Free APSMO Olympiad Solver
Paste any APSMO (Australasian Problem Solving Mathematical Olympiad) problem — Division J or Senior — and get the full step-by-step working. Built for Years 5–9 students who want to build genuine maths problem-solving skill.
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Learn
A worked APSMO problem — estimate, then test
Below is one fully worked example plus a short primer so you can see exactly how our AI reasons through a problem.
Example Problem
DEMO- 1
Recall the triangular number formula
This is a standard result — memorise it. Olympiad problems often reduce to triangular or square numbers.
- 2
Set up the inequality
Multiply both sides by 2.
- 3
Estimate n
n · (n+1) is close to n². So we need n² ≈ 200, which gives n ≈ √200 ≈ 14. Let's test nearby integers.
- 4
Test n = 13: 13 · 14 = 182 < 200 — too small
Not large enough.
- 5
Test n = 14: 14 · 15 = 210 > 200 — works
This is the smallest n that satisfies the inequality.
- 6
APSMO insight — why estimation first saves time
The 'estimate, then test' pattern is a classic Olympiad shortcut. Without estimation you might start at n = 1 and work up to 14 — five minutes wasted. With estimation you check two values in thirty seconds.
Final Answer
APSMO Olympiad strategy — Polya's method and the problem-solving toolbox
APSMO (Australasian Problem Solving Mathematical Olympiad) is a school-based maths problem-solving competition run by the Mathematical Olympiads for Primary Schools (MOPS) organisation. Unlike curriculum-based exams, APSMO problems are designed to develop GENUINE PROBLEM-SOLVING SKILL — the ability to attack novel problems without being told which technique to use. Students sit five short contests across the year, each containing 5 challenging problems solved in 30 minutes.
There are two divisions. Division J (Junior) targets Years 5-6 students. Senior Division targets Years 7-9. Each contest is scored out of 5 (one mark per problem); there are no part-marks. The highest-ranked students per school attend the annual APSMO Celebration, and top performers are invited to participate in the Australian Mathematics Trust (AMT) pipeline — which leads to the International Mathematical Olympiad (IMO) for the very best.
The problem types repeat with consistent flavour across contests. Number theory: divisibility, prime factorisation, modular arithmetic (without naming it), digit problems. Arithmetic: multi-step word problems with tricky setups. Geometry: triangles, squares, areas, perimeters — often requiring ingenious decomposition. Combinatorics: counting, permutations without overcounting, casework. Logic: pattern recognition, truth-tellers and liars, round-robin tournament problems.
The critical skill APSMO develops is the PROBLEM-SOLVING TOOLBOX. Polya's 4-step method (understand, plan, solve, check) is baked into how Olympiad students approach any problem. Specific tools include: look for symmetry, work backwards from the answer, set up algebra with smart variable choice, draw a diagram, enumerate small cases and look for a pattern, use extremes (what's the maximum? minimum?), use invariants (what stays constant?). Students who build fluency with these tools handle NOT just APSMO problems, but also the Australian Mathematics Competition (AMC), the Mathematics Challenge, and later on HSC / VCE Extension-level problems.
The solver above is tuned for APSMO-level reasoning. Rather than just finding the answer, it SHOWS THE PROBLEM-SOLVING MOVE — 'estimate first, then test', 'look for symmetry', 'use a variable for the unknown', 'enumerate small cases'. This is the teaching that APSMO coaches give in person; the solver lets students practice the same thinking at home.
APSMO problems to practise (Division J + Senior)
Tap any problem to solve it with full step-by-step working.
- Solve with AI →1.GeometryAPSMO Division JEasy
- Solve with AI →2.CombinatoricsAPSMO SeniorMedium
- Solve with AI →3.Digit problemsAPSMO Division JMedium
- Solve with AI →4.Number theoryAPSMO SeniorEasy
- Solve with AI →5.Counting / geometryAPSMO SeniorMedium
Frequently asked questions
What is APSMO and who is it for?+
APSMO (Australasian Problem Solving Mathematical Olympiad) is a school-based maths competition for Years 5-9 students in Australia, New Zealand and participating international schools. It's optional — schools opt in and teachers administer — and it's one of the most respected pathways into the Australian Mathematics Olympiad program.
What's the difference between Division J and Senior?+
Division J (Junior) is for Years 5-6 students; Senior Division is for Years 7-9. Senior problems are harder and cover slightly more advanced topics (basic algebra, coordinate geometry), but both divisions test the same problem-solving skills.
Is APSMO the same as AMC or AMO?+
Different competitions. AMC (Australian Mathematics Competition) is a larger, one-off contest sat by hundreds of thousands of students annually. AMO (Australian Mathematical Olympiad) is a higher-tier invitation-only contest for top AMC / APSMO performers. The progression is: APSMO → AMC → AMO → IMO.
Does the solver teach Olympiad technique, or just give answers?+
Both. Each solution labels the problem-solving move explicitly (e.g. 'estimate first, then test', 'work backwards from the constraint', 'use casework by parity'). Students build the toolbox by seeing the moves applied across many problems.
What if I'm in Year 4 or Year 10 — can I still use it?+
Yes. Year 4 students often find Division J achievable with some coaching; Year 10 students can warm up on Senior problems before moving to AMC or higher. The problem-solving skills generalise well outside the APSMO age range.
Can I paste past APSMO contest problems?+
Yes — paste any past contest problem. The solver doesn't distinguish between Olympiad problems and regular curriculum problems; it picks the appropriate technique based on the problem's structure.
Does Olympiad practice help with HSC or VCE?+
Strongly yes. Olympiad-trained students consistently outperform in HSC Extension 1 / 2 and VCE Specialist because they've built genuine problem-solving fluency — not just curriculum coverage. The 'hard' Extension questions usually look just like Olympiad problems.
Is it free for APSMO students?+
Yes. One guest solve per day without signup; a free account gives 5 daily solves plus Olympiad-style quizzes, problem-solving flashcards and a study planner. Step-by-step working is never paywalled.
Build real problem-solving skill — sign up free
Free account in 10 seconds: 5 daily Olympiad-style solves, problem-solving flashcards, contest-pattern quizzes and a year-long planner. No credit card.
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