Re: Mathematical Problem - unsolved

[David Hobby]

>
> The goal is to find general equations for for all 26 Probability
> functions Wi depending on the target vector Pta and other factors
> because the solution is not unique. It is manifold!
>
> W_i=f(?,?,C1,C2,Š)


One simplification is to note that every solution consists of a
"minimal vector" M of W values that meet the other conditions but have
the sum of the W values less than 1, added to a "balanced vector" B of
W values that make X = Y = Z = 0, where the sum of values in B is
chosen so that the sum for B + M is 1.  The possible B are easier to
characterize.  (Or if you just want one solution, take a simple choice
of B, like W_(1,0,0) = W_(-1,0,0) with the rest of the W values zero.)
 As for the minimal vectors M, they will have all their W values zero,
except for those "pointing the same way" as the target vector.  This
should make finding M much easier, since it cuts the number of
variables needed.