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Counting Quadruplets (Posted on 2010-08-20) Difficulty: 3 of 5
Each of A, B, C and D is a positive integer with the proviso that A ≤ B ≤ C ≤ D ≤ 20.

Determine the total number of quadruplets (A, B, C, D) such that A*B*C*D is divisible by 50.

No Solution Yet Submitted by K Sengupta    
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re: wrong Solution | Comment 9 of 11 |
(In reply to Solution by hoodat)

 You say:
""In order to be divisible by 50, two of the integers must be some combination of 5,10,15, & 20.  There are 6 combinations of this [4!/(2!2!)].  Once one of these pairs is picked, there are 153 combinations of the remaining integers [18!/(2!16!)].  This yields 918 total"

 

WRONG !!
   Where are (20,20,20,20)  or  (5,5,5,10) and hundreds of others you have missed??? 
   PLEASE          RECOUNT!     

P.S. Charlie's result is transparent and 100% correct.

Analytical verification is not so easy.

 

                                                                                                             


  Posted by Ady TZIDON on 2010-08-20 20:21:16
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