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 by DJ)

**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.