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(2): Beginning of Analytical Solution by DJ)

Re how to proceed, I believe it is a problem tailored to be solved by a simple straightforward software program, checking all the possible 6tuples, like Charlie did.

Even if you succeed in your way of counting, solving a similar problem with ,say, 8-tuples and the upper limit of integers increased to 50 would be significantly harder, whereas in the program it is a question of adding 2 lines of code and increasing the runtime , still within reason.

Can't beat it.

*Edited on ***May 5, 2011, 4:55 pm**