In a classroom, the number of boys is three times the number of girls. Which of the following totals cannot represent the number of children in the class?

Let the number of girls in the class be $x$.
According to the problem, the number of boys is three times the girls, so:

$$\text{Number of boys}=3x$$

The total number of children in the class is:

$$\text{Total children}=\text{Boys}+\text{Girls}=3x+x=4x$$

This means that the total number of children must be a perfect multiple of 4. Let's verify the options:

* 20 is a multiple of 4 ($4\times 5=20$) $\to$ Possible
* 24 is a multiple of 4 ($4\times 6=24$) $\to$ Possible
* 40 is a multiple of 4 ($4\times 10=40$) $\to$ Possible
* 22 is NOT a multiple of 4.

Therefore, 22 cannot represent the total number of children.