Express each of X, Y and Z in terms of a,b,c,p,q and r so that the equation given below becomes an identity.
(a3+b3+c3 - 3abc)(p3+q3+r3 - 3pqr) = X3+Y3+Z3 - 3XYZ
Note: Disregard any permutations. For example, if (X, Y, Z) = (α, β, γ), then (X, Y, Z) = (β, γ, α) is invalid.
Contrary to the comments posited, there does exist a general solution
to the given problem.
I will wait for a week before officially posting the solution.
I regret my inability to provide any hint, as positing that would render this problem to less than D1 in light of the comment received until now.