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: Beginning of Analytical Solution by Ady TZIDON)

Good catch there, but what I said is perfectly valid. For a number to be divisible by any given number, it must be divisible by each of its prime factors, which in this case must be factors of one triplet sum or the other.

What I didn't list was the situation you mentioned, where all factors are covered within one of the tuples. It's subjective just how "far" from complete that makes the analysis, I guess.

The more difficult problem remains of how to find and remove all invalid triplet possibilities from the now-complete list of sums.

Posted by DJ on 2011-05-05 06:09:15