1994 AHSME Problems/Problem 21
Find the number of counter examples to the statement:
Since the sum of the digits of is and none of the digits are , 's digits must be the elements of the sets or . In the first case, the only possible is , and it can be checked that this is a counterexample because it is divisible by . In the second case, is either or . It can be checked that is indeed prime, while is divisible by . Finally in the third case, both are prime. So the final answer is .