General Information

• The competition has two categories, the elementary category for middle school students and the high school category for high school students.
• Any high school student can apply for the high school category, for the elementary category you need to be a student of elementary or middle school; the competition is primarily intended for the 7th year of school and above, but younger students can also compete.
• The competition is held exclusively on location in one of the competition venues. Participating remotely is not allowed.
• It is only allowed to compete in pairs. If you would like to participate but do not have a partner, feel free to write to us.
• In both categories you will solve 6 tasks ranging in difficulty from easy to hard. You will receive the tasks roughly sorted by difficulty, but don't let that carry you away, as difficulty can be very subjective.
• You can earn up to 6 points for each task.
• You will have 5 hours to solve them.
• The tasks are in the classic mathematical olympiad style. In particular, in the elementary category, there will be mostly computational tasks, and in the high school category, there will be mostly proof-based tasks.

Here is an example of a task of medium difficulty for the elementary category:

In an equilateral triangle $ABC$ with side length $8\,\text{cm}$, point $D$ is the midpoint of side $BC$ and point $E$ is the midpoint of side $AC$. Point $F$ lies on line $BC$ such that the area of triangle $ABF$ is equal to the area of quadrilateral $ABDE$. Calculate the length of segment $BF$.

Here is an example of a task of medium difficulty for the high school category:

We are given an acute-angled triangle $ABC$. On the ray opposite to ray $BC$ lies a point $P$ such that $|AB| = |BP|$. Analogously, on the ray opposite to ray $CB$ lies a point $Q$ such that $|AC| = |CQ|$. Let $J$ denote the excenter of triangle $ABC$ corresponding to side $BC$, and let $D$ and $E$ be the points of tangency of this excircle with the lines $AB$ and $AC$, respectively. Assume that the rays opposite to the rays $DP$ and $EQ$ intersect at a point $F \neq J$. Prove that $AF \perp FJ$.

Rules during the competition

• During the first 30 minutes, it's possible to ask questions about the tasks.
• Teams will solve the problems in one or more rooms. Please be considerate of others: try not to interrupt or disturb other teams. Do not communicate with or listen to participants outside your pair.
• You can communicate frely within your pair, handing over tools, sketches, pieces of the solution, etc.
• Write the solution to each problem on a separate sheet of paper, numbering them if you use multiple sheets (in which case, make sure to write the total number of pages on the first page). Label each sheet with your team's name.
• As soon as time is up, sort your solutions, check that multi-sided solutions are numbered, and submit each task to its appropriate pile.
• If there's a problem you don't want to submit, please give us a blank sheet back for that particular problem (that way, we'll know that the solution hasn't been lost).
• Each team will receive the assignment, along with paper to write down the solutions, and enough blank paper (but additional paper can be requested if necessary).
• The following equipment is allowed to be used during the competition:
  • Writing and drawing supplies (including a protractor).
  • Food and drinks.
  • Mechanical watches.
• On the other hand, the following items are explicitly prohibited (keep them hidden and turned off in your bag):
  • All electronic devices, including calculators.
  • Any sort of books/literature, notes, tables/cheat sheets, slide rules.
  • Custom paper (such as grid, for example).