Olympiad Program
For students working toward national and international Olympiads, from their first proof onwards.
Qualifier → National → InternationalSmall live batches
View syllabusLIMINAL MATH
by Liminal Initiative
Click, tap or press any key to skip
Where young mathematicianslearn math together.
Register for Chapter ZeroNo prep neededExplore careers in mathematics
LIMINAL7-day streakAR
LESSON 2.2 · SEE IT FIRSTWhy odd numbers build squares
1+ 3+ 5+ 7+ 9= 1 = 12Layer 1 of 5
Live classes and video lectures.
Start from the foundations and learn to think like a mathematician. Live and recorded lectures by mentors trained at institutions like CMI, taught through the Socratic method so you learn to reason for yourself from day one.
Classroom
n + 1 objects, n boxes.
⇒ some box holds at least two.
Among any 13 people, two share a birth month.
LIVELiveRecorded
LECTURE 4 · PIGEONHOLE PRINCIPLE
1State the principle
2Prove it by contradiction
3Spot the “boxes” in new problems
Socratic prompt: what if every box held at most one object?Conceptual videos
Sharpen your skills.
Every lecture comes with problems that move from routine to genuinely challenging. Work through them at your own pace, get detailed solutions, try to take forward your own approach, and revisit the topics where you need it most.
Practice
YOUR SKILLS140 XP160 XPNumber theory62%Algebra48%Combinatorics35%Geometry41%
NUMBER THEORY · LEVEL 3 · Q 4 OF 10How many positive divisors does 360 have?
360 = 2³ · 3² · 5Clean factorisation.
3 · 2 · 1 = 6Not quite. Each prime can appear 0 to k times.
(3+1)(2+1)(1+1) = 24Correct. 24 divisors.
Start by breaking 360 into primes.Try 12 = 2² · 3. List its divisors. How many choices for the power of 2?You fixed it yourself. That’s the skill we’re building.
Mock tests.
Sit full-length mock exams modelled on IOQM and other major entrance papers, under real time limits. Every solution you submit gets detailed, critical feedback from our mentors, pointing out gaps in your reasoning and showing how to write a stronger argument.
Mock portal
IOQM Mock 03 · Paper A01:12:44Submit
QUESTIONS
1234567891011121314151617181920
AnsweredFlagged
QUESTION 7 · 4 MARKS
How many positive integers n ≤ 100 have exactly three positive divisors?
Answer (0–999)4
Flag for reviewClear
Problem of the day.
A new problem every day, picked to stretch how you think rather than test what you've memorised. Try it, share your approach, and see how others in the community cracked it differently.
Problem of the Day
The Complement MethodMON 19 OCTMedium
The Complement Method Problem
How many ways are there of using diagonals to divide a regular -sided polygon into triangles such that at least one side of each triangle is a side of the original polygon and that each vertex of each triangle is a vertex of the original polygon?
Limi: Missed a day? Every past problem, with its full solution, waits in your archive once you log in.
Community and blog.
Join a worldwide community of students who take mathematics seriously. Discuss hard problems, share ideas, and learn from peers and mentors. Our blog covers everything from beautiful mathematical ideas to the careers mathematics can lead to.
Communitym/ALL
IMIshaan M.m/ProblemOfTheDay · Approach 3 of 36
Let G be where two medians cross. Compare the ratios AG : GD and BG : GE — both come out 2 : 1, so the third median must pass through G too.
▲ 187 repliesShare
ZM
Zara M. · Class 11I went with coordinates. ugly, but it works…
BLOG5 min readWhy odd numbers always add up to squaresAlso: what does a mathematician actually do all day?
PEER CIRCLEAlgebra · Batch BARPKSNVJIK6 students, 1 mentor, a lot of arguing.
SAT · 11 AM · SEMINARWhat is a Lean proof? Bring questions.
MSMentor · CMI“I don’t mind if you get it wrong. I mind if you can’t tell me why.”
Why us?
A training model refined over years of teaching. It shapes not just what students learn, but how they think, study and practise.
No cliff edgeFrom school maths into abstraction and proof, at a pace that builds real confidence.
Habits that lastPatience with hard problems, precision in reasoning, curiosity to keep asking why.
For parentsA structured, accountable journey with regular updates on how your child is growing.
For studentsMaths as a way of thinking that is entirely your own, not a set of rules to follow.
AFTER SIX MONTHSThe habits that outlast the exam
Patience12 → 26 minTime on a hard problem before asking for a hint
Precision9 → 3Careless errors per 20-question test
Curiosity3 → 11Extra problems attempted beyond the set, per week
Sample progress from a Class 11 student, shared with parents every month. The tick marks where they started.
From Olympiad problems to university mathematics
Olympiad or university entrance, the skill is the same: breaking open a problem you’ve never seen.
UG Mathematics Entrance
For students preparing for university entrance exams in mathematics.
CMIISIForeign universities
View syllabusScholarships up to 100% through Chapter Zero.
Solve problems. Don’t just study solutions.
Real understanding comes from attempting, failing, and finding your own way through.
Ask
Every lesson begins with a question, not an answer. Students express their thought process.
Reason
You work toward an answer yourself, testing ideas and following where they lead.
Challenge
Mentors respond with sharper questions that expose gaps, assumptions, and hidden flaws.
Understand
You reach the idea on your own, so it becomes truly yours and stays with you.
In their words.
Students and parents on what changed.
Liminal has completely changed the way I look at mathematics. Our teachers push us to think deeper and see math as discovery, not memorization. Even difficult topics now feel like fun puzzles waiting to be solved.
Liminal’s classes and carefully curated problem sets have helped me understand Olympiad mathematics in a much more structured way. The detailed solutions, practice tests, and discussion group have improved both my problem-solving skills and confidence.
FEATURED ACHIEVEMENT · IOQM 202682/100
“Liminal has really helped me change the way I solve math problems. Earlier, I used to try random approaches, but now I’m much more organized and focus on what’s given and what I need to prove. The problem sets and explanations have also helped me a lot with Olympiad problems and given me more confidence.”
Achudan RGrade 10In mathematics the art of proposing a question must be held of higher value than solving it.
Questions, answered.
The short version. Ask us anything else.
An online maths test that looks at how you think, not what you’ve memorised.
ARMSKPStill have a question?A real person replies, usually within a day.Email us
Chapter ZeroNo preparation neededRegister for Chapter Zero