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Counting Sextuplets (Posted on 2011-05-04) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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Hints/Tips re(5): Beginning of Analytical Solution Comment 7 of 7 |
(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.

  Posted by Ady TZIDON on 2011-05-07 12:13:30
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