The following fact is needed for solving this problem: a homogeneously magnetized sphere (magnetization vector M is constant) creates an homogeneous magnetic field inside the sphere itself. There are many sources (textbooks, problem solutions) from where you can find a proof of this fact; there are different proofs, some are fairly simple. (More generally, this statement remains also valid for ellipsoids.)
Please submit the solution of this problem via e-mail to firstname.lastname@example.org. The third hint will appear here on 19th December 2021. NB! The second problem will also be published on 19th December 2021. From 12th December to 19th December, the base score is 0.8 pts, and from 19th December to 26th December, the base score will be 0.7 pts. For full regulations, see the “Participate” tab. The next updates of the intermediate results for the Problem 1 will be published after 13:00 GMT, 19th December 2021.