When I was younger, I was fortunate to have the opportunity to represent the United Kingdom at various international mathematics competitions, including the International Mathematical Olympiad. The competitions and the training that preceded them were certainly some of the most valuable experiences of my schooldays.

I am currently director of the UK’s training programme for the IMO. The best source of information about this is the BMOS website. The premier international competition is the IMO, and a comprehensive record of the UK’s participation can be found at the IMO Register, maintained by Joseph Myers.

I’m also responsible for the UK’s problem submissions to international competitions. If you have problems you’d like to submit (and are British or based in the UK), or would like to know if a problem is potentially suitable, please do get in touch. We can certainly put you in touch with the problem chairs for other levels (eg BMO) if that turns out to be more appropriate.

On this blog, there are some reports on various competitions I have attended, which are generally a mix of maths and travelogue, as well as some relevant articles about individual competition problems and generally-relevant topic areas.

**Articles**

Here are some posts about olympiad subject material, sometimes with and sometimes without direct reference to individual problems which have appeared in competitions:

- Characterising fixed points in geometry problems
- Symmedians and configurations
- Geometric subconfigurations
- Chains and antichains
- Antichains in the grid
- Turan’s theorem
- Lagrange multipliers: Part 1 and Part 2
- Lovasz Local Lemma
- Popoviciu’s Inequality
- Local to global in point set combinatorics
- Rearrangement inequality
- Combinatorial nullstellensatz
- Nested closed intervals
- Generating functions for the IMO
- Exponentials kill polynomials

And here are some posts about notable competition papers, or individual problems from such papers. It goes without saying that many of these posts include detailed solutions or solution outlines, so should not be read by anyone keen to try the problems from scratch themselves. Partly, the point of these posts is to discuss *finding approaches* to these problems. Official solutions, for obvious reasons of brevity, often can’t devote time to justifying how a solver might stumble upon the best methods, so in most of these articles, I devote more time to the motivation than the finer details of the argument.

*International*

- EGMO 2018: Problems 2,3,4,6 (non-geometry).
- Balkan MO 2017: Questions 1,3,4 (non-geometry), and a post about configurations and symmedians and Q2
- EGMO 2017: Paper I (mostly about the geometric subconfigurations in Q1)
- RMM 2017: Problems 1,4,5; and Problems 2,3,6,
- EGMO 2016: Paper I, and Paper II
- IMO 2014, shortlist N6: Sums of squares of intervals
- EGMO 2015

*National*

- MOG 2018: Mainly Q4.
- BMO2 2018: Questions 2-4.
- BMO1 2017: Questions 1-4; and Questions 5,6
- BMO2 2017,
- BMO1 2016: a post about Q5 (geometry), a post about the other questions,
- BMO1 2015 Q5: Pencils and Simson’s Line

**Reports**

Here are links to my blog reports on recent IMOs and other competitions, as well as the slightly more formal pdf versions.

- Colombia 2013 (pdf),
- South Africa 2014 (pdf),
- Thailand 2015 (pdf),
- Hong Kong 2016 (pdf);
- Brazil 2017;
- Romania 2018 (pdf);
- Romanian Masters of Mathematics: RMM 2015 (pdf), RMM 2017
- Balkan MO: Albania 2016 (pdf), Serbia 2018 (pdf),

**Ancient History**

Below are reports on some of the competitions I enjoyed as a student. In spite of the occasional smugness, perhaps there is still something of interest, even if only as evidence of how much I enjoyed myself intellectually and otherwise.

Balkan Mathematical Olympiad 2007 – Report – Tom Lovering and DJY