Ava writes a three-digit number on the whiteboard. Then Brandon writes a fourth digit to the right of the previous ones. He says "Look! The number increased by 2024''. What digit did Brandon write?

To solve this problem, we need to understand that adding a digit to the right of a three-digit number is the same as multiplying the three-digit number by 10 and adding the new digit.

Let's denote the three-digit number that Ava wrote as 'a' and the digit that Brandon wrote as 'b'.

So, we have the equation:

10a + b = a + 2024

Solving this equation for 'b' gives us:

b = a + 2024 - 10a b = 2024 - 9a

Since 'a' is a three-digit number, the smallest value it can have is 100.

Substituting 'a' = 100 into the equation gives us:

b = 2024 - 9*100 b = 2024 - 900 b = 1124

But 'b' is a single digit, so it can't be 1124.

This means that 'a' must be larger than 100.

If we keep increasing the value of 'a', we will eventually find a value that makes 'b' a single digit.

By trial and error, we find that 'a' = 225 gives us:

b = 2024 - 9*225 b = 2024 - 2025 b = -1

But 'b' can't be negative, so 'a' must be larger than 225.

If we try 'a' = 226, we get:

b = 2024 - 9*226 b = 2024 - 2034 b = -10

Again, 'b' can't be negative, so 'a' must be larger than 226.

Finally, if we try 'a' = 227, we get:

b = 2024 - 9*227 b = 2024 - 2043 b = -19

This is still negative, so we need to keep increasing 'a'.

If we keep doing this, we will eventually find that 'a' = 225 and 'b' = 4 is the solution to the problem.

So, Brandon wrote the digit 4.