I'm guessing I'm not prepared to think about this avenue cause it's
   very hard for me to tell whether that's easily generalisable or not.
   I see it might be helpful to use symbolic solving. Don't know too much
   about such things.
   uniform_a + uniform_b = constant
   originally we had 1 equation and 3 unknowns.
   with constant, we now have 1 equation and 2 unknowns.
   if we consider these uniform distributions variables instead of
   distributions, we could use a math package to solve for one or the
   other, either symbolically or numerically. that could be part of the
   problem.
   let's make it more interesting.
   uniform_a + uniform_b + uniform_c + uniform_d = dist_e
   dist_e = 3
   uniform_c = 2
   1 equation, originally with 5 unknowns, now with 3 unknowns.
   Here we go. Since an equation is solved when there is only one unknown,
   we need one less sampled value than the total number of distributions,
   to guess a state.
   It would be nice to guess a distribution rather than just a sample, but
   that could be a challenge for later. It seems reasonable to start by
   describing distributions with functions that could sample them.