If each of the a,b,c,d is a decimal digit - for how many ordered quadruplets (a,b,c,d) is the sum S= a+b+6c+d divisible by 3 ?

Answer: within 20 sec.

FOR a = 0 TO 9
FOR b = 0 TO 9
FOR d = 0 TO 9
  s = a + b + d
  IF s MOD 3 = 0 THEN ct = ct + 1
NEXT
NEXT
NEXT
PRINT ct

finds 334, disregarding c.

Any of the ten possible values of c will not affect the divisibility by 3 as the coefficient 6 ensures the entire term is divisible by 3.

The total number of ordered quadruplets meeting the criterion is 3340.

Posted by Charlie on 2014-04-09 12:35:01