@Tobias Let $(m_i)_{i\in [1, 2n+1]}$ be the masses, define $\delta_{i,j} = m_i - m_j$ and let $p_i$ be the mass of one of the stacks when you take out $m_i$.
It follows that $2p_i + m_i = 2p_j + m_j$ ie $\delta_{i,j} = 2(p_j-p_i)$.
However $p_j-p_i$ is in the subgroup $G$ of $\Bbb R$ generated by the $\delta_{i,j}$.
What follows is that for all $i,j$ $\delta_{i,j}\over 2$ is in $G$, which is absurd since $G$ is generated by the $\delta_{i,j}$ (a little more work should be done here, but I'm pretty convinced what I'm saying is true)
$ \nabla^{2}_x \Delta ^{-1}(P)=P $ Is it correct ???? why not?
