Generating a set of pseudorandom numbers satisfying following xor-property?

IMHO this would restrict the maxinum number of subsets to 64 (Pigeonhole principle); for >64 subsets, there will always be a ( non empty ) subset that XORs to zero. For smaller subsets, the property can be fulfilled.

To amplify wildplasser: every hash function that be used to distinguish every n-bit string from every other n-bit string cannot have output shorter than n bits. Shorter hash functions are usable because we only have to avoid collisions in the strings that actually arrive, but we cannot hope to make an intelligent choice offline. Just use a cryptographically-secure RNG and one of two things will happen: (i) your code will work as though the RNG were truly random or (ii, unlikely) your code will break and (if it's not bugged) it will act as a distinguisher between the crypto RNG and true randomness, bringing you fame and notoriety.

I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.