COMC guide: the Canadian Open Mathematics Challenge, 2026
The Canadian Open Mathematics Challenge is the Canadian Mathematical Society's national open contest: one paper of twelve questions, two and a half hours, no calculators, written in the fall by students of any grade. It is also the first gate on the road the CMS describes from the COMC to the Canadian Mathematical Olympiad and, for a very few, to Math Team Canada. In 2026 the CMS changed how the COMC is run: two new divisions, a fixed writing window for the one that leads to the olympiad, questions delivered separately from the answer booklets, and no more Repêchage. This guide is built from the CMS's own 2026 COMC pages. It sets out the dates, every change, the Competitive window converted for each province, how the 80 points are marked, six practice problems of ours and what to do now that 2026 registration has closed.
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The essentials
The COMC (Canadian Open Mathematics Challenge) is the Canadian Mathematical Society's open national math contest: 12 questions in 150 minutes, scored out of 80, on paper and without calculators, written on Thursday, October 29, 2026 in Canada. Top Competitive Division writers can be invited to the Canadian Mathematical Olympiad. Modern Age Coders prepares students live online, in a batch or one to one, in its competition mathematics course.
Where COMC preparation lives
Three courses behind our COMC classes
The competition course carries the olympiad-style problem solving the COMC rewards. The Waterloo contests course builds the written-solution habit on CEMC papers. The high school course secures the curriculum the CMS says most questions are built on.
Every row below comes from the Canadian Mathematical Society's 2026 COMC pages, read on 22 October 2026, which was also the last day the CMS took registrations for this year.
The Canadian Open Mathematics Challenge, 2026, as published by the CMS (read 22 October 2026)
Question
What the CMS says
When
Thursday, October 29, 2026 in Canada and the Americas; Friday, October 30, 2026 elsewhere.
Registration
The CMS set Thursday, October 22, 2026 as the last day to register, with all new orders delivered as PDF files. 2026 registration has now closed.
Who may write
"The COMC is open to students in all locations, at all grade levels." Its competitions table lists it for Grade 12 or under and recommends it for Grades 8 and up.
Official participants
Under 19 as of June 30 of the year, attending school full-time since September 15, and supervised in conditions the CMS approves.
Length
"The competition lasts 150 minutes and consists of 12 questions."
Format
On paper, in the presence of a qualified proctor, normally a teacher at the student's school.
Tools
"No mobile phones, calculators or other electronic devices are permitted." Compasses and protractors are allowed.
Languages
English and French.
Marking
By teams of trained markers at partner universities; top scores are reviewed by a senior mathematician.
Results
Preliminary scores generally in mid-December; final results typically in mid-January.
If the school is not taking part
Registration is normally done by teachers through the CMS portal. For students whose school is not participating, the CMS runs a limited number of places at Open Writing Centres at partner universities, mostly in person.
The CMS also suggests contacting other schools in the area to ask whether they will accept a student from elsewhere for the day.
Why a tutoring company cannot proctor
The CMS requires a Qualified Proctor for official results: someone with a current provincial or government teaching certificate who is not related to any of the students.
Its eligibility page says tutoring and enrichment centres may be run as unofficial unless they arrange such a proctor. We are a teaching company, so our students write at their schools or at an Open Writing Centre, never with us.
Sources: CMS, COMC 2026, its Eligibility page and its FAQs, read 22 October 2026. Modern Age Coders has no connection with the Canadian Mathematical Society.
What changed in 2026
The COMC 2026 changes, one by one
The CMS published a Changes page addressed to teachers, parents and students. These are the changes it lists, in its own terms, with what each means for a student in Canada.
Changes to the COMC from 2026, from the CMS Changes page and COMC home page (read 22 October 2026)
Change
What the CMS says
What it means for a student in Canada
New division names
The Canadian and International divisions are replaced by a Competitive Division and a Global Division
The word "Canadian" no longer decides the division; the conditions below do
Who is Competitive
An official contestant who is a Canadian citizen or permanent resident, or writes at a Canadian school or designated university, and who starts within the fixed window
Most students at Canadian schools qualify, provided the school starts the paper in the window
The window
"the student begins writing between 1:00 p.m. and 3:30 p.m. EDT (UTC-4) and finishes no more than 2.5 hours after beginning"
A morning sitting in Ontario would fall outside it; the table below converts the window by province
What only Competitive writers get
"Only students in the Competitive Division will be eligible for prize money and potential invitations to the CMO."
A student who hopes to reach the CMO must be in the Competitive Division
Question booklets
"Competition questions will no longer appear in the student response booklets."
Students receive a separate question sheet and write in a response booklet with QR codes and answer spaces
Question release
In the Americas, proctors get the question PDF at 12:00 noon EDT on the Thursday, one hour before the earliest Competitive start
Schools print the questions on the day; nothing can be seen in advance
Repêchage
The Repêchage (CMOQR) "has been discontinued as of 2026"
There is no second chance at a CMO invitation after the COMC; the COMC itself is the route
The CMS gives its reasons on a separate Repêchage page: from 2027 it will send more olympiad invitations straight from COMC results instead, and this lets it move the olympiads earlier, away from March spring breaks. In plain terms, the COMC paper in October now carries the whole weight that used to be shared with a take-home second round.
One inconsistency worth knowing about: the CMS student FAQ, read on the same day, still refers to the old "Canadian" and "International" divisions. The Changes page and the Prizes and Awards page use the new Competitive and Global names, and we follow those.
The 1:00 to 3:30 p.m. EDT start window, province by province
The CMS states the window in Eastern Daylight Time, UTC-4. On Thursday, October 29, 2026 the clocks have not yet changed (they move back on 1 November 2026), so Ontario and Quebec are on exactly that offset. The conversion below is ours, using the 2026 tz database offsets.
Competitive Division start window on Thursday, October 29, 2026, in local time (our conversion of the CMS window)
Province or zone
Offset that day
Earliest start
Latest start
Latest finish
Newfoundland
UTC-2:30
2:30 p.m.
5:00 p.m.
7:30 p.m.
Nova Scotia, New Brunswick, Prince Edward Island
UTC-3
2:00 p.m.
4:30 p.m.
7:00 p.m.
Ontario and Quebec
UTC-4
1:00 p.m.
3:30 p.m.
6:00 p.m.
Manitoba
UTC-5
12:00 noon
2:30 p.m.
5:00 p.m.
Saskatchewan and Alberta
UTC-6
11:00 a.m.
1:30 p.m.
4:00 p.m.
British Columbia (most) and Yukon
UTC-7
10:00 a.m.
12:30 p.m.
3:00 p.m.
What this means on the day
In the east the paper is an afternoon sitting that may run past the end of the school day; in British Columbia it can begin mid-morning. Either way, the start time is the school's decision, and families should ask what it will be.
A 150-minute paper started at the last permitted moment in Ontario ends at 6:00 p.m. Students should eat beforehand and plan the trip home.
Writers outside the window
A student who starts outside the window is placed in the Global Division, which has its own awards but, the CMS says, no prize money and no CMO invitation.
The CMS adds that an overseas student who qualifies may write in the Thursday window by registering as an independent student directly with the CMS.
The 80 points
Three sections, three ways of earning points
The CMS FAQ sets out the structure in a few lines. The COMC Problem of the Week page describes the same three parts in words. Together they say exactly how a student should write each section.
COMC structure and marking, from the CMS FAQ and Problem of the Week page (read 22 October 2026)
As Part A; partial marks possible for correct work when the answer is wrong
Problems that "draw on more knowledge" and "need a pencil and paper"
Advanced (Part C)
"Four advanced questions, worth 10 points each"
"Advanced questions require fully developed solutions"
Problems that "require that work be shown and involve arguments to support the answer"
Total
"Maximum score: 80 points."
Same 12 questions for every grade
Same paper from Grade 8 to CÉGEP
One line in the FAQ deserves to be read twice: "You are not obliged to show your work, but if you fail to do so and make a small error in your answer, you will not be awarded any points." Our arithmetic is that Part A and Part B together are worth 16 + 24 = 40 points, half the paper, and every one of those points is exposed to that rule. With no calculator allowed, small arithmetic slips are common. Working is not decoration on the COMC; it is insurance, and it costs a few seconds per question.
Same slip, two answer sheets: an intermediate question of ours worth 6 points (illustration ours; how many partial points are given is the markers' decision)
Sheet 1: answer only
Sheet 2: answer with working
Question (ours)
In triangle ABC, AB = 7, AC = 8 and angle A is 60 degrees. Find BC.
Same question
What is written
"BC = √43"
BC2 = 49 + 64 - 2(7)(8)cos 60 = 113 - 70 = 43, so BC = √43
The slip
2(7)(8)(1/2) is 56, not 70
The same slip, visible on the page
Correct answer
√57
√57
Possible result
No points: a wrong answer with no work
Eligible for partial marks: the cosine law is set up correctly
The CMS Getting Ready page says most COMC problems are based on the math taught in secondary schools and CÉGEPs, and that some need understanding beyond the curriculum. It names twelve potential topics. The names are the CMS's; the notes are ours.
Potential COMC topics, as listed by the CMS (read 22 October 2026), with our notes for calculator-free work
CMS topic
Our note
Probability
Count favourable and total outcomes as exact fractions
Euclidean and analytic geometry
Similar triangles, circle facts, distances and slopes
Trigonometry, including functions, graphs and identities
Exact values at 30, 45 and 60 degrees, learned cold
Exponential and logarithmic functions
Log laws and rewriting with a common base
Functional notation
Substituting cleverly chosen values
Systems of equations
Adding or subtracting whole equations before solving
Polynomials, including relationships involving the roots of quadratic and cubic equations
Sums and products of roots without finding the roots
The remainder theorem
Evaluating instead of dividing
Sequences and series
Arithmetic and geometric sums in closed form
Simple counting problems
Choosing, arranging and the complement
The binomial theorem
Coefficients from combinations, as in our problem 2 below
Elementary number theory, including tests for divisibility, number of divisors, and simple Diophantine equations
Factoring an equation into a product of integers
Every topic on that list has to be done by hand on the day. In our classes, COMC practice is always calculator-free from the first week, and students keep a short sheet of the exact values and identities they must know without looking. A student who can only find a cosine on a calculator has not yet learned it for the COMC.
Six practice problems
COMC-style problems of ours, from Part A to Part C
These six are our practice problems, not CMS problems. We wrote them for our students; none is taken from a past COMC. Two are at introductory level, two intermediate and two advanced, and every answer was checked in Python. Do them without a calculator.
Problem 1.Our practice problem, not a CMS problem. Introductory level. What is the value of 1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100?
Solution. Group the terms in pairs: (1 - 2) + (3 - 4) + ... + (99 - 100). There are 50 pairs, each equal to -1, so the sum is -50.
Problem 2.Our practice problem, not a CMS problem. Introductory level. What is the coefficient of x3 when (2x + 1)5 is expanded?
Solution. By the binomial theorem the x3 term is C(5, 3)(2x)3(1)2 = 10 x 8x3 = 80x3. The coefficient is 80. Forgetting to cube the 2 gives 10, the most common wrong answer.
Problem 3.Our practice problem, not a CMS problem. Intermediate level. How many positive integers less than 100 have exactly three positive divisors?
Solution. If n = p1a p2b..., the number of divisors is (a + 1)(b + 1)... For this to equal 3, which is prime, n must be a single prime squared, n = p2. The primes with p2 less than 100 are 2, 3, 5 and 7, giving 4, 9, 25 and 49. The answer is 4.
Problem 4.Our practice problem, not a CMS problem. Intermediate level. In triangle ABC, AB = 7, AC = 8 and angle BAC = 60 degrees. Determine the exact length of BC.
Solution. By the cosine law, BC2 = 72 + 82 - 2(7)(8)cos 60 = 49 + 64 - 56 = 57, so BC = √57. This is the question from the two answer sheets above: the line 2(7)(8)(1/2) = 56 is the one to check.
Problem 5.Our practice problem, not a CMS problem. Advanced level, full solution. Determine all pairs of positive integers (m, n) with m2 - n2 = 60.
Problem 5 · our fully developed solutiontext
Part C style question (ours). Determine all pairs of positive
integers (m, n) with m^2 - n^2 = 60.
Solution.
Factor: m^2 - n^2 = (m - n)(m + n) = 60.
Since m and n are positive, m + n > 0, so m - n > 0 as well,
and m - n < m + n.
The factors m - n and m + n differ by 2n, which is even,
so they are both even or both odd. Their product 60 is even,
so they cannot both be odd. Hence both are even.
Factor pairs of 60 into two even numbers, smaller first:
2 x 30 and 6 x 10.
(10 x 6 and 30 x 2 repeat these; 4 x 15 and 12 x 5 have an odd
factor.)
m - n = 2, m + n = 30 gives m = 16, n = 14.
m - n = 6, m + n = 10 gives m = 8, n = 2.
Check: 256 - 196 = 60 and 64 - 4 = 60.
Therefore the pairs are (m, n) = (16, 14) and (8, 2).
The parity step is what makes this a solution rather than a search. Without it, a student must test 4 x 15 and 12 x 5 and show they fail; with it, those pairs are ruled out in one sentence. This is the "simple Diophantine equations" topic from the CMS list.
Problem 6.Our practice problem, not a CMS problem. Advanced level, full solution. Three different numbers are chosen at random from 1, 2, 3, ..., 10. Determine the probability that their sum is divisible by 3.
Problem 6 · our fully developed solutiontext
Part C style question (ours). Three different numbers are chosen
at random from 1, 2, 3, ..., 10. Determine the probability that
their sum is divisible by 3.
Sort the ten numbers by remainder on division by 3:
remainder 0: 3, 6, 9 (3 numbers)
remainder 1: 1, 4, 7, 10 (4 numbers)
remainder 2: 2, 5, 8 (3 numbers)
A sum of three remainders is divisible by 3 exactly when the
three remainders are all equal, or are 0, 1 and 2 once each.
all remainder 0: C(3,3) = 1
all remainder 1: C(4,3) = 4
all remainder 2: C(3,3) = 1
one of each: 3 x 4 x 3 = 36
Favourable choices: 1 + 4 + 1 + 36 = 42.
All choices: C(10,3) = 120.
Therefore the probability is 42/120 = 7/20.
Sorting by remainder turns 120 cases into four small counts. The sentence explaining when three remainders add to a multiple of 3 is the argument the markers need to see; the counts alone are not a fully developed solution.
Timing the set
Problems 1 and 2: three minutes each. Problems 3 and 4: six minutes each. Problems 5 and 6: fifteen minutes each, written in full. That is roughly the pace a full COMC paper asks for.
Mark problems 3 and 4 as if no working had been shown, then again with your working. The difference is the insurance.
What the six share
Each one becomes short once the right structure is chosen: pairs, a binomial term, a divisor formula, the cosine law, a factorization, remainders.
Choosing the structure is the skill the COMC tests. Our classes spend more time on that choice than on any formula.
150 minutes
Spending two and a half hours on twelve questions
There is no official advice on pacing. This budget is ours, refined by timing our own students on past COMC papers from the CMS archive.
Our 150-minute budget for the COMC (ours, not the CMS's)
Minutes
Section
Aim
0 to 20
Part A, four questions
All four, each with a line of working beside the answer
20 to 60
Part B, four questions
At least three, with working that a marker can follow
60 to 135
Part C, four questions
Read all four first; write two in full and start a third
135 to 150
Everything
Recheck every Part A and B answer for a slip; finish each Part C solution with a sentence
The Part C budget is deliberately large. Part C is worth 40 of the 80 points, and a fully developed solution takes time to write well. A student who reaches Part C with ninety minutes left can afford to think before writing, which is how the strongest Part C answers are produced.
After the paper
What the COMC leads to, in the CMS's own words
Families ask about this more than anything else. The rows below are only what the CMS publishes, attributed page by page, because its pages give slightly different figures.
What follows the COMC, as stated on the CMS pages named (read 22 October 2026)
Outcome
What the CMS says
Where
CMO and CJMO invitations
About 100 to 120 top-ranking students from the COMC are invited to write the CMO or the Junior CMO
COMC 2026 home page
CMO invitations
"the top 100 (all figures are approximate) qualifying students are invited to the Canadian Mathematical Olympiad (CMO)"
Prizes and Awards page
From 2027
A larger number of olympiad invitations made straight from COMC results
Repêchage page
Awards
"The top six unique scores in any category earn awards"
Prizes and Awards page
Certificates
Quartile certificates: Performance with Distinction, Performance with Honours, Certificate of Participation
Prizes and Awards page
Summer camp
About 24 Canadian students in Grade 10 or earlier with strong COMC results invited to the Canada Math Camp
Prizes and Awards page
Universities
Results shared with partner universities to help them consider academic scholarships
Prizes and Awards page
Our reading, and no more than that: the figures differ slightly between pages, and the CMS itself calls them approximate, so no family should plan around an exact cutoff. What is consistent across every page is that invitations go to Competitive Division writers and are the CMS's alone to make. We prepare students for the paper. We cannot influence an invitation, and we never suggest that preparation guarantees one. The full road beyond the COMC, from the CMO to the International Mathematical Olympiad, is set out on the CMS's CMO and IMO pages.
Now, and next year
One week to 29 October 2026, and a plan for the 2027 COMC
Registration for 2026 closed on 22 October 2026, so there are two kinds of reader: students already registered by their school, and everyone aiming at next year. Our plans for each:
Registered for 2026: days 1 and 2. One past COMC paper from the CMS archive, timed at 150 minutes, calculator-free, marked strictly, with the no-work rule applied to Parts A and B.
Registered for 2026: days 3 to 5. Rewrite every Part A and B answer from that paper with a line of working. Write one Part C solution in full and compare it with the official solution.
Registered for 2026: days 6 and 7. Ask the school its start time and check it against the window table above. Rest the evening before.
Aiming at 2027: from now to June 2027. Calculator-free algebra, geometry, number theory and counting, one fully developed solution a week. CEMC's CIMC or CSMC on 18 November 2026 and its April 2027 contests make good written practice along the way.
Aiming at 2027: September 2027. The CMS says registration typically opens at the start of September, and its COMC Problem of the Week usually starts in the first week of September. Ask the school to register early, then move to timed past COMC papers.
Grade 8 or 9
A first COMC is a rehearsal. Aim at Part A and Part B, and one Part C attempt.
Grade 10 or 11
Aim at three Part C questions; the CJMO is for Grade 10 or below.
Grade 12 or CÉGEP
Often the final COMC year; official writers must be under 19 as of June 30.
Free CMS material
Free COMC preparation from the CMS, and how we use it
The CMS publishes a surprising amount for free. We send students to it rather than reproducing it, and build our own problems beside it.
Free CMS resources for the COMC (read 22 October 2026)
Resource
What the CMS offers
How we use it
COMC exam archive
Past COMC papers, free to download
Timed, calculator-free rehearsals; official solutions read after a full attempt
A weekly problem from early September, with its solution a week later
A Monday warm-up for the whole batch
Crux Mathematicorum
The CMS problem-solving journal; the CMS says all volumes are free to the public on the Getting Ready page
Stretch problems for students aiming at the CMO
A Taste of Mathematics (ATOM)
Enrichment booklets, most of them free PDFs
Topic reading for strong students between contests
Students who also write CEMC contests can find our guides to the Euclid, Fermat and the whole CEMC year. The COMC and CEMC papers reward the same written-solution habit, and many of our students sit both.
Placement
Four stages of a COMC writer
Our stages, used to place a new student in the first class.
From answers to arguments, without a calculator (ours)
Stage
What we see
1. Calculator reliant
Knows the methods but slips on arithmetic done by hand
2. Accurate
Clears Part A and most of Part B, with working shown
3. Arguing
Writes one or two Part C questions as fully developed solutions
4. Olympiad-ready
Attempts all of Part C and argues partial results clearly
For parents
Many strong students begin at stage 1 simply because school lets them use a calculator. The move to stage 2 takes a few weeks of daily hand arithmetic, and it pays off on every contest.
Stages 3 and 4 are about proof. They take months, and they are what the CMO, if it ever comes, will ask for.
For students
Show a line of working on every Part A and Part B answer. It costs seconds and can save points.
Read all four Part C questions before writing any of them.
More courses
Nine courses for a student on the olympiad path
Every course is taught live online by a teacher who knows the student, in a batch or one to one, from any province.
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.
Weekdays
Evening groups planned in Eastern time and shown in your own zone.
Weekends
Longer morning sessions for full 150-minute papers.
1-on-1
A private plan built around school and contest dates.
No calculators
Every COMC session is pencil and paper only.
Our own problems
New COMC-style sets each week, beside the CMS archive.
Working as insurance
Part A and B answers always shown with a line of working.
Part C marked
A fully developed solution returned with comments weekly.
Coast to coast
One class shared by students from Halifax to Victoria.
Your choice of size
A class of fifteen to twenty, or private lessons.
Student work
Code our olympiad students write
Some of our COMC students also learn to program, often to test a conjecture before proving it. A few projects are below, with more on the student labs page.
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
The CMS charges its registration through the school or the Open Writing Centre. Our monthly fee covers live teaching and nothing else, and it can stop at the end of any month.
What parents and students wrote on Google, unchanged.
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Parents and students ask
COMC: answers to common questions
What is the COMC?
The Canadian Open Mathematics Challenge is the Canadian Mathematical Society national open math contest. It has 12 questions in 150 minutes, scored out of 80, written on paper without calculators, and it is the main route to an invitation to the Canadian Mathematical Olympiad.
When is the COMC in 2026?
The CMS lists Thursday, October 29, 2026 in Canada and the Americas and Friday, October 30, 2026 elsewhere. The last day to register was Thursday, October 22, 2026.
What changed in the COMC in 2026?
The divisions are now called Competitive and Global. Only Competitive Division writers are eligible for prize money and possible CMO invitations, and they must start between 1:00 p.m. and 3:30 p.m. EDT. Questions now come separately from the response booklets, and the Repechage has been discontinued.
Who can write the COMC?
The CMS says it is open to students in all locations and at all grade levels, and recommends it for Grades 8 and up. Official participants must be under 19 as of June 30 and attending school full-time.
Are calculators allowed on the COMC?
No. The CMS says no mobile phones, calculators or other electronic devices are permitted. Compasses and protractors are allowed, so all arithmetic is done by hand.
How is the COMC marked?
Four introductory questions are worth 4 points, four intermediate questions 6 points and four advanced questions 10 points. The first two sections give full marks for a correct answer, but a small error with no work shown earns nothing. Advanced questions need fully developed solutions.
Can my child register without the school?
Only if the school is not participating. The CMS then offers a limited number of places at Open Writing Centres at partner universities, mostly in person, and suggests asking other local schools too. For 2026, registration has closed.
Does the COMC lead to the Canadian Math Olympiad?
Yes, for top Competitive Division writers. The CMS COMC page says about 100 to 120 top-ranking COMC students are invited to the CMO or the Junior CMO, and its Prizes page gives about 100 for the CMO. Invitations are decided by the CMS only.
Can you guarantee a CMO invitation?
No. We teach the mathematics and the written solutions, and we make no promise of a score, an award or an invitation.
When are your COMC classes?
Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays. We plan in Eastern time and confirm each class in your own time zone.
Related reading
Related pages
Other pages for students in Canada following the contest and olympiad path.
In the first class your child solves two calculator-free questions of ours and writes one Part C solution with a teacher, who marks it on screen against what the CMS asks for. You learn which of the four stages your child is at and what a year toward the 2027 COMC could look like.
Our teachers work from India and teach every class live on video, so students join from home anywhere in Canada. The quickest reply comes on WhatsApp.
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.
