The British Mathematical Olympiad Round 2 was sat on Thursday 21 January 2026, with results announced by the BMO Subtrust in mid-February. This article is the editorial analysis of the 2025–26 Round 2 results, the implications for the Trinity Camp invitation list, and what the results suggest for the IMO 2026 team selection.
This article is editorial commentary, not a primary results record. For the verified Round 2 results list, see the BMO Subtrust site at bmos.ukmt.org.uk.
Headline results
Approximately 100 candidates sat BMO Round 2 in January 2026, drawn from the top BMO Round 1 cohort sat in November 2025. The paper followed the standard format: four open-ended problems, three hours thirty minutes, marked centrally by the BMO Subtrust problems panel. The maximum possible mark was 40 (ten marks per problem).
Distinction certificates were awarded at the top score tier. As is typical in BMO Round 2, the Distinction cohort is small — historically between 15 and 25 students nationally. The 2025–26 distinction list is dominated by Year 13 students, with a notable presence of Year 12 students who are likely to feature prominently in the IMO 2027 team selection cycle.
Problem-by-problem editorial analysis
This section is normally where the BMO Subtrust publishes its full mark scheme analysis. We will not duplicate that work here; instead the editorial focus is on what the problem choices suggest about the Subtrust’s view of the cohort.
Problem 1 in 2026 was a number theory problem on modular arithmetic and divisibility — a classic BMO Round 2 opener, marginally harder than the 2025 equivalent but in the same family of techniques. The cohort solved this at the expected rate; partial credit was the norm rather than full marks, suggesting the calibration was correct for the Round 2 audience.
Problem 2 was a combinatorial geometry problem requiring a counting argument over a configuration of points and lines. The solution required recognising a bijection between two parameterisations of the configuration; the marking panel reports that approximately one-third of the cohort identified the bijection in full.
Problem 3 was an inequality problem in three variables with an unusual symmetric structure. The standard SOS (sum-of-squares) approach gave a clean solution; less than a quarter of the cohort closed the argument, with most candidates running out of time at the final substitution step. This was the discriminating problem of the paper.
Problem 4 was a functional equation, with the answer requiring a casework argument over the structure of the function’s image. The Subtrust panel reports this as the hardest problem of the paper, with only a handful of candidates earning full marks.
Round 2 is calibrated so that the top performers solve approximately two problems completely; the discriminating problems are the ones where partial credit decides invitations to Trinity Camp.
Trinity Camp invitations
The Trinity Camp invitation list for Easter 2026 will be published by the BMO Subtrust in mid-March, following the Easter holidays preparation phase. Approximately 20 students are typically invited. The selection is by Round 2 score, with ties broken by the Subtrust panel’s qualitative assessment of the candidate’s written solutions.
From the Trinity Camp, six students are selected to represent the United Kingdom at the International Mathematical Olympiad in July 2026, held in Shanghai, China — a notable location for British students given the international travel implications.
What this tells us for 2026–27
Three observations for the cohort planning Year 12 in autumn 2026: (1) the calibration of Round 2 has been stable for several seasons — preparation for Round 2 in 2027 should follow the same patterns as 2026; (2) the inequality problem (Problem 3) was the discriminating question, suggesting Year 12 students should invest in the standard inequality techniques (AM-GM, Cauchy-Schwarz, SOS, rearrangement) more heavily than they often do; (3) the functional equation (Problem 4) was unusually demanding, but functional equations remain a less-frequent BMO Round 2 question type than inequalities or number theory.
The IMO Team UK announcement follows the Trinity Camp performance and is typically published in mid-May. Our IMO 2026 coverage will follow in a separate editorial article in May.