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.

(In reply to Thoughts by tomarken)

6*c is divisible by 3, so it will only cause multiplication  by 10 of the "abd" result.

if a+b+d is divisible by 3 , so is the decimal string abd.

The number of "qualifying" strings from 000 to 999 is  999/3+1=334.

Hence the answer 3340.

Posted by Ady TZIDON on 2014-04-09 15:35:05