British Mathematical Olympiad Round 2

Olympiad date: Wednesday 20th January 2027

As a follow-on Round to the BMO1, the British Mathematical Olympiad Round 2 (BMO2) is a 3.5 hour Olympiad consisting of four problems requiring full written solutions.

BMO2 is the UK’s hardest national mathematics competition, and is intended to stretch students who have experienced success at BMO1

The competition is open to eligible students. UKMT invites around 100 qualifying students from BMO1, those who did not participate in BMO1 can be entered at the discretion of their schools. For more information and past papers visit the BMO site here.

How it works

Purchase entries

Sit challenge

Receive results

For full information on how to host the British Mathematical Olympiad Round 2 please visit the Competition Handbook.

Instructions

Full written solutions – not just answers – are required, with complete proofs of any assertions you may make. Work in rough first, and then draft your final version carefully before writing up your best attempt.

One or two complete solutions will gain far more credit than partial attempts at all four problems.

The use of rulers and compasses is allowed, but calculators and protractors are forbidden.

You should write in blue or black ink, but may use pencil and other colours for diagrams.

To accommodate candidates in other time zones, please do not discuss any aspect of the paper on the internet until 8am GMT on Friday 23rd January. Candidates in time zones more than 2 hours ahead of GMT must sit the paper on Thursday 22nd January (as defined locally).

Around 24 high-scoring students eligible to represent the UK at the International Mathematical Olympiad, will be invited to a training session held in Cambridge around the Easter holidays.