Problem 2, hint 1

There were many contestants who got very close to the correct solution. Because of that, the first hint is a subtle one.

i. While the crystal is a three-dimensional (3D) structure, you can solve the problem considering a two-dimensional (2D) model by which you assume that the crystal is infinitely stretched along the $z$ -axis (see the section iii below).

ii. Studying the solution of the underlying EuPhO problem is highly recommended.

iii. If you want to aim for the best solution, you might try studying the full 3D geometry of a nearly-cubic crystal. However, if you do so, you’ll see that in that case, the suggested power law for the step width (as a function of the order number $n$) is no longer precise, and is valid only for large, but not-too-large values of $n$. This can be taken into account, and if you do everything correctly while studying the realistic 3D geometry, you should obtain the same result for $\mu$ as in the case of the simplified 2D model of the crystal. NB! it is recommended to send the 2D solution before trying this 3D approach.