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Counting Quadruplets III (Posted on 2011-02-06) Difficulty: 3 of 5
Determine the total number of quadruplets (A,B, C, D) of positive integers with A ≤ B ≤ C ≤ D ≤ 25, such that (A+B)*(C+D) is divisible by |A*D B*C|, whenever A*D ≠ B*C.

Note: |x| refers to the absolute value of x.

No Solution Yet Submitted by K Sengupta    
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re(2): computer solution ... Do me a favor , Charlie | Comment 4 of 6 |
(In reply to re: computer solution ... Do me a favor , Charlie by Ady TZIDON)

I think the formula you need is combi(25,4)+3*combi(25,3)+combi(4,2)*combi(25,2)//2+25

as there are three choices for which of 3 chosen numbers to appear twice, and there are C(4,2)/2 = 3 ways of pairing off two chosen numbers. We agree on the first term: four different numbers, and on the last: one number repeated 4 times.


  Posted by Charlie on 2011-02-07 12:30:22
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