from the pool (a value can not be picked more than once)
- the integers are combined with an arithmetic OR into a new 32 bit value
Given only the result integer, and knowledge about all possible values (= the pool), all integers taken from the pool must be uniquely identified (at this time, the number of input integers is unknown, it could be anything from 1 to 8)
Task: Maximize the size of the pool of integers
Currently i only have the trivial case: 32 values in the pool, every value has only one bit from 0 to 31 set
Is there any way to increase the size of the pool of integers?