I posted a comment where I described this method as my preferred solution. You did not need to patch it up though..its fine to just generate the 3 numbers and t

I posted a comment where I described this method as my preferred solution. You did not need to patch it up though..its fine to just generate the 3 numbers and then choose a random assignment from them to x y and z. This fixes the bias that would be present if you always generated x first.