To score well consistently, you must build mastery across four core pillars:

1. Algebra

• Inequalities
• Functional equations
• Polynomials
• Sequences & transformations
• Structural manipulation

2. Number Theory

• Divisibility
• Modular arithmetic
• Diophantine equations
• Prime factor structures
• Orders and residues

3. Geometry

• Classical Euclidean geometry
• Transformations
• Similarity & homothety
• Circles, inversion (advanced stage)
• Pure logical deduction

4. Combinatorics

• Counting principles
• Pigeonhole principle
• Graph reasoning
• Invariants
• Constructive logic

A weakness in any one pillar limits your overall score.

How to Score Well in Math Olympiads: The Right Way

1. Follow Structured Learning — Not Random Problem Solving

Randomly solving Olympiad problems is inefficient and frustrating.

Instead:

• Learn one topic at a time
• Break it into subtopics
• Study standard ideas, not just solutions

For example:

Inequalities → Symmetry → Homogenization → Normalization → Equality cases

Structure builds intuition. Intuition builds confidence.

2. Go Deep Into Every Topic and Subtopic

Superficial learning fails in Olympiads.

You must ask:

• Why does this method work?
• When does it fail?
• How can it be modified?

Depth transforms problems from “impossible” to “recognizable.”

3. Spend More Time With Problems — Stay Longer

This is the most ignored yet most powerful rule.

Do not:

• Read a problem for 5 minutes
• Panic
• Jump to the solution

Instead:

• Sit with the problem
• Try small cases
• Rewrite conditions
• Look for symmetry
• Attempt partial results

Olympiad ability grows in silence and struggle, not speed.

4. Use Hints, Not Full Solutions

When stuck:

• Take one small hint
• Try again
• Think afresh

Only after exhausting yourself should you read the full solution.

Reading solutions too early kills creative growth.

5. Upgrade Difficulty Gradually

Confidence matters.

Start with:

• Easier Olympiad-style problems
  Then:
• Medium difficulty
  Finally:
• National / IMO-level problems

Sudden jumps discourage learning. Gradual difficulty builds momentum.

6. Solve Extensively — But Reflectively

Quantity alone is useless.

After every problem, ask:

• What was the key idea?
• Can this idea be reused?
• Was there an alternative approach?

Reflection converts problems into long-term assets.

7. Build Confidence Through Small Wins

Olympiad preparation is a long journey.

Celebrate:

• Solving one hard problem
• Discovering one new idea
• Understanding one elegant solution

Confidence fuels persistence—and persistence wins Olympiads.

The Real Secret of Olympiad Success

There is no shortcut. No magic formula.

But there is a method:

Structured learning + deep understanding + patient problem solving + gradual difficulty upgrade

Olympiad Mathematics is not about being gifted.
It is about becoming mathematically mature.

Those who stay longer with problems, think deeper, and respect the learning process—eventually succeed.

Final Thought

If Olympiad Mathematics feels difficult, that’s a good sign.
It means the subject is stretching your thinking beyond routine learning.

Stay with the struggle.
Trust the process.
And build mathematics—not just scores.