Math Olympiad Books: Best Picks by Level for 2026

Which Book Is Best For Math Olympiad?

No single book is best for every child. The right first book is one your child can solve about half of without help: easy enough to keep going, hard enough to make them think.

Table 1: A quick pick for each level (all titles verified, 11 October 2026).

The word "olympiad" also means different things in different countries. In India, class-wise olympiad guide books for school-level olympiads are mostly past-paper practice; the proof-based Regional Mathematical Olympiad needs the higher-level books further down this list. If you are still deciding which contest suits your child, our overview of math olympiad competitions compares them side by side.

Which Math Olympiad Books Work For Beginners And 4th Grade?

For a beginner in grades 3 to 5, the best math olympiad books are short, puzzle-style problems with full solutions. The aim at this stage is enjoyment and stamina, not technique.

• Beast Academy (Art of Problem Solving). A comic-style math series with practice books for ages 6 to 13, in five levels, per Beast Academy's site. It teaches school topics through harder puzzles, which makes it a gentle bridge into contest thinking.

• Math Olympiad Contest Problems, Volume 1 (MOEMS). 400 Division E problems from the elementary contests of 1979/80 to 1994/95, according to the MOEMS store. Each problem is a short, self-contained puzzle, ideal for one problem a day.

• Math Olympiad Contest Problems, Volume 2 (MOEMS). 375 problems: 200 elementary and 175 middle-school problems from the mid-1990s to 2004/05. It is the natural follow-on once Volume 1 feels comfortable.

• Creative Problem Solving in School Mathematics (MOEMS, second edition). A strategy book rather than a problem collection, organised around ways of attacking problems.

MOEMS runs two divisions, Division E for grades 4 to 6 and Division M for grades 6 to 8, according to its home page. Volumes 3, 4 and 5 continue the series with later contests, so a child who enjoys the first two has years of material ahead.

Which Math Olympiad Books Help In Grades 6 To 8?

From grade 6, the most useful books teach the topics that school covers lightly but contests test heavily: number theory, counting and probability, and clever algebra. This is also the level of the AMC 8 and MATHCOUNTS.

• Prealgebra (Rusczyk, Patrick and Boppana, AoPS, 2011). A full course written in a problem-first style, where each section starts with problems before the explanation. It suits a child who finds school math too easy.

• Introduction to Number Theory (Mathew Crawford, AoPS, 2008). Divisibility, prime numbers, remainders and modular arithmetic, the topic most children have never met in school.

• Introduction to Counting and Probability (David Patrick, AoPS, second edition 2007). Counting principles, permutations, combinations and probability, with many contest-style problems.

• MATHCOUNTS School Handbook (current year). The 2026-27 edition gives registered coaches 250 problems for grades 6 to 8 with answer keys and step-by-step explanations, and it is free for registered coaches and for parents of non-school competitors.

• Mathematical Circles (Russian Experience) (Fomin, Genkin and Itenberg). A problem book from Russian math circles, covering parity, the pigeonhole principle, graphs and invariants. India's Regional Mathematical Olympiad resources page recommends it.

Our existing guides already map these books onto contest timelines, so they are not repeated here: how to prepare for AMC 8 sets out a nine-month plan, and how to prepare for MATHCOUNTS covers the four rounds.

Which Math Olympiad Books Are Right For High School?

High school olympiads (the national rounds that lead toward the IMO) ask for written proofs, so the books shift from "find the answer" to "explain why it must be true". These are the classics most coaches name, and each one is verified below.

Table 2: High school olympiad books, what each covers, and who it suits.

Evan Chen's book page says the geometry book needs no geometry beyond the ability to read proofs, gives hints for every problem and solutions for about a quarter. Wiley's page describes Zeitz's book as a problem-solving approach rather than an exercises approach, drawn from his work coaching olympiad teams.

One book sits outside every level: George Pólya's How to Solve It (Princeton University Press, first published 1945). It is short, has almost no hard problems, and teaches the four-step habit (understand, plan, carry out, look back) that every book above assumes. A curious ten-year-old and a seventeen-year-old get different things from it.

Are Art Of Problem Solving Books Good?

Yes, for the right child. The AoPS books are among the most widely used contest-preparation books in the US, and four of the titles in this guide come from that publisher. They are written problem-first, so your child meets a question before the explanation.

The honest caveat: they are dense. A child who likes to be told the method and then practise it may find the problem-first style frustrating at first. Try one chapter together before buying the full set, and pair each chapter with a few contest problems so the book does not feel like more homework. (We name these books because parents ask about them; they are not affiliated with us.)

In What Order Should Your Child Read Math Olympiad Books?

Read in this order, moving on only when your child can solve about half of a book's problems without help. Skipping ahead is the most common reason children abandon olympiad books.

1. Puzzle stage (grades 3 to 5). Beast Academy at the child's level, alongside How to Solve It read aloud in short pieces.

2. First contest problems (grades 4 to 6). MOEMS Math Olympiad Contest Problems Volume 1, then Volume 2.

3. Strategy (grades 5 to 7). Creative Problem Solving in School Mathematics, then Mathematical Circles.

4. Topic depth (grades 6 to 8). Prealgebra, then Introduction to Number Theory and Introduction to Counting and Probability, with the current MATHCOUNTS School Handbook for mixed practice.

5. Bridge to proofs (grades 8 to 10). The Art of Problem Solving, Volume 1, then The Art and Craft of Problem Solving.

6. Olympiad level (high school). Problem-Solving Strategies, Mathematical Olympiad Challenges and Euclidean Geometry in Mathematical Olympiads, with the Indian RMO books for families on that track.

This is a several-year sequence, not a single summer. For the plan that sits around the books (how many hours, when to start contests, what to do month by month), see how to prepare for a math olympiad.

How Should Your Child Use A Math Olympiad Book?

Use it slowly. One hard problem, attempted honestly for fifteen to twenty minutes, teaches more than ten problems copied from the solutions page.

1. Read the problem twice and restate it. Ask your child to say what is given and what is asked, in their own words.

2. Try small cases. If the problem says "any number", test 1, 2, 3 and 10 first.

3. Write one line before looking anything up. "I tried X and got stuck at Y." This single habit stops the reflex of flipping to the answer after two minutes.

4. Read the solution, then close the book and redo it. If your child cannot reproduce the solution a day later, they read it but did not learn it.

5. Keep a problem log. One sentence per missed problem: what idea they did not see. Reread the log weekly.

The problems below show what this looks like at each level.

Examples Of Math Olympiad Book Problems

These six original problems match the styles found in the books above, from an elementary puzzle to a short high school proof. Every answer was checked twice.

Example 1

I am a two-digit number. My digits add to 11, and I am 27 more than the number with my digits reversed. What number am I?

Call the digits $a$ (tens) and $b$ (ones). Reversing the digits changes the value by:

$$(10a + b) - (10b + a) = 9(a - b) = 27$$

$$a - b = 3$$

$$a + b = 11$$

Adding the two equations gives $2a = 14$, so $a = 7$ and $b = 4$.

Check: $74 - 47 = 27$ and $7 + 4 = 11$.

Final answer: 74.

Example 2

A frog is at the bottom of a 10-metre well. Each day it climbs 3 metres; each night it slips back 2 metres. On which day does it get out?

The tempting answer: the frog gains $3 - 2 = 1$ metre a day, so it needs 10 days.

Test that against the story. At the end of day 7 (after the night's slip) the frog is 7 metres up. On day 8 it climbs 3 metres and reaches the top before night comes, so it never slips again. The "1 metre a day" rule only holds while the frog is still inside the well.

$$7 + 3 = 10$$

Final answer: day 8.

Example 3

What is the remainder when $2^{20}$ is divided by 7?

Look for a repeating pattern in the powers of 2:

$$2^{3} = 8 = 7 + 1$$

So $2^{3}$ leaves remainder 1, and so does every power of $2^{3}$. Now split the exponent:

$$2^{20} = (2^{3})^{6} \times 2^{2}$$

The first part leaves remainder 1, and $2^{2} = 4$.

Check: $2^{20} = 1048576$ and $7 \times 149796 = 1048572$, which is 4 less.

Final answer: 4.

Example 4

How many three-digit numbers have only odd digits?

There are five odd digits: 1, 3, 5, 7, 9. Each of the three places can be any of them, and none of them is 0, so the hundreds digit is never a problem.

$$5 \times 5 \times 5 = 125$$

Final answer: 125.

Example 5

Two fair dice are rolled. What is the probability that the total is 7?

There are $6 \times 6 = 36$ equally likely outcomes. The pairs that total 7 are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1), which is 6 outcomes.

$$\frac{6}{36} = \frac{1}{6}$$

Final answer: $\frac{1}{6}$.

Example 6

Prove that the product of any three consecutive whole numbers is divisible by 6.

Among any three consecutive whole numbers, one is a multiple of 3, because multiples of 3 come every third number. At least one is even, because even numbers come every second number.

So the product has a factor 2 and a factor 3. Since 2 and 3 share no common factor, the product is divisible by $2 \times 3 = 6$.

Check with an example: $4 \times 5 \times 6 = 120 = 6 \times 20$.

Final answer: proved for every set of three consecutive whole numbers.

What Signs Show Your Child Is Ready For The Next Book?

Your child is ready to move up a rung when the current book has stopped surprising them. Watch for these signs over two or three weeks:

• They solve about half the problems without hints, and the misses are near-misses rather than blank pages.

• They explain their method out loud without looking at the page.

• They start inventing variations, such as "what if the well were 20 metres deep?"

• They finish problems faster but still enjoy them; boredom, not difficulty, is the signal to move on.

The reverse signs matter too. A child who reads solutions after two minutes, or who says "I am just not an olympiad person", is on a book that is too hard. Step back a rung; nothing is lost. If you want help reading these signals more broadly, the characteristics of gifted math students guide covers what strong problem solvers tend to do.

Where Do Families Go Wrong With Olympiad Books?

Most problems with olympiad books come from the choice of book or the way it is used, not from the child. These are the four we see most.

Mistake 1: Buying The Famous Book First

Where it slips in: A parent reads that Engel's book is the classic and buys it for a twelve-year-old.

Don't do this: Do not start with a proof-based olympiad text before your child has worked through contest-problem collections.

The correct way: Start one rung lower than you think. The pattern we see most often is a child who stops reading a hard book after chapter one and then decides olympiad math "is not for them"; the right book at the right time prevents that.

Mistake 2: Reading Solutions Too Soon

Where it slips in: The rusher gives each problem two minutes, then flips to the back.

Don't do this: Do not treat the solutions as part of the reading.

The correct way: Set a minimum: fifteen minutes of honest attempt and one written line of what was tried. The struggle is where the learning happens, which is the idea behind productive struggle in math.

Mistake 3: Collecting Books Instead Of Finishing One

Where it slips in: A shelf of five half-started books, each abandoned at the first hard chapter.

Don't do this: Do not buy the next book because the current one feels slow.

The correct way: Finish most of one book before buying another. Depth in one book beats a taste of five.

Mistake 4: Using Unofficial PDFs

Where it slips in: Searching "math olympiad books for beginners pdf" leads to scanned copies of uncertain origin.

Don't do this: Do not rely on pirated scans; pages go missing and solutions are often cut.

The correct way: Use legitimate free material first. The real-world version: the MATHCOUNTS School Handbook is free for registered coaches and for parents of non-school competitors, and the contest bodies sell past problems at modest prices.

Example 2 is worth a final word. Children almost always reach for the "net 1 metre a day" rule with complete confidence, and it is the habit of testing an answer against the story, not the trick itself, that carries into every book on this list.

When Should You Get Outside Help?

Many children work through olympiad books happily on their own. Consider outside help when:

• Your child has stalled on the same book for two months and the problem log shows the same missing idea again and again.

• The books expose a gap in school topics (fractions, ratios, algebra basics) that keeps blocking progress.

• Your child wants to aim for a specific national olympiad and you are unsure how to pace several years of reading.

• Books have started to cause tears or avoidance rather than curiosity.

In the last case, slow down before adding anything. A break of a few weeks often does more than a tutor.

How Does Bhanzu Support Children Reading Olympiad Books?

Bhanzu teaches live online classes from UKG to Grade 10, built around why a method works before how to use it. That is the same habit olympiad books demand: a child who understands why a counting principle works can apply it to a problem they have never seen.

Trainers start each child at their real level through a Level 0 diagnostic, which often shows exactly which rung of the ladder a child is on and which school topic is holding them back. Classes are not olympiad coaching and do not work through these books chapter by chapter.

Fit signal: this fits a child who enjoys reasoning and would benefit from a teacher who builds understanding alongside their reading. It is not the right fit if you want a dedicated proof-writing coach for national olympiad selection.

Where Can Your Child Get Extra Help With Olympiad Math?

If your child wants structured challenge beyond the books, these programs match different stages:

• Math enrichment programs for puzzle-style problem solving alongside school.

• Advanced math classes for kids online for children working beyond their grade.

• Middle school math tutor support for the grades 6 to 8 topic books.

• High school math tutor support for students moving toward proof-based olympiads.

Wrapping Up

• The best math olympiad books match your child's current level, not their age or the book's fame.

• MOEMS contest volumes and Beast Academy suit grades 3 to 6; AoPS topic books and the MATHCOUNTS Handbook suit grades 6 to 8.

• Engel, Zeitz, Andreescu and Gelca, and Evan Chen belong to the high school, proof-based stage.

• Move up when your child solves about half a book's problems without help.

• Fifteen minutes of honest effort before reading a solution matters more than which book you choose.

What Should You Do This Week?

Pick one book from your child's current rung, choose three problems from its first chapter, and try them together without the solutions for fifteen minutes each. Note which one made them most curious; that is where to start. If you would like a trainer to find your child's level first, book a free demo class with a Bhanzu trainer.

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