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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: Beginning of Analytical Solution | Comment 3 of 7 |
(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 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.


  Posted by Ady TZIDON on 2011-05-04 23:45:09
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