Problem: http://domino.research.ibm.com/comm/.../June2011.html

Solution:
http://domino.research.ibm.com/comm/.../June2011.html

I didn't understand the solution at all but my reasoning was this:

Maximum number of cars: 50 as 100/2;
Minimum number of cars: 34 if 1 space between each car.

So difference of 16 cars.If random then 50% of 16= 8.
8 add 34 = 42.

This is very close to the approx answer. Is my reasoning faulty and it is just a coincidence?