Lynnelle and Moor love toy cars, and together, they have $27$ red cars, $27$ purple cars, and $27$ green cars. The number of red cars Lynnelle has individually is the same as the number of green cars Moor has individually. In addition, Lynnelle has $17$ more cars of any color than Moor has of any color. How many purple cars does Lynnelle have?
1. Let \( r, p, g \) be the number of red, purple, and green cars Lynnelle has respectively. Then Moor has \( 27-r, 27-p, 27-g \) red, purple, and green cars respectively.
2. Given that the number of red cars Lynnelle has is the same as the number of green cars Moor has, we have:
   \[
   r = 27 - g
   \]
   Thus, we can write:
   \[
   r + g = 27
   \]
3. Next, we know that Lynnelle has 17 more cars than Moor. Therefore, we can write the equation:
   \[
   (r + p + g) - ((27 - r) + (27 - p) + (27 - g)) = 17
   \]
4. Simplifying the equation:
   \[
   r + p + g - (81 - r - p - g) = 17
   \]
   \[
   r + p + g - 81 + r + p + g = 17
   \]
   \[
   2(r + p + g) - 81 = 17
   \]
   \[
   2(r + p + g) = 98
   \]
   \[
   r + p + g = 49
   \]
5. From step 2, we know \( r + g = 27 \). Substituting this into the equation from step 4:
   \[
   27 + p = 49
   \]
   \[
   p = 22
   \]

The final answer is \(\boxed{22}\)