**Problem**

The number where and are digits is divisible by . What is the largest possible value of ?

**Solution**

A number is divisible by 6 if it is divisible by 2 and it is divisible by 3. For a number to be divisible by 2, it must be even. Therefore, must be even. So, the possible values of b are, 0, 2, 4, 6, and 8.

A number is divisible by 3 if the sum of the digits are divisible by 3. Therefore, we must be sure that in all the cases, the numbers are divisible by 3. Continue reading