X is a 5 digit number. Let Y be the sum of the digits ofX. Let Z be the sum of the digits of Y. Then themaximum possible value of that Z can have is

1. Break Down the Problem

To find the maximum possible value of $Z$, we need to follow these steps:

1. Determine the maximum value of $Y$, the sum of the digits of the 5-digit number $X$.
2. Calculate $Z$, the sum of the digits of $Y$.

2. Relevant Concepts

1. A 5-digit number can range from 10000 to 99999.
2. The maximum value of a single digit is 9. Therefore, the maximum sum of the digits $Y$ for a 5-digit number occurs when all digits are 9.

3. Analysis and Detail

1. Calculating $Y$: The maximum value of $Y$ occurs when: $X = 99999$ Thus, $Y = 9 + 9 + 9 + 9 + 9 = 45$

2. Calculating $Z$: Now, we need to find $Z$, which is the sum of the digits of $Y$: $Y = 45 \Rightarrow \text{Digits of } Y = 4 \text{ and } 5$ Therefore, $Z = 4 + 5 = 9$

4. Verify and Summarize

We calculated $Y$ as 45 by taking all digits of $X$ as 9, which is accurate. Then, $Z$ calculated from $Y = 45$ is 9, which is the maximum possible sum of the digits of 45.

Final Answer

The maximum possible value of $Z$ is $9$.