perplexus.info :: Just Math : Counting Quadruplets III

Counting Quadruplets III (Posted on 2011-02-06)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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