How does Newton's cradle actually work?

Question

I've seen multiple attempts, trying to explain it:

1. Because of the formulas for momentum and kinetic energy, only the same number of balls can fly of at the other side. (found like this in many textbooks)

2. The first ball hits the second ball, the second the third…(often explained with billard balls) If multiple balls are lifted at the start, it works the same, but two times directly after each other

3. At the point of collision, two Shockwaves start to travel in both directions, reflect of the respective end of the cradle, and the cradle separates at the point they meet again.

So which one is correct?

Answer 1

As @Steeven remarked already:

Ad #1 and #2:

$\vec p = const.$

You may want to review the video Stack of balls from this perspective, to change perspective. Though it are inelastic collisions, violating the "const." condition, you still can explain it. If easier, replace by hard balls, e.g. on a billard table with diffently sized balls.

Ad #3:

As matter also has wave properties it's a microscopic view, which leads to the same result.

E.g. if you lift one ball, collision point is between 1st and 2nd. There is a deleay of $1+1=2$ balls between both waves, which meet again at the $(n-1)$-th ball at the other side.