# Problem 2 – Hint 3

Major hint: consider shape deformation where the topmost step(s) is (are) removed or one or more steps are added.

Be very careful when doing mathematical calculations: many solutions were correctly based on this central idea, but made incorrect assumptions. One of the typical mistakes was assuming that for the new profile, the position of the n-th step is given by $x_n=\Delta + \lambda n^{2/3}$, with no change in the value of $\lambda$. The power law $x_n \propto n^{2/3}$ remains definitely to be valid (it has been shown to minimize the energy), but the constant $\lambda$ will change!

When doing your mathematical calculations, you might find it useful to exploit the fact that a small displacement $\delta$ of any of the steps yields the same change $\epsilon_n(\delta)$ in the interaction energy, cf the solution of the EuPhO’s problem.