International Mathematics Competition
for University Students

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IMC 2022
  Problems & Solutions

29th IMC

to take place at the

Blagoevgrad, Bulgaria

1 - 7 August 2022

London’s Global University



AUBG Tour, Blagoevgrad
This year's competition is organized by University College London and will be hosted by the American University in Bulgaria. It will take place in Blagoevgrad, Bulgaria, 1 - 7 August 2022, if conditions allow. Otherwise it will again be ON-LINE as last year.

Traditionally every participating university sends several students and one or more Team Leaders. Individual students and teams of students, with or without a Team Leader, that do not represent any university are also welcome. Each Team Leader is expected to hold an academic position in some university level institution and participate in the marking of the work of all participants.

The competition is planned for students completing their first, second, third or fourth year of university education with a maximum age of participants being 23 years of age at the time of the competition, although some exceptions can be made. There is no minimum age limit. Problems are from the fields of Algebra, Analysis (Real and Complex), Geometry and Combinatorics. The working language is English.

This is a residential competition and a condition of participation is that all participating students stay in the Hall of Residence provided by the organisers. Over the past twenty seven competitions we have had participants from over two hundred institutions from over fifty countries.

Selection of the Problems
The problems are chosen at the Meeting of the Jury from those received in advance by the President of the Jury, Professor John Jayne.

The students' work is evaluated by Team Leaders and other Professors and Assistant Professors using criteria provided by the Jury.

Rules and Regulations
IMC Ethics Committee

Although this is an individual event, the Universities traditionally divide their participants into groups of four each. The number of students in the teams is, however, not fixed. This year students from Russia can only participate as individuals, unaffiliated and unattached to any university; and they will not be included in any teams.

News and announcements

Warning. The on-line exam times has been modified.

  • In-person, Balgoevgrad: 9:00 - 13:00, Sofia time (UTC+3)
  • Europe, Asia, Africa: 6:00 - 10:00 UTC
  • America: 13:00 - 17:00 UTC

Problem selection

The contest problems will be selected by the in-person members of the International Jury, on the jury meeting on 2 August.

Contest Days

The two contest days are 3 and 4 August.

On each day, there will be 4 problems for 4 hours each day. The students must write their solutions on A4 or US letter papers. Only the standard drawing tools (pens, straightedges etc.) and printed dictionaries are allowed. Using any electronic tool or printed material is not allowed. The scripts should not contain any text, name or mark from which the student can be identified. The language of the contest is English; solutions written in other languages will not be evaluated.

Both contest days, there will be three exams.

  • In person competitors have the exam at the AUBG campus, in Blagoevgrad, from 8:30 to 13:00 Sofia time; the exam starts at 9:00.
  • On-line students and teams from Europe, Asia and Africa must take the exam between 6:00am and 10:00am UTC (same as the in-person exam).
  • On-line students and teams from America must take the exam between 1:00pm and 5:00pm UTC.
All members of each team should start at the same time, with downloading and printing the problems.

Opening and Closing Ceremony

The Opening and Closing Ceremonies will be held in Blagoevgrad. We plan to record the ceremonies, and share them with 2 hours later at the IMC's YouTube channel.

We will organize two Virtual Contest Halls for teamless students.

  • In the EurAsian Hall we will start the contest at 6:00 UTC and finish at 10:00 UTC. For example, this is 13:00 to 17:00 in Hanoi and Novosibirsk and 12:00 to 16:00 in Bangladesh.
  • In the American Hall we start at 13:00 UTC and finish at 17:00 UTC. This is 8:00 to 12:00 in Mexico City and 10:00 to 14:00 in Rio de Janeiro.
The links to the Contest Halls will be sent by e-mail.


The Team Leaders have to organize the invigilation of all their students and ensure that their work is fair. Students who are not invigilated will be removed from the results.

If personal invigilation is not possible, the team leader watches the students by video calls like Zoom, Google Meet, Skype etc. In that case the students have to set up a webcamera that captures the place. The video must show the student and his desk. No computer screen is allowed in front of the students and the students should not wear ear- and headphones. (See the pictures below.)

If you are a teamless student, you have to set up a webcamera yourself that captures you and your desk. It is allowed to use only one camera if there are more students in the same room. By 15 minutes before start, you have to connect the video, download and print the problems. The video link will be sent you by e-mail.

Preparing and uploading solutions

At the end of the exam, each student has to produce 5 files, containing the solutions:

Day 1Day 2

The scripts must be uploaded as soon as possible after the 4 work hours has passed.

For creating the files it is recommended to use the application named CamScanner, available both for Android and Apple based cell phones. Using CamScanner it is easy to make photographs of the papers, crop, resize and rearrange the pages and save the pictures into a PDF. If your phone has internet connection, you can upload the files immediately.

Each student will receive his personal upload link. Please use only your own link.

For a demonstration, we made a short video. Please view it to see how to use CamScanner. Test different camera settings; perhaps it is better if flash is switched on.


All leaders are expected to participate in grading. We created a project at ZulipChat for the grading discussion. All Team Leaders will be invited there. Further information for Team Leaders will be posted in ZulipChat.

Registration Closed.

In-person participants should pay the registration fee at the IMC site at AUBG in Blagoevgrad when they arrive.

For on-line particpants, the deadline for paying the registration fee has exprired. All on-line students who did not pay, and all leaders who are not leaders or deputy leaders of a team, will be deleted.