Welcome to the British Mathematical Olympiad

• A PDF file containing lots of BMO problems from the past (1993–2022). 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

Balkan Mathematical Olympiad report available (22 May 2022)

The Balkan Mathematical Olympiad information now includes Robin Bhattacharyya’s report on the 2022 olympiad.

Balkan Mathematical Olympiad 2022 student report (12 May 2022)

A competition diary written by the UK team members at the Balkan Mathematical Olympiad in Cyprus is available here.

Balkan Mathematical Olympiad results (7 May 2022)

The UK team at the Balkan Mathematical Olympiad in Agros, Cyprus have achieved the following scores (each question marked out of 10). The medal cut-offs were 31 for gold, 22 for silver and 12 for bronze. The problems were proposed by the UK (Dominic Yeo), Greece, Greece and the UK (Tommy Walker Mackay), respectively.

EGMO results (12 April 2022, press release added 19 April)

The UK team in the eleventh European Girls’ Mathematical Olympiad have achieved the following results, coming 14th out of 57 participating teams (9th out of 31 official European teams). The medal boundaries are 29 for gold, 22 for silver and 15 for bronze.

A competition diary written by the UK team members is available here. A UKMT press release is also available.

European Girls’ Mathematical Olympiad problems (9 April 2022)

The problems (day 1, day 2) from the eleventh European Girls’ Mathematical Olympiad, held yesterday and today in Eger, Hungary with some teams taking part remotely, are now available. The problems were submitted by the Netherlands, Ukraine, the United Kingdom, Romania, the USA and Australia, respectively; problem 3 is by Joe Benton and Dominic Yeo.

Balkan Mathematical Olympiad team selected (4 April 2022)

The UK has been invited as a guest nation to send a team to the Balkan Mathematical Olympiad, to be held in Agros, Cyprus, 4–9 May. The team will be accompanied by Robin Bhattacharyya (Trent College) as Leader, Jamie Bell (University College, London) as Deputy Leader and Ina Hughes as Observer. After the training camp held at Trinity College, Cambridge, the team has been selected as follows.

IMO squad selected (4 April 2022)

At the training camp held at Trinity College, Cambridge, the following IMO squad of eleven was selected. These students will participate in further training and selection tests before the IMO team of six and the first reserve for the IMO in Norway are chosen.

The Team Leader is Geoff Smith (University of Bath), the Deputy Leader is Freddie Illingworth (University of Oxford) and Dominic Yeo (King’s College London) will be Observer with Leader. The IMO will take place in Oslo, 6–16 July.

IMO training and selection camp (3 April 2022)

The annual IMO training and selection camp was held March 29 to April 3. After two years online, we were delighted to return to the usual residential format at Trinity College, Cambridge.

An announcement about selection will be released at noon on Monday 4 April.

EGMO 2022 team (24 February 2022)

The 11th European Girls’ Mathematical Olympiad will be held 6–12 April in Eger, Hungary (in a hybrid format with some teams taking part remotely). The UK team (taking part in person in Eger) will be:

The reserve is Tatiana Mouzykantskii (Sevenoaks School). The Team Leader is Jenny Owladi of the Bank of England and the Deputy Leader is Kasia Warburton of Trinity College, Cambridge.

Olympiad training camps and competitions (21 February 2022)

The 2022 edition of the annual spring olympiad camp in Cambridge will be held in person at Trinity College. We will shortly be contacting students with high scores on BMO1 and BMO2 to invite them to this event.

The UK will also send a team to the Balkan Mathematical Olympiad, to be held in Cyprus, 4–9 May. Details will be confirmed soon, and the team will be selected after the training camp.

BMO Round 2 high scores and solutions (18 February 2022)

The following BMO2 candidates scored 20 or more out of 40. Solutions are also available.

BMO Round 2 (28 January 2022)

This year’s BMO Round 2 paper was taken yesterday. The problems were by Robin Bhattacharyya (problem 1), Sam Bealing (problem 2), Ed Kirkby (problem 3) and Dominic Yeo (problem 4).

BMO Round 1 high scores (12 January 2022, New Zealand results added 20 January 2022)

BMO Round 1 was marked remotely in December. The following candidates scored 43 or more out of 60.

BMO Round 1 markers’ report (10 January 2022)

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

BMO Round 1 (4 December 2021)

This year’s BMO Round 1 paper was taken on 2 December; video solutions are available online. Production facilities for the video were donated by the University of Bath Audio Visual Unit. The problems were by Dominic Rowland (problems 1 and 3), Daniel Griller (problems 2 and 6), Stuart Haring and Maya Brock (problem 4) and Jeremy King (problem 5).

UK MOG report (7 November 2021)

The report for schools on the 2021 UK Mathematical Olympiad for Girls paper, with statistics of results, is now available.

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).