Scroll below if you want to learn more about our future and past events and about all the different disciplines faced by participants.
Click here for some CMSA sample disciplines and training tools.
The 2023 National Mental Math Championship will be held on Sunday November 12 in Montreal!
The results of 2023 Honorary Mental Math Challenge have just been published!
Please refer to the front page of this website for more details about those events.
Past CMSA Mental Math events
- The full results of the 2023 Honorary Mental Math Challenge are up on this page.
- Congratulations to Hua Wei Chan for his second Canadian mental math champion title! Click here for the full results of the 2022 National Mental Math Championship.
- The full results of the 2022 Honorary Mental Math Challenge are up on this page.
- Thanks and congratulations to everyone who participated in our unofficial 2021 Honorary Mental Challenge! Congratulations to Hua Wei Chan in Alberta, Canada, for managing the best results overall. Congratulations to Jean Beland in Granby, Canada, for his second place. Congratulations to 10-years-old Kaloyan Danielov Geshev for his third place and for his amazing demonstration a few days ago at Bulgaria’s Got Talent. Click here for the full results, for more “fun facts” about the participants and for a link to a video of young Kaloyan showing off his skills on tv.
- Congratulations to Hua Wei Chan for his victory at the 2019 National Mental Math Championship and for his 2 new national mental math records! And thanks and congratulations to everyone who participated in one way or another. The 2019 National Mental Math Championship was held Saturday November 23 in Montreal. Click here for the highlights and the full results.
- Congratulations to Jean Béland for his victory at the 2018 National Mental Math Championship! And thanks and congratulations to everyone who participated in one way or another. The 2018 National Mental Math Championship was held on September 15 simultaneously in Montreal, Toronto and Vancouver. Click here for the highlights and the full results.
Updated CMSA mental math events and rules
This is the format that, until further notice, we will use for all future in-person official mental math events as well as all honorary challenges.
Competitors will be tested on their ability to solve as many additions, multiplications and divisions as possible during a series of brief 5-minute exercises. Most adults and students are fully capable of solving all those problems, but it will be impossible to answer them all correctly during the very limited time available.
Our events are open to people of all ages and all skill levels. No matter how good or how bad you are at mental calculations, one of our three sections should be well-adapted to your skill level.
- The Beginner section: With easier problems, and the possibility to write down all your calculations.
- The Regular section: Same problems as the Advanced section, but you’re allowed to write down all your calculations.
- The Advanced section: You have to calculate everything mentally before writing your answers. Your points won’t be counted if you write down your calculations.
The three main challenges: additions, multiplications and divisions
Although many more optional challenges will later be presented, only the first three challenges will determine the final ranking. For each of those three challenges, competitors will have two 5-minute long attempts separated by a short break. In each case, only the best of those two results will be counted.
- For participants in the Regular and Advanced sections, the first challenge will be additions of ten 2-digit numbers like 36+44+78+14+97+32+28+81+96+25. /// Participants in the Beginner section will instead have to add five 2-digit numbers instead of ten. A possible problem would be something like 34+71+93+28+29.
- For participants in the Regular and Advanced sections, the second challenge will be multiplications of two 2-digit numbers like 47 multiplied by 82. /// Participants in the Beginner section will instead have to multiply one 2-digit number by one 1-digit numbers like 43 multiplied by 6.
- For participants in the Regular and Advanced sections, the third and last mandatory challenge will be divisions of a 3-digit number by a 1-digit number between 2 and 9. So 732 divided by 9 would be a possible example. When necessary, you will need to write a dot or a comma and the next correct 2 decimals*. For 732 divided by 9, you would need to write 81.33 (or 81,33) for your answer to be considered valid /// Participants in the Beginner section will have to divide a 2-digit number by a 1-digit number. When necessary, they will need to write a dot or a comma and the next correct 1 decimal. You could be asked to divide 61 by 7, and you would have to answer 8.7 (or 8,7). *See the section below for more precisions on that point.
- As mentionned previously, other optional challenges will be presented for those who might enjoy them. Whether or not you choose to try them won’t influence the final ranking of a championship. The nature and rules of those optional challenges will be explained at the bottom of this page.
All the problems presented will have been generated randomly by specially designed Excel documents. You can find those documents in the sample disciplines and training tools section.
During an in-person event, by default most participants you will be shown 2 pages with 30 additions each, 2 pages with 64 multiplications each and 2 pages with 49 divisions each. Those extremely rare participants who might be able to solve more than this can write to us in advance to request more pages. During an honorary challenge, the documents provided will be long enough for partipants of any conceivable skill levels.
* One important precision about the correction of divisions: When you will need to add the correct following 2 decimals (or 1 decimal in the Beginner section) to your answer, we will accept either the straight non-rounded up or down answer, or when applicable the correctly rounded up or down answer. For example, the complete answer to 149/7 is 21.28571428571… We only want you to write 2 decimals past the dot, so 21.28 would be an acceptable answer and 21.29 (correctly rounded up) would be another acceptable answer. However, 21.27 wouldn’t be considered acceptable because in that case, rounding down wouldn’t make sense. For 155 divided by 7, the more complete result gives us 22.142857… In this case, rounding does not change anything and 22.14 is the only acceptable answer. If the practice documents we provide include answers with 3 decimals and not 2, that’s only to help for those cases where rounding up or down might make sense.
Overall scoring rules
- For additions we simply add up the number of good answers. All the questions presented are about equally difficult.
- For multiplications and divisions, we also add up the number of good answers, but half a point will be subtracted for every wrong or missing answer. This is to avoid giving an incentive to skip the most apparently difficult questions. No penalty will be given for unanswered questions past the last question that was answered.
DON’T SKIP ANY PROBLEM! Except for additions where all problems are about equally difficult, all missing answers will be penalized.
Final ranking calculations
*During an honorary challenge, you don’t have to worry about that part. We’ll take care of compiling everything and coming up with an overall result for everyone.
As we’ve said only the first three challenges will determine the final ranking. All the other optional challenges are mostly just for fun and bragging rights. For each of the three official challenges, each contestant will be awarded a score that can range from 0 to 100. Those three scores will be added at the end and whoever get the most points wins.
For each challenge, the person who obtained the very best score will automatically have a score of 100. Other contestants will have their score calculated by taking the number of good answers they obtained and by dividing that number by the number of good answers obtained by the best competitor and by multiplying the result by 100. So if the best performance in the division challenge was 50 good answers and you obtained 40 good answers, your official score for that challenge will be 80 (40 divided by 50 and multiplied by 100).
We’ll present three different scoreboards for competitors in the Beginner, Regular and Advanced sections. When applicable, honorific titles will also be given to whoever manages to the best results among the Senior (60 years old or older), Junior (13 to 17 years old) and Kid (12 years old or younger) age groups. Non-Canadian citizens can’t become the official “Canadian Mental Math Champion”, but they are more than welcome to compete in any section and show everyone who’s boss!
Optional challenges for the highly motivated
As we’ve already said: 5 additional challenges will be offered, but they will be completely optional and they will each be judged separately. None of those optional challenges will influence the final ranking of any event. You don’t have to practice them if you don’t want to. We’re only offering them because they can be fun and because we want to see some new national records being established.
The 5 optional challenges will be the following:
- Advanced multiplications: Multiplications of a 3-digit number by another 3-digit number. So 872 multiplied by 643 would be a possible example. As many as you can in 5 minutes. 1 point for each correct answer. Half a point penalty for each wrong or missing answer. Here’s one possible method you can learn to use to do this faster. And here are some more complete explanations for the same method.
- Squaring: Squaring as many increasingly large numbers as you can. As many as you can in 5 minutes. First set of 15 problems will be 2-digit (63² for example). Those first few problems will probably be more than enough for most participants. For those who manage to get through all the 2-digit numbers, the next series of 15 problems will be 3-digit (352² for example). All the rest will be 4-digit problems like 6507². 2 points for each 2-digit numbers. 3 points for each 3-digit numbers. 5 points for each 4-digit numbers. Half a point penalty for each wrong or missing answer. Note that there are relatively simple techniques you can learn that makes squaring much easier and faster than other forms of multiplications. It’s one of the first “impressive tricks” that beginner mental calculator can learn to show off to their friends. Doesn’t mean you’ll instantly become good without practice!
- Square roots: Calculate the square roots of 6-digit numbers. As many as you can in 5 minutes. 1 point for the first correct digit of each answer. 2 points for the second. 3 points for the third. 4 points for the fourth. 5 points for the fifth. 6 points for the sixth. 7 points for the seventh. 8 points for the eight. So up to 36 points for a completely correct answer. Less for a partially correct answer. Half a point penalty for a completely wrong or missing answer. Note that once you become familiar with the techniques involved, calculating the square roots of a 6-digit numbers isn’t necessarily more difficult than doing the same thing for a much smaller number.
- Calendar calculations: Can you quickly tell me what day of the week was October 23, 1743? Jean Béland and many others can correctly calculate the correct answer for dozens of similar problems in just one minute! It may seem borderly impossible, but it’s actually something that with practice you can learn to do very quickly in your head. How? Here’s one simple way. And if you have a system for memorizing numbers, there’s a much quicker way explained in French here and in English here. To save time you can answer using the numbers 1 to 7 instead of writing down the words “Monday”, “Tuesday” and so on. We can ask for any date from the year 1600 to 2099. You will have one 1-minute attempt and one 5-minute attempt. 1 point for each correct answer. Half a point penalty for each wrong or missing answer.
- Insane multiplications: Multiplications of an eight-digit number by another eight-digit number. So something like 79,960,546 multiplied by 25,349,034. As many as you can in 5 minutes. 1 point for each correct answer. Half a point penalty for each wrong or missing answer. Yep…
- No “beginner versions” of those optional challenges will be offered.
- For all the optional challenges, the main scoreboard will be for those who didn’t write down their calculations before arriving at their answers. A second scoreboard will be for those where not everything was calculated mentally and some calculations were written down. Difficult problems are much less difficult when you don’t have to do them all in your head! Whether or not you signed up for the Advanced or the Regular section, you can choose to try some optional challenges while writing down your calculations and try some other optional challenges while calculating everything in your head. If you’re noting down anything else but the final answer, you’re considered to be participating in the Regular section for that event.
- We’ve tried to simultaneously allow some participants to attempt some optional challenges more than once while also limiting the amount of time needed to get through everything. Here’s the solution we came up with: You’re allowed a maximum of 5 attempts in total for all optional events, and you can choose to distribute those 5 attempts however you prefer! So you could for example choose to attempt advanced multiplications twice and calendar calculations twice while skipping all the other optional events. Or you could try everything once. Or skip everything. Important note: –
ThreeTwo attempts* is the maximum for any single optional challenge. – The one-minute and five-minute versions of calendar calculations count as just one attempt. So if you decide to use two of your five attempts on this one, you would be able to try the one-minute and five-minute formats two times each. – When you attempt the same optional event more than once, only your best result is counted at the end. – You have to decide in advance how you plan to use your 5 attempts. You can’t change your mind depending on your results!
*2023 update: To avoid having to prepare 3 different versions of everything, we’ve recently decided to allow a maximum of two attempts instead of three for each optional discipline. You’re still allowed a maximum of 5 attempts in total for all the different optional disciplines.
And sometimes, we may add one more “special event”
We initially added this optional at the very last minute to one of our honorary challenges. Preparing it can very time-consuming and we can’t guarantee that it will be coming back.
It’s called “Unpredictable Calculations”. It’s inspired by one event faced by the participants of the Des chiffres et des lettres TV show. For all kinds of reasons, it operates under different rules than all the others, hence the “special event” designation.
- This “special event” was one more optional part to the “2022 Honorary Challenge”. We don’t currently know whether or not we’ll add this to any of our future events.
- You can either choose to try it or choose to ignore it. It doesn’t count for the “maximum of 5 attempts in total” rule for all the other optional events.
The problems you will see might look like this one:
((((( 32 x 13) – 46) / 5) + 17) x 4).
- The exact format will be unpredictable, but they will always include six different numbers along with some combination of additions, subtractions, multiplications and divisions.
- The problems presented can always be solved by simply proceeding from left to right. All the parenthesis are only there to make it clear that you don’t need to bother with any of the rules about the order of operations. As you probably know, those rules state that all the multiplications and divisions are supposed to be done before all the additions and substractions. So 12 – 2 x 5 = 2 and not 50. With parenthesis (12 – 2) x 5 = 50 and not 2. For all the problems you will see in this challenge, you can choose to just mentally ignore the presence of all those parentheses and simply always calculate everything from left to right.
5 minutes in total. One point for each correct answer. Half a point penalty for each mistake.