# German contest “Bundeswettbewerb Mathematik $2021$"

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:

• Everyone should be suspicious of any questions specifying the natural number 2021 right about now! Dec 27, 2020 at 19:52
• @amWhy in both cases the user studiously avoided mentioning 2021. Dec 27, 2020 at 20:07
• I'm not suggesting, @TomTom, that this was the casses you highlight! Rather, sometimes users can not that other users posting competition questions from where-ever, given the date. Dec 27, 2020 at 21:38
• @amWhy I'm planning on running a competition around April, how do you recommend I protect the integrity of the competition from stack without revealing the questions directly? Dec 28, 2020 at 1:28
• @DonThousand See this for an example of a person who had trouble with the kind of situation you are in. He was conducting an exam (whose questions were not revealed) and he tried stopping a student from cheating but his flag was stopped (and fairly so, by MSE rules) . You can take suggestions from the thread following Xander's answer. Dec 28, 2020 at 4:44
• @DonThousand What I would say is the best approach, is to first put up a meta post and say you are conducting a competition and won't be revealing the questions, and hence request the trust of the moderators for the next few days on the action you take on copied questions. The next , and more difficult part, is (because no one knows the questions other than you) to get to such questions as soon as they are posted on the site and take action (includes commenting "from an exam, don't answer", flagging, downvoting etc.) This is the best you can do, I think. Dec 28, 2020 at 4:47
• I've added a translation of the tasks as not anyone might able to read German. Feel free to edit mistranslations or remove them (the tasks) entirely if you think including them doesn't fit the post. I've posted a similar thread (see here) two years ago and missed the opportunity last year. Dec 28, 2020 at 14:16
• @mrtaurho Thanks! My english isn't good enough to provide a proper translation :) Dec 28, 2020 at 16:08
• @amWhy Sorry I misunderstood your comment. 2021 is certainly an indicator for a current exam / competion task. Dec 28, 2020 at 16:11
• I think MSE users should answer only if the questioner provides the context or the source of the problem, and that is a must need for contest math type problem. I think this guys are ethically quite wrong so at the end of the day education basically math education worthless for them at least. Dec 31, 2020 at 6:43
• Wow, one user even tried to make this appear like an old question by replacing $2021$ with $2018$ ... Dec 31, 2020 at 13:32
• This is the first time I've seen a question with MathJax in the title appearing on the hot posts, I always thought all such questions were blocked from entering HNQ/site-specific HQ.
– TheSimpliFire Mod
Jan 1, 2021 at 20:37
• @TheSimpliFire I guess it makes sense to show on Hot Meta Posts since the site already supports MathJax and will render correctly (just like MathJax on related & linked posts), compare to Hot Network Questions where many sites don't support MathJax and they will just not render. Jan 2, 2021 at 7:55
• In Task 3, $A',B',C'$ should be the intersections of the angle bisectors with the opposite sides. Jan 6, 2021 at 22:09