Problem source

Particles  $A_1$, $A_2$, $A_3$, 
$\ldots$, $A_n$ (where $n\ge 2$) lie at rest in that order in a smooth straight horizontal
trough. The mass of $A_{n-1}$ is $m$ and the mass of $A_n$ is
$\lambda m$, where $\lambda>1$.
Another particle, $A_0$, of mass $m$, 
slides along the trough with speed $u$ towards the particles and collides with  $A_1$. 
Momentum and energy are conserved in all  collisions.

\begin{questionparts}
\item Show that 
it is not possible for  there to be exactly one particle 
moving after all collisions have taken place.
\item Show that 
it is not possible for  $A_{n-1}$ and $A_n$ to be the only particles
moving after all collisions have taken place.
\item Show that 
it is not possible for  $A_{n-2}$, $A_{n-1}$ and $A_n$ to be the only particles
moving after all collisions have taken place.
\item Given that there are exactly two 
particles 
moving after all collisions have taken place, find the speeds of these
particles in terms of $u$ and $\lambda$.
\end{questionparts}