Recently I've seen two questions related to the German contest “Bundeswettbewerb Mathematik $2021$" - both voluntary removed by the author (both new users). Therefore I ask you to be aware of further attempts in that direction.
These questions were about natural solutions of $\frac{3}{n} = \frac{1}{a} + \frac{1}{b}$ for a given $n\in\mathbb{N}$. The current task $3$a) (see below) is, to determine how many solution you get for $n=2021$.
Deadline is March $8$th, $2021$. Link to the contest and a translation of the questions:
Task $\textbf1$
A cube with side length $10$ is dissected into two rectangular cuboids with integral side lengths by a planar cut. One of these rectangular cuboids is then again dissected into two more rectangular cuboids with integral side lengths.What is the minimal possible volume of the largest of these three rectangular cuboids?
Task $\textbf2$
There are exactly two ways of representing $\frac3{10}$ as the sum of two unit fractions: $$\frac3{10}=\frac15+\frac1{10}=\frac14+\frac1{20}$$ a) In how many ways can $\frac3{2021}$ be expressed as the sum of two unit fractions?
b) Is there a positive integer $n$, which is not divisible by $3$, and such that $\frac3n$ can be expressed in exactly $2021$ ways as the sum of two unit fractions? $\small\text{Remark: A unit fraction is a fraction of the form $\frac1z$, where $z$ is a positive integer.}$Task $\textbf3$
In a triangle $ABC$ let $\angle ACB=120^\circ$ and let the points of intersection of the interior angle bisectors through $A$, $B$ and $C$ be $A'$, $B'$ and $C'$.What is $\angle A'C'B'$?
Task $\textbf4$
The base of a pyramid is a regular $n$-gon. Every line connecting two vertices of the pyramid, except the sides of the base, are coloured either red or blue.Prove that: For $n=9$ there are three vertices of the pyramid which are connected by three lines of the same colour for every colouring, while this is not the case for $n=8$.
For users who can see deleted: