Welcome to the British Mathematical Olympiad

• A PDF file containing lots of BMO problems from the past (1993–2021). No answers are supplied! Hints and solutions for BMO1 problems from 1996–1997 to 2010–2011 are included in A Mathematical Olympiad Primer, available from the UKMT, while BMO2 solutions are included in A Mathematical Olympiad Companion, available from the UKMT; video solutions for BMO1 are available from 2005–2006 onwards.
• Information about the BMO papers and notes on BMO marking (PDF)
• The Christopher Bradley elegance prize
• The UK Mathematical Olympiad for Girls (UK MOG)
• A brief article on areal co-ordinate methods in Euclidean geometry (PDF), by Tom Lovering
• National events: events calendar, UK Olympiad Training; the annual IMO Lecture and Celebration
• International events, including reports on each year’s events: the International Mathematical Olympiad, the Balkan Mathematical Olympiad, the Romanian Master of Mathematics, the China Girls’ Mathematical Olympiad, the European Girls’ Mathematical Olympiad, the Mathematics Ashes
• BMOS and UKMT supporters may elect to make a small tax efficient regular donation to these organizations.
• Committee information: a short history of the BMOC, list of current committee members; list of other people involved in BMOS activities
• BMO policies on use of BMO1 DVDs and on eligibility
• Contact details
• Past news and events

UK Mathematical Olympiad for Girls (8 October 2021)

The UK Mathematical Olympiad for Girls (UK MOG) paper was taken yesterday. Solutions are also available.

IMO 2021 report available (24 September 2021)

The reports on past IMOs now include Dominic Yeo’s report on IMO 2021.

Balkan Mathematical Olympiad results (10 September 2021)

The UK team in the Balkan Mathematical Olympiad have achieved the following scores (each question marked out of 10). The medal cut-offs were 35 for gold, 24 for silver and 16 for bronze.

Balkan Mathematical Olympiad problems (8 September 2021)

The Balkan Mathematical Olympiad paper was sat today, with the UK team sitting the paper in Leeds. The problems were proposed by the UK (Aron Thomas), Greece, Serbia and the UK (Sam Bealing and Alexander Betts), respectively.

Balkan Mathematical Olympiad team (16 August 2021)

The UK has been invited as a guest nation to send a team to the Balkan Mathematical Olympiad, organised by Cyprus and to be held online, 6–10 September, with the exam on 8 September. The UK team will be:

The Leader is Freddie Illingworth (Emmanuel College, Cambridge) and the Deputy Leader is Emily Beatty (Trinity College, Cambridge).

IMO 2021 results (23 July 2021)

The IMO papers were sat on 19 and 20 July. The results of the UK team members are shown below. We obtained two gold and three silver medals and an Honourable Mention and a score of 131 out of 252, coming equal 9th out of 107 participating countries. The medal boundaries were 24 for Gold, 19 for Silver and 12 for Bronze. A press release about the UK performance is available.

The IMO problems were submitted by Australia, Canada, Ukraine, Poland, Spain and Austria, respectively.

IMO team selected (6 June 2021)

The UK team for IMO 2021 will be:

The first reserve is Tommy Walker Mackay (Stretford Grammar School). Congratulations to all students who participated in this year’s selection tests.

The Team Leader is Dominic Yeo (University of Oxford) and the Deputy Leader is Sam Bealing (Trinity College, Cambridge). The IMO will take place as a remote event, organised by Russia with the exams on 19 and 20 July.

IMO squad selected (20 April 2021)

Following the first round of selection tests, the squad of ten from which the team of six for IMO 2021 will be selected has been chosen as:

The IMO will take place 14–24 July, organised by Russia in a format to be determined.

Romanian Master of Mathematics 2021 UK participants (20 April 2021)

The Romanian Master of Mathematics competition will be held online, 20–26 May. The students to represent the UK will be:

The team is led by Geoff Smith (University of Bath).

EGMO results (15 April 2021, press release added 16 April)

The UK team in the tenth European Girls’ Mathematical Olympiad have achieved the following results, coming 5th out of 55 participating teams (3rd out of 37 official European teams). The medal boundaries are 21 for gold, 14 for silver and 8 for bronze. A UKMT press release is available.

European Girls’ Mathematical Olympiad problems (13 April 2021)

The problems (day 1, day 2) from the tenth European Girls’ Mathematical Olympiad, held as a virtual competition because of the COVID-19 pandemic, are now available. The problems were submitted by Australia, Slovakia, Ukraine, Australia, Austria and Austria, respectively.

Olympiad training camps and IMO selection (6 March 2021)

The 2021 edition of the annual residential olympiad camp, normally hosted in Cambridge, was cancelled because of the ongoing UK restrictions. The 2020 edition of the annual summer school for students new to olympiads, normally hosted in Oxford, was also cancelled.

BMOS is currently planning an online event from April 6th to 9th as partial replacement for both of these cancelled residential activities. Invited students will be contacted shortly.

A first round of selection tests for the team to represent UK at IMO 2021, will be held on 17th and 18th April in an online format.

EGMO 2021 team (26 February 2021)

The 10th European Girls’ Mathematical Olympiad, organised by Georgia, will be held 9–15 April. The UK team, taking part remotely because of the COVID-19 pandemic, will be:

The reserve is Rebekah Glaze of West Kirby Grammar School. The Team Leader is Jenny Owladi of the Bank of England and the Deputy Leader is Kasia Warburton of Trinity College, Cambridge.

BMO Round 2 high scores and solutions (19 February 2021)

BMO Round 2 was marked remotely over the period 6–7 February. The following candidates scored 20 or more out of 40. Solutions are also available.

BMO Round 2 (29 January 2021)

This year’s BMO Round 2 paper was taken yesterday. The problems were by Ivan Chan (problem 1), Dominic Rowland (problem 2), Freddie Illingworth and Dominic Yeo (problem 3) and Jeremy King (problem 4).

RMM 2021 selection (4 January 2021)

BMOS hopes to enter a UK team in the Romanian Master of Mathematics in late February 2021, likely to be held in an online format without travel requirements.

Top-scoring students from BMO1 will be invited shortly to take part in a selection test for the UK team. BMOS is hopeful that this can take place on Saturday 16th January. We are closely watching the developing situation about the return to UK secondary schools in January 2021, and we hope to contact invited students via their school in the coming days.

BMO Round 1 markers’ report (18 December 2020)

The markers’ report on BMO1, with discussions of different approaches to the problems, is now available.

BMO Round 1 high scores (16 December 2020)

BMO Round 1 was marked remotely over the period 5–12 December. The following candidates scored 39 or more out of 50.

BMO Round 1 (2 December 2020)

This year’s BMO Round 1 paper was taken on 26 November; video solutions are available online. Production facilities for the video were donated by the University of Bath Audio Visual Unit. The problems were by Daniel Griller, Tom Bowler, Daniel Griller, Nick Mackinnon, Dominic Yeo, Luke Pebody and Daniel Griller, respectively.

Balkan Mathematical Olympiad results (5 November 2020)

The UK team in the Balkan Mathematical Olympiad have achieved the following scores (each question marked out of 10). The medal cut-offs were 32 for gold, 25 for silver and 20 for bronze.

Balkan Mathematical Olympiad problems (1 November 2020)

The Balkan Mathematical Olympiad paper was sat today. The problems were proposed by the UK (Sam Bealing), Albania, Cyprus and North Macedonia, respectively.

UK MOG report (22 October 2020)

The report for schools on the 2020 UK Mathematical Olympiad for Girls paper, with statistics of results, is now available.

Balkan Mathematical Olympiad team (18 October 2020)

The UK has been invited as a guest nation to send a team to the Balkan Mathematical Olympiad, organised by Romania and to be held online from 31 October to 5 November with the exam on 1 November. The UK team will be:

The Leader is Robin Bhattacharyya (Loughborough Grammar School) and the Deputy Leader is Kasia Warburton (Trinity College, Cambridge).

UK MOG solutions (15 October 2020)

Solutions for this year’s UK MOG paper are now available.

UK Mathematical Olympiad for Girls (9 October 2020)

The UK Mathematical Olympiad for Girls (UK MOG) paper was taken over the period 6–8 October. Solutions will be released on Thursday 15 October.

IMO 2020 results (27 September 2020, press release added 29 September)

The IMO papers were sat on 21 and 22 September. The results of the UK team members are shown below. We obtained one gold, four silver and one bronze medal and a score of 167 out of 252, coming 9th out of 105 participating countries. The medal boundaries were 31 for Gold, 24 for Silver and 15 for Bronze. The following press release is now available.

The IMO problems were submitted by Poland, Belgium, Hungary, India, Estonia and Taiwan, respectively.

Our thanks to this year’s IMO supporter, Oxford Asset Management.

IMO 2020 problems (23 September 2020)

The IMO 2020 papers were sat on 21 and 22 September in exam centres around the world; the problems are available.

Our thanks to this year’s IMO supporter, Oxford Asset Management.

Mathematics Ashes results (1 October 2020)

Australia has won the 13th Mathematics Ashes competition, decided on the results of the last joint pre-IMO practice exam; the results for the two teams were as follows, with the UK scoring a total of 87 and Australia scoring a total of 93:

Our thanks to this year’s IMO supporter, Oxford Asset Management.

Cyberspace Mathematical Competition (22 July 2020)

The inaugural Cyberspace Mathematical Competition was held on 13th and 14th July 2020. This invitational online contest was organised by the Mathematical Association of America and the Art of Problem Solving. The UK team of eight students in Years 11 and 12 was chosen based on the results of the virtual selection tests in April.

The problems of the contest can be found here.

The UK team placed 11th out of 75 participating countries and our students achieved the following excellent individual results (out of the maximum 56 marks):

Congratulations to all students involved for some impressive solutions to the problems of this contest, and thanks to Dr Vesna Kadelburg for leading the UK team’s participation, and to the co-leaders Emily Beatty, Joe Benton, Robin Bhattacharyya, Kasia Warburton and Dr Dominic Yeo who assisted with marking.

Recent IMO programme activity, and IMO team selected (1 June 2020, updated 5 June)

The 2020 edition of the annual residential olympiad camp, due to be hosted at Trinity College, Cambridge, was cancelled because of the UK’s Coronavirus lockdown. In its place, BMOS organised a virtual camp, held April 6th to April 9th, for the twenty-six invited students, with lectures and problem-solving sessions delivered via video-conferencing software by a team of twelve volunteers. Following this, two rounds of selection tests were conducted online during the weekends of 25th April and 30th May. Based on these results, the students to represent UK at IMO 2020 are:

The reserves are:

Congratulations to all students who qualified for these final rounds, and thanks to their parents and guardians for supporting the exams, and to our team of volunteers for setting and marking the papers, and leading discussions with the students. Thanks also are due to Oxford Asset Management for their support of the UK IMO programme in 2019–2020.

IMO 2020, originally planned for St. Petersburg, will now be hosted by Russia in an online format. The two papers will be sat on September 21st and 22nd. BMOS hopes that it will be possible for the UK team and their leaders to be together in one venue for IMO 2020, and we will offer updates and further details when the possibilities are more clear.

EGMO results (21 April 2020)

The UK team in the ninth European Girls’ Mathematical Olympiad have achieved the following results, coming 5th out of 53 participating teams (4th out of 39 official European teams). The medal boundaries are 26 for gold, 18 for silver and 11 for bronze.

European Girls’ Mathematical Olympiad problems (18 April 2020)

The problems (day 1, day 2) from the ninth European Girls’ Mathematical Olympiad, held as a virtual competition because of the COVID-19 pandemic, are now available. The problems were submitted by Australia, Slovakia, Ukraine, Slovakia, the United Kingdom and Denmark, respectively; problem 5 is by Agnijo Banerjee.

IMO training and selection camp cancelled (16 March 2020)

The Cambridge IMO camp, scheduled for 31 March to 5 April, has been cancelled, as a result of the ongoing COVID-19 situation. Obviously this is a great shame for the invited students and the volunteer staff. Our thoughts are also with all students, volunteers and their families who might be facing challenges or uncertainty this week and over the coming period. BMO will be in touch with affected students as and when it becomes more clear what form IMO programme activities can reasonably take for the rest of this academic year.

IMO training and selection camp and COVID-19 (11 March 2020)

The UK IMO training and selection camp is scheduled to be held at Trinity College, Cambridge, 31 March–5 April. The UKMT is keeping the situation and government advice under continuous review, and liaising with Trinity College. We will update students and parents as soon as possible if changes to the camp become necessary. We are working on contingency plans for some of the camp programme, including selection tests, to be delivered remotely.

Romanian Master of Mathematics results (1 March 2020)

The UK participants in the Romanian Master of Mathematics competition have achieved the following results, coming 5th out of 19 teams in the team competition. The medal boundaries are 29 for gold, 24 for silver and 18 for bronze. Problem 2, a UK submission, is by Dominic Yeo.

EGMO 2020 team (13 February 2020)

The 9th European Girls’ Mathematical Olympiad will be held in Egmond aan Zee, Netherlands, 15–21 April. The UK team will be:

The reserve is Shuqi Huang of Westminster School. The Team Leader is Jenny Owladi of the Bank of England and the Deputy Leader is Kasia Warburton of Trinity College, Cambridge.

BMO Round 2 high scores (12 February 2020)

BMO Round 2 was marked in London on 8 February. The following candidates scored 25 or more out of 40.

BMO Round 2 (31 January 2020)

This year’s BMO Round 2 paper was taken yesterday. The problems were by Sam Maltby, Sam Bealing, Dominic Yeo and Jeremy King, respectively.

IMO 2019 lecture video available (16 January 2020)

Video of Jeremy King’s IMO lecture at Central Hall Westminster is now available.

BMO Round 1 markers’ report (11 January 2020)

The markers’ report on BMO1, with discussions of different approaches to the problems, is now available.

Walter Hayman (8 January 2020)

Professor Walter Hayman FRS, who co-founded the British Mathematical Olympiad together with his late wife Margaret, has died on 1 January. For more information on his career, see the notice from the London Mathematical Society.

Romanian Master of Mathematics 2020 UK participants (5 January 2020)

Following the annual IMO Winter School held in Hungary, 27 December to 4 January, the students to represent the UK at the Romanian Master of Mathematics competition have been selected as:

The team is led by James Gazet (St. Paul’s School), Freddie Illingworth (Emmanuel College, Cambridge) and Georgina Majury (Peterhouse, Cambridge). The RMM will take place in Bucharest, 26 February–2 March.

BMO Round 1 high scores (13 December 2019)

BMO Round 1 was marked in Cambridge on 6–8 December. The following candidates scored 50 or more out of 60.

BMO Round 1 marked (9 December 2019)

BMO Round 1 was marked in Cambridge on 6–8 December. Data entry is currently ongoing. Invitations to the IMO winter camp in Hungary will be issued later this week, and the list of high-scoring students will appear on this site.

BMO Round 1 (30 November 2019)

This year’s BMO Round 1 paper was taken yesterday; video solutions are available online. Production facilities for the video were donated by the University of Bath Audio Visual Unit. The problems were by Nick MacKinnon, Tom Bowler, Daniel Griller, Daniel Griller, Dominic Rowland and Sam Bealing, respectively.

UK MOG markers’ report and prize winners (5 November 2019)

The markers’ report for the 2019 UK Mathematical Olympiad for Girls paper is now available, including extended discussions of the problems and the approaches taken by candidates. The following participants scored 46 or more out of 50 and have been awarded book prizes.

UK Mathematical Olympiad for Girls (9 October 2019)

The UK Mathematical Olympiad for Girls (UK MOG) paper was taken yesterday. Solutions are also available. The paper will be marked on the weekend of 19–20 October.

IMO 2019 results (19 July 2019)

The IMO papers were sat on 16 and 17 July. The results of the UK team members are shown below. We obtained one gold, two silver and three bronze medals and a score of 149 out of 252, coming 20th out of 112 participating countries. The medal boundaries were 31 for Gold, 24 for Silver and 17 for Bronze.

The achievements of this year’s UK olympiad teams will be celebrated at Central Hall Westminster on Monday 23 September, when Dr Jeremy King will give the 42nd annual IMO lecture.

Our thanks to this year’s IMO supporter, Oxford Asset Management.

IMO 2019 problems (17 July 2019)

The IMO 2019 papers were sat on 16 and 17 July in Bath; the problems are available. The problems were submitted by South Africa, Ukraine, Croatia, El Salvador, USA and India respectively.

Our thanks to this year’s IMO supporter, Oxford Asset Management.

Mathematics Ashes results (13 July 2019)

Australia has won the 12th Mathematics Ashes competition, decided on the results of today’s practice exam at the joint pre-IMO training camp in Bath; the results for the two teams were as follows, with the UK scoring a total of 77 and Australia scoring a total of 104:

Our thanks to this year’s IMO supporter, Oxford Asset Management.