Harvard problem of the week: stacked ball collision

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I found a set of question from Harvard here;
https://www.physics.harvard.edu/academics/undergrad/problems [URL repaired by a mentor]
I solved the Week 1 problem like this;
The basketball would fall to the floor, because the collision is elastic the velocity will change from -v to v (where v is \\sqrt{2gh}\. There for the change of momentum is \(2Mv\) (where M is the mass of the basketball).

The tennis ball therefore would have the sum of the change of momentum which would be
\2Mv+2mv\, and tennis ball's velocity would satisfy the equation
\2Mv+2mv=mv+m{v}'\ (when the tennis ball's velocity after collision is \-{v}'\)

According to this \{v}'\ should be \\frac{(2M+m)\sqrt{2gh}}{m}\
and further calculation tells me that h equals \(\frac{2M+m}{m})^{2}h\

If you take a look at the solution (on the right hand side) you would find out that this is wrong, what did I do wrong in solving this problem? Why can't the change of momentum be used?

 

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The tennis ball therefore would have the sum of the change of momentum

Why?
And what does that even mean?

 

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I thought that the tennis ball should receive the impulse of the basketball as well as the impulse of itself. What I mean is that when the basketball bounces off the floor it's momentum changes because it received an impulse from the floor and the tennis ball, which would bounce off the basketball and also have a change in momentum would receive an impulse from the basketball but because the basketball received an impulse as well, the tennis ball would (probably) get the sum of those two momentum.

 

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If you hit a resting tennis ball with a car, do you expect the car to transfer its full momentum to the tennis ball (and therefore stop)?

That would also violate energy conservation, by the way.