--- title: "Australian Mathematical Olympiad Preparation: AMO Explained" description: "The Australian Mathematical Olympiad since 2026: AMO Summer, Winter and Finals, the invitation route through the AMC and AIMO, and how olympiad proofs work." canonical: https://learn.modernagecoders.com/australian-mathematical-olympiad-preparation source: src/pages/australian-mathematical-olympiad-preparation.html --- > The Australian Mathematical Olympiad since 2026: AMO Summer, Winter and Finals, the invitation route through the AMC and AIMO, and how olympiad proofs work. In short From 1 January 2026 the Australian Mathematical Olympiad became three exams: AMO Summer and AMO Winter, each 6 questions in 3 hours sat at school by about 250 invited students, and AMO Finals, two days of 4 questions in 4 hours for about 60 students. Invitations go to students in Year 11 or below, made by AMOC State Directors. Every problem requires a proof. Where to start ## Three courses on the road to olympiad maths Olympiad readiness rests on strong problem solving and the habit of proving things. [![Maths Olympiad & Competition Course course thumbnail](/images/olympiad-competition-maths.webp) AMO / 01 Competition maths From AMC-style problems to olympiad proofs, with number theory, combinatorics, geometry and inequalities. Open the syllabus →](/courses/olympiad-competition-mathematics-mastery)[![Middle School Mathematics Mastery course thumbnail](/images/middle-school-maths.webp) AMO / 02 Middle years maths Secure algebra and geometry for younger students, the base AIMO problems build on. Open the syllabus →](/courses/comprehensive-middle-school-mathematics-mastery)[![Problem Solving for Teens course thumbnail](/images/problem-solving-teens.webp) AMO / 03 Problem solving for teens Structured reasoning and careful case analysis, useful in both olympiad maths and informatics. Open the syllabus →](/courses/problem-solving-dsa-masterclass-teens) The new AMO ## Three exams instead of one, from 2026 Before 2026 the AMO was a two-day contest of four questions each day, sat under school supervision by about 200 invited students. The Australian Maths Trust now runs it as three separate competitions. | | AMO Summer | AMO Winter | AMO Finals | | --- | --- | --- | --- | | Date in 2026 | Wednesday 25 February | Wednesday 29 July | Tuesday 1 and Wednesday 2 September | | Where | At school | At school | AMT-organised exam hubs | | Students | About 250, invited | About 250, invited | About 60, invited | | Format | 6 questions in 3 hours | 6 questions in 3 hours | 2 papers over two days, 4 questions in 4 hours each day | | Purpose | Selects for the Autumn School of Excellence and State Director mentoring | Selects for AMO Finals | Selects for the Spring School of Excellence | Invitations to AMO Summer and AMO Winter are made by Australian Mathematical Olympiad Committee (AMOC) State Directors, and go to around 200 to 250 students in Year 11 or below across Australia. Students who attended the AMOC School of Excellence or the Autumn School of Excellence are invited, along with some participants in the Australian Training Tournament. The AMT describes AMO Summer as six challenging problems requiring sound mathematical proofs, and adds that even solving one of them is a significant achievement. For AMO Summer 2026, the AMT published award cut-offs of 35, 27 and 16 points for gold, silver and bronze, given approximately to the top 20, top 50 and top 100. Honourable mentions go to students with full marks on at least one problem who miss out on those awards. Those numbers are published to describe results, not targets. The AMO is about the quality of reasoning on problems most strong students cannot finish. Source: [Australian Maths Trust, Australian Mathematical Olympiad](https://amt.edu.au/amo), read 7 October 2026. 2027 dates had not been published there. Getting invited ## The open competitions that lead towards the AMO Nobody enters the AMO directly. The AMT says students considered for invitational maths training need outstanding results in the Australian Mathematics Competition or one of the modules under Maths for Young Australians. | Competition | Who | Format | 2026 date | | --- | --- | --- | --- | | Australian Mathematics Competition (AMC) | Years 3 to 12 | 60 minutes primary, 75 minutes secondary | 4 to 6 August | | Australian Junior Mathematics Olympiad (AJMO) | Up to Year 8 | 10 problems, 90 minutes, online, integer answers 0 to 999 | Thursday 10 September | | Australian Intermediate Mathematics Olympiad (AIMO) | Years 7 to 10, pitched at Year 10 | 4 hours; 10 questions, 8 integer answers and 2 written solutions; 35 marks | Thursday 10 September | The AJMO is new: the AMT describes it as an accessible introduction to olympiad-style problems for students up to Year 8 who are not yet ready for the AIMO. Because both run on the same day, schools choose one per student, and students in Year 8 or below who are ready for the AIMO should still sit it. The AIMO, according to the AMT, can be used to identify students for its olympiad pathway. Its written questions may include proofs, so it is the first open paper where proof writing is tested directly. Beyond the AMO, the AMT lists training schools, the AMOC Senior Contest and the Asian Pacific Mathematics Olympiad. Each year four Australian girls are selected for the European Girls' Mathematical Olympiad and six students for the International Mathematical Olympiad. The AMT and Australian Science Innovations do not let a student take part in more than one olympiad program in the same year, so students invited to several must choose one subject. Sources: [AMT Olympiad and Pathways](https://amt.edu.au/olympiad-programs); [AIMO](https://amt.edu.au/aimo); [AJMO](https://amt.edu.au/ajmo); [AMC](https://amt.edu.au/amc). Read 7 October 2026. Entry prices printed there are not shown. Worked lesson ## The postage-stamp problem, from experiment to proof A classic olympiad style question, with values chosen by us: a game awards either 5 points or 8 points per move. Which totals can never be reached, and what is the largest one? ### 1. Experiment List reachable totals: 5, 8, 10, 13, 15, 16, 18, 20, 21, 23, 24, 25, 26, 28 and onwards. The gaps are 1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 17, 19, 22 and 27. After 27, nothing seems to be missing. ### 2. Conjecture The largest unreachable total is 27, and there are 14 unreachable totals. For coprime scores a and b, a known result says the largest is ab minus a minus b, which is 40 minus 13, so 27. ### 3. Prove it A list is evidence, not proof: we must show every total from 28 upwards is reachable, and that 27 is not. The neat way is to sort totals by their remainder when divided by 5. | Number of 8-point moves | Points from those moves | Remainder when divided by 5 | Smallest reachable total with that remainder | | --- | --- | --- | --- | | 0 | 0 | 0 | 0 | | 2 | 16 | 1 | 16 | | 4 | 32 | 2 | 32 | | 1 | 8 | 3 | 8 | | 3 | 24 | 4 | 24 | The proof follows from the table. Adding 5-point moves never changes a total's remainder on division by 5, so for each remainder the smallest reachable total is the multiple of 8 shown, and every larger number with the same remainder is reachable by adding fives. The largest of those smallest values is 32, with remainder 2. So 32 minus 5, which is 27, has remainder 2 but is below the first reachable total with that remainder: 27 cannot be reached. Every number from 28 onwards lies at or above the first reachable total for its remainder (28 is 8 plus four fives, 29 is 24 plus 5, 30 is six fives, 31 is 16 plus three fives, 32 is four eights), so every one can be reached. That completes the proof that 27 is the largest unreachable total. ### What an olympiad marker looks for A complete answer states the claim, explains why the remainder idea works, shows that 27 fails and that every larger number succeeds, and ends with a clear conclusion. Missing the "every larger number" half is the most common reason for losing marks. Writing the proof in short numbered steps, each justified, helps a marker follow it and helps the writer spot gaps. ### Going further The same argument, with a in place of 5 and b in place of 8, proves the general formula ab minus a minus b for any two coprime scores. Counting the unreachable totals, which gives (a minus 1) times (b minus 1) divided by 2, is a good next challenge: here it is 4 times 7 divided by 2, which is 14, matching the list. Why must the scores be coprime? Try 6 and 9: every reachable total is a multiple of 3, so infinitely many totals are unreachable and there is no largest. How we train ## Olympiad preparation that respects how selection works Invitations are decided by the AMOC from competition results and its own programs. Our role is to build the problem solving and proof writing those results reflect. Classes work through problems by area: number theory, combinatorics, geometry, algebra and inequalities. Each problem is explored, conjectured and then proved, with students writing full solutions that a teacher marks as an olympiad marker would. Younger students build towards the AJMO and AIMO first, where integer-answer questions sit alongside the first written proofs. Older students practise full proof papers under time. We never reproduce AMT papers or solutions; past papers belong to the AMT, which sells them on its own site. All our problems are original or classical results proved from scratch in class. We do not promise an invitation, a medal or selection to any team. Only the AMOC makes those decisions, and they rest on the student's own results. | Weeks | Focus | Sign of progress | | --- | --- | --- | | 1 and 2 | Experiment, conjecture, prove | Separates evidence from proof in their own words | | 3 and 4 | Number theory: remainders and divisibility | Writes a complete remainder argument | | 5 and 6 | Combinatorics: counting and cases | Covers every case without overlap | | 7 and 8 | Geometry: angles and similar triangles | Justifies every step of a diagram argument | | 9 and 10 | Timed mixed papers with written solutions | Produces at least one fully correct proof per paper | Growing towards olympiad level ## Four rungs from AMC problems to olympiad proofs Year level is less important than the kind of reasoning a student can sustain. | Around | Rung | The sign it is secure | | --- | --- | --- | | Years 5 to 7 | 1. Enjoys hard problems | Persists with an unfamiliar problem for thirty minutes | | Years 7 to 8 | 2. Explains answers | Says why an answer must be right, not only what it is | | Years 8 to 10 | 3. Writes proofs | Produces a complete written argument for a simple claim | | Years 10 to 11 | 4. Olympiad proofs | Proves unfamiliar results under time pressure | ### If progress stalls Go back to small cases. Most olympiad breakthroughs begin by working out a pattern by hand. Read model proofs slowly and rewrite them in your own words; it builds the language of proof. ### Related reading Our [Australian Maths Trust page](/australian-maths-trust-amc-aio-cat-preparation) covers the AMC, CAT and AIO. For broader competition preparation, see [maths olympiad tutoring](/math-olympiad-amc-tutoring). The catalogue ## Nine courses for mathematically ambitious students From secure foundations to olympiad proofs. Each card opens its syllabus. I ### Foundations Before olympiad problems AMO / FD / 01 #### Middle years maths Algebra and geometry done properly. [Open the syllabus](/courses/comprehensive-middle-school-mathematics-mastery) AMO / FD / 02 #### Mental maths for kids Number sense for younger students. [Open the syllabus](/courses/mental-maths-mastery-kids) AMO / FD / 03 #### Algebra foundations Fluent, accurate symbol work. [Open the syllabus](/courses/algebra-foundations-masterclass)II ### Competition AMC, AJMO and AIMO AMO / CP / 01 #### Competition maths From contest problems to proofs. [Open the syllabus](/courses/olympiad-competition-mathematics-mastery) AMO / CP / 02 #### Statistics and probability Counting and chance in depth. [Open the syllabus](/courses/statistics-probability-maths-course) AMO / CP / 03 #### Computational thinking Patterns and logic for younger students. [Open the syllabus](/courses/problem-solving-and-computational-thinking-for-kids)III ### Beyond Proof and computation AMO / BY / 01 #### Problem solving for teens Rigorous case analysis. [Open the syllabus](/courses/problem-solving-dsa-masterclass-teens) AMO / BY / 02 #### Competitive programming For students also drawn to informatics. [Open the syllabus](/courses/competitive-programming-for-teens-course) AMO / BY / 03 #### Maths through coding Testing conjectures with code. [Open the syllabus](/courses/maths-through-coding) How lessons run ## Live olympiad classes from India Our olympiad teachers are based in India. The time difference works in favour of families: when it is 6pm in Sydney it is 1:30pm India time in winter and 12:30pm in summer, and 6pm in Perth is 3:30pm India time all year. Evening problem sessions in Australia therefore sit inside the Indian working day. Weekday evening One area of olympiad maths per week. Weekend A timed proof paper and marking. Before AIMO or AMO Mixed papers and proof clean-up. ### Proof first Every answer is written as a complete argument. ### Original problems Never copied from AMT papers. ### Marked like a marker Feedback on gaps, not only on the final answer. ### Matched squads A squad of five to ten olympiad students working on the same problems. ### One-to-one option For a student already on the olympiad pathway. ### No selection promised Invitations and teams are the AMOC's decision. Student work ## Work our students have published Projects made for their own sake. Browse the [student labs](/student-labs). ![NutriLife AI nutrition coach project screenshot](/images/projects/nutrilife.webp) AI and ML #### NutriLife An AI nutrition coach that reads what you eat and works you toward a target. by Bhavya · [Open it](https://nutrilife-bhavya.lovable.app) ![Misti AI chatbot for maths and coding screenshot](/images/projects/misti.webp) AI and ML #### Misti A chatbot that answers mathematics and programming questions, built and deployed by a student. by Harshit · [Open it](https://misti.modernagecoders.com) ![GuardianX AI internet safety assistant screenshot](/images/projects/guardianx.webp) AI and ML #### GuardianX An assistant that helps a young person recognise unsafe situations online. by Vivaan · [Open it](https://guardianx-cybersaver.lovable.app) ![SkyCast weather forecast application screenshot](/images/projects/skycast.webp) Web app #### SkyCast A weather forecasting site with live conditions for any location. by Krish Fees ## Fees Olympiad classes cost a flat monthly amount in US dollars, the rate we use outside India; nothing is payable to join and you can stop at the end of any month. AMT competition entries are a matter between schools and the AMT, not us. Free first class USD 0 no card required - A first olympiad class, free - An honest read on proof-writing level - No card details Book it Group batch USD 100 a month, billed in US dollars - Fifteen to twenty students at one level - One teacher across the term - Solutions marked and discussed - A certificate at the end Start here One to one USD 150 a month, billed in US dollars - A teacher for one student - Work shaped around that student's weakest area - Weekly times arranged with you Enquire What families say ## Rated 4.9 across 547 Google reviews Google reviews, exactly as written by families. ★★★★★ "The one step solution for my son. Modern Age Coders make learning coding so simple that kids love it. The teachers explain complex concepts clearly with practical exercises and interactive content." Ria Mukherjee Parent ★★★★★ "Modern Age Coders has been a game-changer for me. I struggled to grasp IT concepts and coding before joining, but their classes transformed everything. I can now confidently write complex programs with ease." Samriddha Mondal Student ★★★★★ "One of the most wonderful education centres out there. Education is not limited to school syllabus but focuses on skill development." Vansh Agarwal Student ★★★★★ "My child Dhairya is really enjoying the Modern Age Coders classes. This is his first online class and he eagerly looks forward to it. I can already see his improvement, and the teachers are very cooperative." Sonam Oswal Parent of Dhairya ★★★★★ "Modern Age Coders have wonderful teachers who teach in a clear, easy and practical way. The teacher boosts students' confidence and inspires them to learn without hesitation." Sonu Goyal Parent ★★★★★ "I highly recommend this computer coding class! The teachers are incredibly knowledgeable and passionate about coding." Ritu Kedia Parent Questions about the AMO ## What students and parents ask ### What is the Australian Mathematical Olympiad? An invitation-only proof-based mathematics exam run by the Australian Maths Trust for students in Year 11 or below. Since 2026 it has three parts: AMO Summer, AMO Winter and AMO Finals. ### How do students get invited? Invitations are made by AMOC State Directors. The AMT says students considered for invitational maths training need outstanding results in the AMC or a Maths for Young Australians module. ### When were the 2026 AMO exams? AMO Summer on Wednesday 25 February, AMO Winter on Wednesday 29 July, and AMO Finals on Tuesday 1 and Wednesday 2 September 2026. ### What is the format of AMO Summer and Winter? Six questions in three hours, sat at school, by about 250 invited students each. AMO Finals is two papers of four questions in four hours, for about 60 students. ### What is the postage-stamp problem? Finding which totals can be made from two fixed amounts, such as 5 and 8. For coprime amounts a and b, the largest total that cannot be made is ab minus a minus b. ### What should a younger student enter first? The AMC, then the AJMO (up to Year 8) or the AIMO (Years 7 to 10). The AIMO's written questions are the first open papers that test proof directly. ### Can a student do maths and informatics olympiads together? Not in the same year. The AMT and Australian Science Innovations allow a student to take part in only one olympiad program per year. ### Do you use AMO past papers? No. The AMT sells its own past papers. We teach with original problems and classical results proved in class. ### Can lessons guarantee an invitation? No. Only the AMOC decides invitations and selections. We teach the problem solving and proof writing that strong results reflect. ### What happens in the free class? A student works one olympiad style problem with a teacher, from experiment to written proof, and gets honest feedback on the proof. Related pages ## More for mathematically able students Competitions and maths pathways in Australia. ### [AMT competitions](/australian-maths-trust-amc-aio-cat-preparation) The AMC, CAT and AIO in depth. ### [Maths olympiad tutoring](/math-olympiad-amc-tutoring) Contest preparation at every level. ### [Competitions calendar](/australian-coding-maths-and-ai-competitions-calendar) Every contest by month. ### [Year 10 Methods preparation](/year-10-maths-methods-preparation) Strong algebra before senior maths. ### [Maths tutoring online](/online-maths-tutoring-australia) Weekly maths alongside olympiad work. ### [Coding classes in Australia](/coding-classes-in-australia) The national guide, state by state. Start here ## Book a free olympiad class Tell us the year level and which competitions the student has sat. The free class works one problem from experiment to proof and ends with honest advice on next steps. To look before booking, browse the full syllabi on our [course atlas](/course-atlas) or read [how we teach](/how-we-teach). [WhatsApp us](https://wa.me/919123366161?text=Hello%20Modern%20Age%20Coders%2C%20I%20would%20like%20a%20free%20olympiad%20maths%20class%20for%20a%20student%20in%20Australia.) · [+91 91233 66161](tel:+919123366161) · [connect@modernagecoders.com](mailto:connect@modernagecoders.com) Messages on WhatsApp tend to be answered first. You will see an Indian number, since our teachers and office are in India, not Australia. ### Want a class sooner? Book a priority demo A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off. [Book a priority demo](/book-demo) ## Keep exploring Modern Age Coders ### More maths tuition - [Maths Competitions for Primary Kids in Australia: A Guide](/australian-maths-competitions-for-primary-kids) - [Australian Informatics Olympiad Preparation](/australian-informatics-olympiad-preparation) - [Australian Curriculum Maths Yea to 10 Help](/australian-curriculum-maths-year-7-to-10-help) - [Best Online Math Tutoring 2026: Ranked Honestly, With Sources](/best-online-math-tutoring-2026) - [Best Online Maths Classes for Kids 2026: Ranked Honestly](/best-online-maths-classes-2026) - [Advanced Higher Maths Tuition Online](/advanced-higher-maths-tuition-online) - [Maths Tutor in Box Hill](/maths-tutor-box-hill) - [Maths Tutor in Brisbane](/maths-tutor-brisbane) - [Maths Tuition in Liverpool](/maths-tuition-in-liverpool) ### Learn more - [Olympiad Mathematics: IOQM, INMO and AMC Preparation](/courses/olympiad-mathematics-premium-course) - [JEE Foundation Maths Class 8-10: Proofs & Problem Solving](/courses/jee-foundation-maths-course-class-8-10) - [IOQM, RMO and INMO Preparation Online: India's Olympiad Pathway](/ioqm-rmo-inmo-preparation) - [GCSE Maths Resit Course Online: Post-16 and Adults](/courses/gcse-maths-resit-course) ### From the blog - [Maths Learning Guides](/blog/topic/maths) - [Modular Arithmetic: Clock Maths for Olympiads and Code](/blog/modular-arithmetic-explained) - [How Coding and Mathematics Work Together in Engineering & Science](/blog/coding-mathematics-engineering-science) - [The Pigeonhole Principle: 4 Olympiad Problems Solved](/blog/pigeonhole-principle-explained) ### Start here - [Try a free trial class with a Modern Age Coders mentor](/free-trial) - [About Modern Age Coders, teaching since 2020](/about) Free class[Priority demo](/book-demo)[Call us](tel:+919123366161) --- *Canonical: https://learn.modernagecoders.com/australian-mathematical-olympiad-preparation*