## Hypatia 2024 Question 2, CEMC UWaterloo

Best Submissions

#### Difficulty: 5

#### This problem is tagged with hypatia, hypatia24, highschool.

**(Hypatia 2024, Question 2, CEMC - UWaterloo)**

For a positive $3$-digit integer $n$, $f(n)$ is equal to the sum of $n$ and the digits of $n$. For example, $f(351)=351+3+5+1=360$.

Note: The decimal representation of a $3$-digit number $abc$ is $a \cdot 10^2 + b \cdot 10 + c$. For example, $836 = 8 \cdot 10^2 + 3 \cdot 10 + 6$.

(a) What is the value of $f(132)$?

(b) If $f(n)=175$, what is the value of $n$?

(c) If $f(n)=204$, determine all possible values of $n$.

*Answer Submission Note(s)*

In part (c), sort your answers in ascending order and separate them with a comma.

Separate the answers for each part with a single space.

For example: "a b c1,c2"

You should report content if:

- It may be offensive.
- There is something wrong with it (statement or difficulty value)
- It isn't original.