How to Build Olympiad Problem-Solving Habits at Home

Most olympiad preparation fails for the same reason: the family buys a book of past papers, the child gets most questions wrong, everyone gets discouraged, and the book goes on a shelf.

Problem solving is a habit, not a syllabus. It is built in short sessions with the right kind of question, and it takes a few months rather than a few weeks. Here is how to build it at home.

Start with the right difficulty

The most common mistake is starting too hard. A child learns nothing from a problem they cannot begin.

Aim for questions where your child can make a start unaided but not always finish — roughly, they should solve about 60% of what they attempt. Below that and they lose heart; above it and they are not being stretched.

If past papers give a 20% success rate, put them away. Work on easier problem sets for two months and come back.

The fifteen-minute session

Long sessions do not suit problem solving. The brain fatigues quickly on unfamiliar reasoning.

A workable shape:

Four sessions a week beats one long weekend session, every time.

Teach the four-step routine

Give your child a fixed procedure so they never face a blank page without a plan.

1. Understand. Read twice. What is given? What is asked? Say it back in your own words.

2. Plan. Have I seen a problem like this? Can I try a smaller version? Can I work backwards? Can I draw it?

3. Do. Carry out the plan, writing each step.

4. Check. Does the answer make sense in size? Does it satisfy the original conditions?

Step 4 is the one children skip and the one that recovers the most marks.

The six strategies that unlock most problems

Rather than teaching topics, teach these approaches. Nearly every olympiad problem yields to one of them.

Try a smaller case. Stuck on "how many diagonals in a 20-sided figure?" Try a square, then a pentagon, then a hexagon. The pattern appears.

Work backwards. For "I did this and got that", start at the answer and reverse each operation.

Draw it. Ratios, journeys, ages and geometry all become easier as a picture.

Look for a pattern. Compute the first three or four cases and look at the differences.

Assume the worst case. Any question with "at least" or "to be certain" is asking about the worst possible arrangement.

Count in two ways. If counting one way is hard, count the opposite and subtract from the total.

Our 15 classic olympiad problems demonstrate each of these on real questions.

What parents should and should not do

Do:

• Ask "what have you tried?" rather than giving a hint immediately
• Let a problem sit unfinished overnight — insight often arrives later
• Praise the attempt and the method, not the correct answer
• Sit and try the problem yourself, visibly, including getting stuck

Do not:

• Solve it for them when they hesitate
• Time every question early on — speed comes later
• Compare with other children
• Treat a wrong answer as a failure rather than information

That last one matters most. In problem solving, a wrong attempt that reveals why it does not work is genuinely productive. Children only believe that if the adults around them act like it is true.

The error notebook

This one habit is worth more than any book.

Keep a notebook with one page per missed problem:

• The problem
• What my child tried
• Where it went wrong
• The idea that would have cracked it

Review it every fortnight. Patterns emerge quickly — "he always forgets the worst case", "she rushes the reading". Those patterns are the actual curriculum for the next month.

A realistic six-month plan

Months 1–2: arithmetic fluency plus easy pattern and logic puzzles. No past papers.

Months 3–4: one strategy per fortnight from the list above, with problems chosen to need that strategy.

Month 5: mixed problems, still untimed. Error notebook reviewed weekly.

Month 6: past papers, timed, one per week, with a full review of every error.

Families who follow roughly this order almost always do better than those who start at month six.

Frequently asked questions

How much time per week is enough? An hour, split into four short sessions, is plenty for Classes 3 to 6. Older or more serious students might do two.

My child gives up after two minutes. What do I do? Lower the difficulty until they experience success, then raise it slowly. Persistence is built by winning, not by being told to persist.

Should I buy a problem book or use free material? Either works. What matters far more is the difficulty level and the review habit, not the source.

Is coaching necessary? Not for the early classes if a parent can sit with the child. It becomes more useful from Class 7, when problems need techniques most parents have not met.

Does this help with school maths? Yes, noticeably. Careful reading, checking answers and working backwards all transfer directly to school exams.

Structured practice, if you want it

Our Maths Olympiad course for Grades 3 to 8 follows this progression — strategies first, past papers last — in small live batches.

Book a free demo class and see how your child approaches an unfamiliar problem.

Cover image: Shixart1985 — CC BY 2.0.