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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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Solution computer solution | Comment 1 of 7

FOR a = 1 TO 25
FOR b = a TO 25
FOR c = b TO 25
FOR d = c TO 25
FOR e = d TO 25
FOR f = e TO 25
  tst = (a + b + c) * (d + e + f)
  IF tst MOD 75 = 0 THEN PRINT a; b; c, d; e; f, tst: ct = ct + 1
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT

PRINT ct

finds 26550 such sextuplets out of 593775 formable sextuplets.

 


  Posted by Charlie on 2011-05-04 19:28:28
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