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

Beginning of Analytical Solution by DJ)

DJ,

Your list is far from being complete.

You say :

**"However many of these factors is contained in the first triplet sum (a+b+c), the others must be factors of the other sum (d+e+f). By definition, a+b+c ¡Ü d+e+f"**

Not true. What if d=e=f=25,... a+b+c can be 3,4,5...75.

So here 72 sixtuples are omitted. I DID NOT SEARCH FOR OTHERS.