You can't be 1/33 any race. The denominator needs to be a power of two.

No, not even with inbreeding.


No person can be their own ancestor, so the breeding graph is directed and acyclic, so it has an ordering where all of a given person's ancestors come before that person. This ordering permits induction:


For the basis cases, all the 'pure white' and 'pure black' people are 1/2⁰ and 0/2⁰.


The other cases, are children of a p₁/2^q₁ and a p₂/2^q₂ - which comes to (p₁2^q₂ + p₂2^q₁)/2^q₁+q₂+1, which is of the required form.