Each of A, B, C, D, E and F is a positive integer with A ≤ B ≤ C ≤ D ≤ E ≤ F ≤ 25.
Determine the total number of sextuplets (A ,B, C, D, E, F) such that (A+B+C)*(D+E+F) is divisible by 75.
(In reply to re(4): Beginning of Analytical Solution
Yes, it can be done.
It is just unbelievably long process.
1st. List all candidates x*Y s.t. the product is divisible by 75.
2. For each x and for each y apply the method desribed by the solvers of a problem I've posted (I even gave away a recursive equation).
It is called " So many quintuplets " . You may apply the method mutatis mutandis to the triplets forming x and y within the appropriate cinstraints.
Hope you are not going to actually do it.