[Combinatorics]
Problem: Ada starts with $x=10$ and $y=2$, and applies the following process:

Step 1: Add $x$ and $y$. Let $x$ equal the result. The value of $y$ does not change. Step 2: Multiply $x$ and $y$. Let $x$ equal the result. The value of $y$ does not change.

Step 3: Add $y$ and 1. Let $y$ equal the result. The value of $x$ does not change.

Ada keeps track of the values of $x$ and $y$ :

|  | $x$ | $y$ |
| :---: | :---: | :---: |
| Before Step 1 | 10 | 2 |
| After Step 1 | 12 | 2 |
| After Step 2 | 24 | 2 |
| After Step 3 | 24 | 3 |

Continuing now with $x=24$ and $y=3$, Ada applies the process two more times. What is the final value of $x$ ?

Solution: We apply the process two more times:

|  | $x$ | $y$ |
| :---: | :---: | :---: |
| Before Step 1 | 24 | 3 |
| After Step 1 | 27 | 3 |
| After Step 2 | 81 | 3 |
| After Step 3 | 81 | 4 |


|  | $x$ | $y$ |
| :---: | :---: | :---: |
| Before Step 1 | 81 | 4 |
| After Step 1 | 85 | 4 |
| After Step 2 | 340 | 4 |
| After Step 3 | 340 | 5 |

Therefore, the final value of $x$ is 340 .

Final answer: 340