Problem number 8 states, how many three-digit numbers formed using only the digits 1, 3 and 5 are divisible by 3? You may use digits more than once. So first, let's review how we know if a number is divisible by 3. To figure out if it's divisible by 3, what we do is we take all of its digits and add them up. If this number is divisible by 3, then we know the original number is also divisible by 3. So let's consider our three possible digits. There are only four unique combinations of digits possible, 135, 555, 333 and 111. These numbers work because if you add up all of the numbers, you will get a number that is divisible by 3. For the numbers where all the digits are the same, only one number can be created. However, for 135, the numbers can be arranged in six separate ways, 135, 153, 315, 351, 513 and 531. This can be calculated as 3 factorial. So in total, we have nine possible three-digit numbers. So the question asked us, how many three-digit numbers formed using only the digits 1, 3 and 5 are divisible by 3? The answer is 9, letter C.

three-digit numbers

divisible by 3

digit combinations

unique arrangements

mathematical problem