Peru · Maths olympiads · Primaria to 5° de secundaria
Maths olympiad coaching in Peru
Peru takes olympiad mathematics seriously: the national school olympiad drew more than 1.7 million secundaria students in 2026, and Peru has sent teams to the International Mathematical Olympiad since 1987. This page maps the contests a student in Peru can enter, explains how the national teams are chosen, shows Peru's recent IMO results, and teaches one olympiad idea properly, with a proof and a Python check.
Teaching live online since 2020 · 10,000+ students worldwide · original problems, written by us
The answer first
Modern Age Coders gives maths olympiad coaching to students in Peru: live online classes taught in English by mentors based in India, for children from primaria up to 5° de secundaria. Students learn the ideas olympiads reward, such as invariants, counting, number theory and written proof, with problems we write ourselves, never an organiser's. Coaching suits students heading for ONEM, the Canguro Matemático or the national selection exams, in a group of fifteen to twenty or one to one, at an hour that suits the family in Peru time.
Olympiad courses
Three courses for olympiad students in Peru
One for younger contest students, one that runs from school competitions to proof, and one that turns the same reasoning into code.
For students who already like mathematics and want more than school gives them. It is not catch-up tutoring: the problems are harder, slower and stranger than classwork, and that is the point.
Curious younger students
Children in upper primaria who finish class exercises fast and enjoy puzzles. They meet contest problems that need an idea rather than a formula, and learn to try small cases before guessing.
ONEM and Canguro regulars
Secundaria students who already compete through their school and want to go further than the first round. They need proof, not just answers, because the later ONEM stages ask for full solutions.
Selection-exam candidates
Strong students considering the national selection exams for international teams. Those exams give a few hard problems and hours to solve them, which calls for stamina and clear writing as much as knowledge.
Coaching is in English. For a student in an English-medium or IB school that is natural; for a student whose contests are in Spanish it adds practice in a second language, while the ideas stay the same. We are honest that national contests in Peru are set in Spanish, so we also make sure students can read a statement in Spanish precisely. If you would like the Spanish-language overview of maths taught in English, read our page on a profesor de matemáticas en inglés; for a 12 year old weighing ONEM against the computing olympiad, our Spanish page on programming at 12 compares them.
Olympiads in Peru
Which maths olympiads can students in Peru enter?
Several, run by different organisers, with different ages and entry rules. The table lists the main ones with their 2026 dates as each organiser published them; check the organiser's own page for 2027, because none of the 2027 dates below are published yet.
Maths and computing olympiads open to students in Peru, 2026
Olympiad
Organiser
Who
2026 dates
How students enter
ONEM, national school maths olympiad
MINEDU, with Aceros Arequipa
1° to 5° de secundaria, three levels
School stage 8 July; national stage 11 October
Through the school
Canguro Matemático
Binaria Matemática
3° de primaria to 5° de secundaria
First stage 16 and 17 April
Through the school; no individual entry
UNI-Olimpiada Nacional de Matemática
Universidad Nacional de Ingeniería
4° and 5° de secundaria, plus early-year university students
Phases 3 May and 31 May; final 28 June
Registration 15 March to 15 April
Selection exams for Ibero 2026
Comisión de Olimpiadas, Sociedad Matemática Peruana
Born 2008 to 2013
Two exams, 28 and 29 August
School tutor or, failing that, a parent
Selection for PAGMO 2026 (girls)
Comisión de Olimpiadas, Sociedad Matemática Peruana
Girls born 2010 to 2014
Preliminary 28 September; finals 2 and 3 October
School tutor or a parent; free
OPI, computing olympiad
UTEC
All secundaria students, free
Final 11 April
Registration on the OPI site
Sources, all read on 9 November 2026: UGEL 06 (MINEDU) Oficio Múltiple 00164-2026 and El Peruano, 11 October 2026 (ONEM); canmatperu.com, the site the Kangaroo association lists for Peru (Canguro); admision.uni.edu.pe (UNI-Olimpiada, held for UNI's 150th anniversary); selectivos-peru.blogspot.com, the national olympiad site linked from the IMO's Peru page (selection exams); opi.utec.edu.pe (OPI). We are not connected with any of these organisers.
The school route: ONEM and Canguro
ONEM is the largest. El Peruano reported that ONEM 2026 drew more than 1.7 million secundaria students from the first stage, and that 237 reached the national stage at the Huampaní centre on 11 October 2026. It runs from the school through UGEL and regional stages to the national final, at three levels by grade.
The ONEM bases add a detail coaches should notice: from the regional stage onwards, the papers move step by step towards the standards of international competitions. The first round rewards accuracy; the later rounds reward proof.
The open route: selection exams
The national teams for the Ibero-American olympiad and the girls' Pan-American olympiad, PAGMO, are chosen by the Comisión de Olimpiadas of the Sociedad Matemática Peruana, which the IMO lists as Peru's official contact. Its rules let a school tutor, or a parent where the school does not, register a student.
Canguro, by contrast, is school-only: its Peru site says the first stage runs inside each school, so individual entry is not possible. If your child's school does not take part in a contest, ask the school first.
National teams
How are Peru's olympiad teams chosen?
By exams that look nothing like school tests: a few problems, several hours, full written solutions. The commission's own 2026 announcements describe the process for two teams.
Selection in 2026 for two international teams, as published by the commission
Team
Competition
Who may sit
Selection format
Team size
Ibero 2026
41st Ibero-American Mathematical Olympiad, Buenos Aires, 6 to 13 September 2026
Students born 1 January 2008 to 31 December 2013; school leavers allowed
Two in-person exams, each 3 problems in 4 hours
4 students
PAGMO 2026
Pan-American Girls' Mathematical Olympiad, Bucaramanga, 18 to 24 October 2026
Secundaria girls born 1 January 2010 to 31 December 2014
A preliminary of 4 problems in 3 hours, then two final exams
4 students
Source: Comisión de Olimpiadas de la Sociedad Matemática Peruana, announcements of 24 August and 22 September 2026 on selectivos-peru.blogspot.com, read on 9 November 2026. Both competitions limit a student to representing their country at most twice. The PAGMO preliminary could be sat online only by girls at schools outside Lima Metropolitana and Callao.
What four hours for three problems means
By our division that is eighty minutes a problem, and a single complete solution can be worth more than three half-ideas. Students who have only done timed multiple choice tend to rush, find a pattern, and write the pattern down as if it were a proof.
Coaching for this format is mostly about patience: trying small cases on paper, naming what stays the same, writing the argument so a stranger could check it, and knowing when to switch problems.
What we do and do not do
We teach the mathematics and the habits these exams reward, in English, with our own problems. We do not run selection exams, see papers in advance, or have any role in choosing teams, and we make no promise about any result.
Students who reach the later stages often enjoy programming as well, and Peru runs a separate computing olympiad for them. Our coding olympiad track covers that side.
Peru at the IMO
How has Peru done at the International Mathematical Olympiad?
Consistently well for a country of its size. The IMO's own records show Peru first took part in 1987 and has taken part 33 times, winning 7 gold, 48 silver and 67 bronze medals and 36 honourable mentions.
Peru's team at the IMO, 2022 to 2026
Year
Team rank
Team points
Gold
Silver
Bronze
Honourable mentions
2026
27
137
0
3
2
1
2025
27
158
2
1
2
1
2024
29
122
0
2
3
1
2023
32
133
0
2
3
0
2022
19
173
0
3
3
0
Source: International Mathematical Olympiad, official site, Peru country page and Peru team results, read on 9 November 2026. All-time totals are as the IMO prints them; the sum of 122 medals is our own addition of its three medal counts. An empty medal cell on the IMO site is shown here as 0.
Two things in that table matter to a family. First, 2025 brought two gold medals, so the very top of the competition is within reach of students trained in Peru. Second, the points vary a lot between years, from 122 to 173, because six problems set by an international jury suit some teams better than others. A medal is not a guaranteed outcome of any coaching, and anyone promising one is selling something.
IMO problems are published in dozens of languages, Spanish and English among them, so language is not the barrier. Depth is. A student who has learnt to prove things in one language can prove them in another; a student who has learnt only to recognise question types cannot prove them in either.
An olympiad idea
What is an invariant? A lesson with lamps, a proof and Python
An invariant is something a move can never change. It is one of the first ideas we teach olympiad students, because it turns "I tried for an hour and could not do it" into "it cannot be done, and here is why". The problem below is ours.
The problem
Seven lamps stand in a row, all switched on. A move consists of choosing exactly two lamps and flipping both: on becomes off, off becomes on. Can you reach a position where all seven lamps are off?
Students start by trying, which is right. After a few minutes they notice that however they play, some lamp is always left on. Noticing is not proving, though.
The proof
Look at the number of lamps that are on. A move changes it by +2, 0 or −2, so its parity never changes. It starts at 7, an odd number, so it is odd after every move. All lamps off would mean 0 lamps on, an even number, so no sequence of moves can reach it.
Three sentences, and they work for seven lamps or seven thousand. That is the strength of an invariant: it does not care how many moves you try.
Version 1: search every pattern reachable by flipping twoPython
from itertools import combinations
N = 7 # seven lamps, all switched on
start = (1,) * N
def reachable(k):
# every pattern we can reach if each move switches exactly k lamps
seen = {start}
todo = [start]
while todo:
lamps = todo.pop()
for group in combinations(range(N), k):
new = list(lamps)
for i in group:
new[i] = 1 - new[i]
new = tuple(new)
if new not in seen:
seen.add(new)
todo.append(new)
return seen
two = reachable(2)
print("Patterns reachable, switching 2:", len(two))
print("All off reachable?", (0,) * N in two)
print("Lamps on, in every reachable pattern:", sorted({sum(p) for p in two}))
It prints Patterns reachable, switching 2: 64, All off reachable? False and Lamps on, in every reachable pattern: [1, 3, 5, 7]. Exactly half of the 128 possible patterns, and only those with an odd number of lamps on.
Version 2: change the rule to flipping threePython
three = reachable(3)
print("Patterns reachable, switching 3:", len(three))
print("All off reachable?", (0,) * N in three)
Run after Version 1, it prints Patterns reachable, switching 3: 128 and All off reachable? True. A move of three changes the count by an odd number, so parity is no longer kept, and every pattern can be reached.
We use the program to check the proof, never to replace it. The search visits all 128 patterns of seven lamps in a blink, but for a thousand lamps there are more patterns than atoms in the observable universe and no computer could list them. The parity argument covers every size at once. In an olympiad paper, the search would earn nothing and the proof would earn everything; in a classroom, the search is how a student learns to trust the proof.
Version 2 teaches the second half of the idea: an invariant belongs to a rule, not to a puzzle. Change the move and the invariant may vanish. Good olympiad students test their invariant against the exact wording of the problem before they rely on it.
Practice set
Three invariant problems to try (ours, with answers)
All three problems were written by us for this page; none is taken from ONEM, Canguro or any other contest. Each answer was checked by an exhaustive search in Python, and each has a short proof that does not need a computer.
Differences on a board. The numbers 1 to 10 are written on a board. A move erases two numbers and writes their difference (larger minus smaller). After nine moves one number is left. Can it be 0?
Odd handshakes. At a meeting of five students, could every student shake hands with an odd number of the others? (Two people shake hands at most once.)
Beetles on a grid. A 3 by 3 grid has a beetle on each of its nine squares. At a whistle every beetle moves to a square sharing a side with its own. Must some square end up empty?
Answers
1. No. The sum 1 + 2 + ... + 10 = 55 is odd, and replacing a and b with their difference keeps the parity of the total, because a + b and a − b are both even or both odd. The last number is odd. Our search printed P1 possible last numbers: [1, 3, 5, 7, 9] zero? False.
2. No. Each handshake adds 2 to the total of everyone's counts, so that total is even; five odd numbers add up to an odd number. Our search over all 1,024 ways to shake hands printed P2 graphs with every degree odd: 0.
Answer 3, and why colouring helps
3. Yes. Colour the grid like a chessboard: five squares of one colour, four of the other. Every beetle changes colour when it moves, so the five beetles on the first colour all land on the four squares of the second. Two must share, and a square is left empty.
Our search over every possible set of moves printed P3 ways to leave no square empty: 0. Colouring is an invariant in disguise: it names what a move always does, here "change colour", and counts what that forces.
Thinking, not copying
Will coaching teach my child to think, or just to recognise tricks?
To think. Tricks run out on the first unfamiliar problem; reasoning does not. We teach students to explore, conjecture, prove and write, in that order.
Small cases first
Before anything clever, try two lamps, three lamps, four. Patterns found by hand are the raw material of every proof, and they are found faster than students expect.
Written proof
Every solution is written in full sentences that another student could check. In English, which is good practice for the many students heading to universities where proofs are written that way.
No AI answers
Olympiads test the student, so coaching does too. Peru's own computing olympiad, OPI, run by UTEC and free for all secundaria students, bans generative AI for solving problems in its 2025 rules, and we work the same way.
Children under 18 do not use adult AI chatbot accounts in our classes; tools such as Claude are for adults only, and ChatGPT needs a parent's permission under 18. Our problems come from our mentors, and organisers' past papers stay on the organisers' own sites, where students can read them as the organisers intend.
Lima times
When would coaching happen in Peru time?
At whatever hour your family picks. Peru stays at UTC minus 5 through the whole year and India at UTC plus 5:30, so India runs 10 hours 30 minutes ahead on every date. The rows show a few conversions; they are not a schedule.
Converting Peru time to India time
Peru time
India time
When a student might use it
07:30
18:00
A problem session before school
09:00
19:30
A long Saturday proof workshop
13:00
23:30
A lunchtime check of written solutions
17:30
04:00, next day
After school, one to one
19:30
06:00, next day
An evening mock with three problems
Source: IANA time zone database (America/Lima, UTC minus 5, no summer time since 1994; Asia/Kolkata, UTC plus 5:30) and INACAL's official Peru time, checked on 8 November 2026. The conversions are our own.
The selection exams described above run for three or four hours. Before them we can arrange a long one-to-one session at the same Lima hour as the exam, so the student practises sustained work at the time of day it will happen. Neither country moves its clocks, so the hour you agree in April is still the hour in August.
Stages
From puzzles to proofs: our olympiad stages
These stages are ours. They are not contest levels and they promise no result; they tell us what to teach next and tell parents how far a student has come.
Olympiad stages (ours)
Stage
Typical school years
The student can
Contest it prepares for
1. Explorer
3° to 6° de primaria
Try small cases and spot a pattern
Canguro, early levels
2. Counter
1° and 2° de secundaria
Count cases without missing or repeating any
Canguro, ONEM Nivel 1
3. Explainer
2° to 4° de secundaria
Say why an answer is right, not only what it is
ONEM school and UGEL stages
4. Prover
3° to 5° de secundaria
Write a complete proof, including impossibility
ONEM regional and national stages
5. Finisher
4° and 5° de secundaria
Hold one problem for an hour and write it cleanly
National selection exams
6. Specialist
Final school years
Choose tools across number theory, geometry, combinatorics and algebra
International-style papers
For parents
A student can move between stages quickly or slowly; what matters is that each stage is secure before the next.
Our notes after class describe problems attempted and ideas used, not just scores.
For students
When you are stuck, ask what a move cannot change.
A pattern in ten cases is a guess. A reason is a proof.
More courses
Nine more courses for strong mathematicians in Peru
All live and in English, with the same mentor each week, in a group or one to one.
I
Younger problem solvers
Ages 8 to 13
MAO / YOUNG / 01
AMC 8 preparation
An international contest for grades 5 to 8, good training for Canguro.
Any day, any time, flexible: choose a batch, or for a very personalised plan choose 1-on-1 at the hour that suits your family.
Mornings in Peru
Evening in India, an easy hour for a long problem session.
After school
Later Lima hours work as well; name the time and we find the mentor.
One to one
For a student preparing a selection exam on a fixed date.
Problems we write
Fresh problems each week, so nothing has been seen before.
Solutions read aloud
Students explain their proof; the mentor asks where it could break.
Written feedback
Every proof comes back with the gap marked, not just a score.
Spanish statements too
Practice reading problems in Spanish exactly, for national contests.
Age-matched groups
Primaria explorers and secundaria provers never share a class.
One mentor
The same person each week, who knows the student's habits.
Student work
Where mathematics leads in code
Many of our strongest olympiad students also build programs, and their projects often start from a mathematical idea. Here are a few; the student labs page shows more.
AI and ML
NutriLife
An AI nutrition coach that reads what you eat and works you toward a target.
A weather forecasting site with live conditions for any location.
by Krish
Fees
Fees for olympiad coaching from Peru
We price in US dollars and take payment by card. Your bank converts every payment into soles at its rate for the day, so the amount shown on your statement can shift slightly from month to month.
Free first class
Free
no card required
A first class at no cost
Two problems and a conversation about how your child thinks
Parents and students in their own words, from Google, unedited.
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Questions from Peru
Maths olympiad coaching in Peru: questions and answers
Are the classes in Spanish?
No. All coaching is live, online and in English. Mentors speak clearly and at the student's pace, and they write every key term on screen. Because national contests in Peru are in Spanish, we also practise reading problems in Spanish carefully, but the teaching itself is in English.
Can my child enter ONEM or the Canguro through you?
No. ONEM and the Canguro Matemático are entered through the school; the Canguro site says individual entry is not possible. We are not connected with MINEDU, Aceros Arequipa or Binaria Matemática. We prepare students for the mathematics; the school handles entry.
How does a student get into Peru's international teams?
Through selection exams run by the Comisión de Olimpiadas of the Sociedad Matemática Peruana. In 2026 the Ibero team was chosen from two exams of three problems in four hours each, and a school tutor or a parent could register a student. Check the commission's site for each year's rules.
Do you use past ONEM or Canguro problems?
No. Every problem we teach with is written by our mentors. Organisers publish their own past papers on their own sites, and students are welcome to read them there; we do not copy or reproduce them.
What age should my child start?
Around 8 to 10 for puzzle-style contests such as the early Canguro levels, which start in 3° de primaria. Proof-based coaching suits most students from about 12 or 13. A strong student can start at any point; the stages table shows where they would begin.
When would classes be in Peru time?
Any day, any time, flexible: choose a batch, or for a very personalised plan choose 1-on-1 at the hour that suits your family. Peru is on UTC minus 5 all year and India on UTC plus 5:30, so 09:00 in Lima is 19:30 in India.
Can you promise a medal?
No, and nobody honestly can. Results depend on the student, the year's problems and the other competitors. Peru's IMO team points ranged from 122 to 173 between 2022 and 2026. What we promise is careful teaching of the ideas that olympiads reward.
Does coding help with olympiad maths?
It helps with checking, as the lamps lesson shows, and it opens the computing olympiad, OPI, which UTEC runs free for secundaria students. It never replaces proof. Students who enjoy both often take our problem-solving and algorithms course alongside olympiad maths.
Are you connected with any university or olympiad body?
No. We are an independent online school with mentors in India, not connected with MINEDU, UNI, PUCP, UTEC, the Sociedad Matemática Peruana or the IMO. Students who finish a course receive our own certificate of completion, not a contest award.
How are fees paid?
By card, in US dollars; your bank converts the charge into soles, so the figure on your statement can vary a little between months. The first class is free, and booking it needs no card.
In the free class your child works on two of our problems with a mentor, one to try and one to explain. The mentor watches how they explore and how they argue, then suggests a stage, a course, and whether group or one-to-one coaching would suit them.
Before booking, you may like How we teach, which shows a class from the inside, and the full course list with each course's outline.
Every class is live over video with a mentor in India, and in English. WhatsApp us in English for the fastest reply.
Want a class sooner? Book a priority demo
A priority demo is a full class of about 45 to 60 minutes. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.
