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    Hamilton Mathematical Olympiad

    by UK Maths Trust

    A demanding UKMT follow-on maths challenge where students tackle six Olympiad-style problems and write full, reasoned solutions under exam conditions.

    Last verified: 18 Aug 2026Reviewed by:SSSean Stevens
    Hamilton Mathematical Olympiad

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    Hamilton Maths Olympiad at a glance: cost, dates and eligibility

    Current status

    Open now

    Eligibility

    IMC qualifier or discretionary school entry

    Age range / Year group

    Year 10 equivalent

    Location / Region

    Registered UKMT schools worldwide

    Cost

    Free qualifier; £25 discretionary

    Prize highlight

    Medals, certificates and book prizes

    Entry format

    In-school written Olympiad

    Deadline

    19 March 2027

    Save deadline

    Hamilton Maths Olympiad summary

    The Hamilton Mathematical Olympiad is a UKMT follow-on challenge built around unfamiliar, proof-style mathematics rather than short multiple-choice questions.

    Students solve six problems independently and must explain their methods with complete mathematical reasoning. Exact answers and clear presentation both matter.

    It suits confident problem-solvers who enjoy sustained reasoning and are ready to practise writing rigorous solutions, not just finding the final answer.

    What is Hamilton Mathematical Olympiad?

    The Hamilton Mathematical Olympiad is one of UKMT's follow-on rounds to the Intermediate Maths Challenge. It replaces quick-response questions with six extended Olympiad-style problems designed to test mathematical thinking and proof.

    Students work through the paper independently under supervised exam conditions. They must present full written solutions, justify their methods and give exact, fully simplified answers, creating an experience closer to formal problem solving than an ordinary classroom test.

    Why Succeed highlights Hamilton Maths Olympiad

    • The six-problem format rewards depth of reasoning rather than rapid answer selection.

    • Students receive credit for clear mathematical presentation, including partial marks where appropriate.

    • Free official past papers, solutions and investigations provide a strong preparation pathway.

    • Performance can lead to certificates, medals and book prizes, while Olympiad participants can also access marker comments.

    • Qualification through the Intermediate Maths Challenge creates a meaningful progression route, while discretionary school entry offers another route.

    Who is Hamilton Maths Olympiad for?

    Best for

    Year 10-equivalent students who enjoy demanding, unfamiliar maths problems and can explain their reasoning carefully.

    Not ideal if

    You prefer multiple-choice questions, want to compete independently from home or are not yet comfortable writing complete mathematical proofs.

    Is Hamilton Maths Olympiad worth it?

    Yes, for a student who wants a serious test of mathematical reasoning. Preparing for the paper can strengthen proof writing, persistence and the ability to communicate a solution clearly, whether or not the student earns an award.

    The limitation is that entry depends on school involvement and the challenge is intentionally demanding. A medal is not guaranteed, so the strongest value comes from the preparation and feedback rather than treating recognition as the only worthwhile outcome.

    How much preparation does Hamilton Maths Olympiad need?

    Effort level

    High.

    Best started

    Begin timed past-paper practice several weeks before the March sitting.

    Main challenge

    Turning a promising idea into a complete, clearly presented proof.

    Typical preparation

    • Complete one problem at a time without checking the solution too quickly.

    • Rewrite successful answers as clean proofs with every important step justified.

    • Use timed past papers to learn when to persist and when to move to another problem.

    • Review official solutions and compare their clarity and efficiency with your own.

    Useful if

    You already enjoy non-routine maths and want to develop Olympiad technique.

    What do students do on Hamilton Maths Olympiad?

    Students complete a supervised paper of six Olympiad-style problems, recording exact answers and the reasoning that proves each method works.

    Step-by-step process

    1. 1

      Qualify through the Intermediate Maths Challenge or secure a discretionary school entry.

    2. 2

      Prepare with official Hamilton past papers, solutions and investigations.

    3. 3

      Sit the two-hour paper at school under strict exam conditions.

    4. 4

      Write full solutions and mathematical reasons rather than answer-only responses.

    5. 5

      The school scans and uploads the completed paper answer sheets.

    6. 6

      Access results, certificates and marker feedback through the UKMT Competition Profile.

    Hamilton Maths Olympiad dates and deadlines

    Competition date

    18 March 2027

    The two-hour supervised sitting.

    Upcoming

    Answer sheets upload

    19 March 2027

    Schools must upload scans by 11:59pm.

    Upcoming
    Save deadline

    Eligibility and requirements

    • England, Wales and overseas: Year 10

    • Scotland: S3

    • Northern Ireland: Year 11

    • Qualifying Intermediate Maths Challenge score, or discretionary entry

    • Entries must come through a registered UKMT centre

    • UK and overseas schools may participate

    How much does Hamilton Maths Olympiad cost?

    Entry cost

    Free qualifier; £25 discretionary — Automatic qualifiers do not need a paid order.

    How to enter Hamilton Maths Olympiad

    1. 1

      Ask the school's UKMT coordinator whether you qualified through the Intermediate Maths Challenge.

    2. 2

      If you qualified automatically, the school should use the invitation already added to its account.

    3. 3

      If you did not qualify, ask whether the school will purchase a discretionary entry.

    4. 4

      The coordinator confirms the participant details through the UKMT Competition Profile.

    5. 5

      The school downloads and prints the Olympiad materials before supervising the paper.

    Save this competition in Succeed, keep the deadline visible, and track your progress before you submit.

    Start your entry checklist

    Submission requirements

    Solutions should be rigorous enough for a marker to follow the method and verify why it is correct.

    • Full written solutions

    • Mathematical reasons for each method

    • Exact, fully simplified answers

    • Blank paper permitted for rough work

    • No squared paper

    • No calculators or measuring instruments

    • Do not submit rough work

    • Paper answer sheets uploaded by the school

    Prizes and recognition

    Certificate awards

    The top 25% receive Distinction and the next 40% receive Merit.

    Medal awards

    The top 20 receive gold, the next 30 silver and the next 50 bronze.

    Book prize

    Every medal recipient also receives a book prize.

    What this may help with

    Demonstrating sustained mathematical problem solving and proof writing.

    What it does not guarantee

    A medal, university offer or future Olympiad qualification.

    Judging criteria

    • 60 marks available across the paper
    • 10 marks available for each problem
    • Partial marks for clear mathematical presentation
    • Full solutions must justify why the method is correct
    • Incomplete or poorly presented solutions lose marks
    • Answers should be exact and fully simplified

    No separate judging weighting is published beyond the 60-mark scoring structure.

    How to stand out

    1. Write each solution as a logical argument that another student could follow without guessing missing steps.
    2. State why every important construction, equality or conclusion is valid.
    3. Keep exact forms such as fractions, roots and π instead of using decimal approximations.
    4. Use official past papers under timed conditions, then rewrite weaker solutions after studying the worked approach.
    5. Make diagrams and notation neat, but spend most of the response on the mathematical reasoning.
    6. Check that the final answer is fully simplified and directly answers the problem.

    Hamilton Maths Olympiad FAQs

    Students can be invited after achieving a qualifying Intermediate Maths Challenge score. Eligible students may also be entered through a discretionary entry purchased by their school.

    No. Entries must normally be managed by an institution registered as a UKMT centre, not by an individual student, parent or private tutor.

    It is a two-hour written challenge containing six Olympiad-style problems. Students must develop and communicate full mathematical solutions.

    No. Calculators, measuring instruments and squared paper are forbidden. Blank paper may be used for rough working, but rough work should not be submitted.

    The paper is worth 60 marks, with 10 marks available per question. Markers can award partial credit based on the clarity and completeness of the mathematical presentation.

    Yes. UKMT Olympiads are available to UK and overseas schools, although overseas schools must download and print their papers rather than receive posted copies.

    Students may receive performance-based certificates and medals. Medal recipients also receive a book prize, with the title varying by year.

    Yes. UKMT provides free past papers, while its preparation guidance also points students and teachers toward solutions and investigations.

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    Sean Stevens

    Content reviewed by

    Sean Stevens

    Co-founder, Succeed | Founder, Immerse Education (2012–2026)

    Sean works at the intersection of academic enrichment, programme quality and university preparation, with expertise in evaluating pre-university experiences for ambitious secondary school students.

    View author page

    Sources and verification

    Source types reviewed

    • Competition Handbook - Overseas Schools
    • Competition Handbook - Access Arrangements
    • Competition Handbook - Order T&Cs
    • Competition Handbook - Solutions, Results & Qualifiers
    • Competition Handbook - Quick-Step Guide
    • Competition Handbook - Orders & Payments
    • Competition Handbook - UKMT Competitions
    • Login - Cuttle
    • Cayley, Hamilton and Maclaurin Mathematical Olympiads Awards - UKMT
    • Competition Calendar 2026-27 - UKMT
    • Cayley, Hamilton and Maclaurin Mathematical Olympiads - UKMT

    Succeed uses official provider information where available, but keeps this public page focused on comparison and planning inside Succeed.

    What we verified (on 18 Aug 2026)

    • Competition date checked

    • Eligibility stages reviewed

    • Entry routes confirmed

    • Format rules verified

    • Cost routes checked

    • Awards structure reviewed

    • Access guidance checked

    • School process confirmed

    How Succeed uses this information

    We use source material to verify core facts, then show older cycle dates as reference when a current cycle is not available. Always check current submission instructions before entering.