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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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Some Thoughts FULLY DEBUGGED; thanks Comment 6 of 6 |

WAS:

Tot= C(25,4)+25*C(24,2)+2*C(25,2)+25=20175    WRONG!

SHOULD BE:

Tot= C(25,4)+25*C(24,2)+3*C(25,2)+25=20475   OK

1ST TERM: xyzv

2nd: xyyz

3rd :    xxyy;  xyyy;  xxxy  (one not taken in account)

4th:   xxxx

12650+6900+900+25 = 20475    correct

 

 

THANK YOU , Charlie. After getting your result it took me 5 sec to locate the" missing 300" 

look forward to a problem posted by me- based on this evaluation.

 

 


  Posted by Ady TZIDON on 2011-02-07 16:20:47
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