To check if a number is divisible by $3$, we can check if the sum of its digits is divisible by $3$.
The digits of $757$ sum to $7+5+7=19$, which is not divisible by $3$.
Thus, to make the four-digit number divisible by $3$, the digit that was written must be a multiple of $3$.
There are three multiples of $3$ between $0$ and $9$ inclusive, so there are $\boxed{3}$ possibilities for the digit that was written.
The answer is: 3
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A digit is written to the right of the units digit of $757$.  If the resulting four-digit number is divisible by $3$, how many possibilities are there for the digit that was written?

### Answer:
