newtonian mechanics - Why doesn't the 9th ball move in the break in the nine-ball pool game?

In the game of nine-ball pool, we break the rack like shown below:

In the break, we hit the 1st ball with the cue ball. Many people familiar with pool games say that if the rack is constructed properly (i.e. there're no gaps between adjacent balls), the 9th ball won't move a bit.

As far as I've seen, this folklore is very true. Usually, the 9th ball moves little.

I've googled much and failed to reach any mathematical or physical proofs about this. Does anyone know whether this is true?