The Junior Mental Calculation World Championship 2026 will take place in September 2026 in Bielefeld 🇩🇪.
The official website of the JMCWC has the official information about the program, rules (PDF), and contact details in case you have any questions about the competition. 📧
This page contains various resources for participants, so that you can prepare effectively. I hope it will help you! 😊
Changes between 2024 → 2025 Competitions
- New version of the Primes category, where the numbers are smaller and the primes could be much larger (see Simulator).
- There are minor changes to the number and difficulty of Currency and Fraction Multiplications (see Simulator)
- One of the Surprise categories is announced to be highest common factors (HCF) and lowest common multiples (LCM). It is worth more than 100 points. No further information is provided, because it is anyway a Surprise. To be clear:
- HCF(20, 30) = 10 because 10 is the largest number that divides into both 20 and 30.
- LCM(20, 30) = 60 because 60 is the lowest positive number that is a multiple of both 20 and 30.
- You will no longer be penalized for correcting an answer a second time. But anything that looks like intermediate calculations will be penalized.
JMCWC Simulator
The exam contains 20+ pages of standard questions, plus a few pages of Surprises.
George Lane has prepared Simulators of the standard questions for 2024, which you can download here to see what the exam will look like. You will need Excel, or an open-source alternative such as LibreOffice.
Note: these Simulators were updated on 12-Aug-2025. These are now the 2025 Simulators.
- Simulator for Juniors 1 (ages up to 11 years)
- Simulator for Juniors 2 (ages 12–14 years)
- Simulator for Seniors (ages 15+ years)
The Surprises use similar skills, but they are not in any simulator, because they are a surprise 😉
Instructions for Simulator
The simulators randomly regenerate new questions every time you open or edit the file. The answers are written in white, and you can reveal them simply by changing the answer column to your choice of colour, for example red.
Be caseful not to edit or close the file between solving the questions and revealing the answers, otherwise you won’t be able to check them! On LibreOffice, changing the colour also regenerates all the questions, which is unhelpful. However, you can turn off auto-calculation to avoid this problem.
The print ranges are already set. but they can still be checked before printing. If anything looks bad, just go to Page Layout & Margins, and set the page to print on 1 tall by 1 wide.
As an alternative to printing, you can simply write the answers on paper and then check them against the answers in the document.
General Advice
Generally, it is recommended that participants start at the beginning of the paper and work through systematically. However, most participants will not finish the paper, so it may be a good strategy to skip questions or sections that you find difficult, so you have time for your favourite types of question and to check the Surprises.
It is strictly forbidden to write any method or intermediate calculations anywhere during the test. All calculation must be done mentally, and only the answers may be written.
Mental Calculation Techniques & Training Tools
Some of the categories are best solved using advanced techniques, that you might not learn at school! Here are some resources and tools for the most difficult categories. Many participants in the competition will only know the basics—they won’t know most of these extra methods!
Calendar Dates
- Human Calendar Algorithm: the fastest human calendars use a variation of this method.
- Online Training Tool: this was developed by Katie Kermode—a world record-holder at memory sports.
Multiplication
- Cross-Multiplication Method: how to multiply large numbers like 3772 × 2843 = 10723796
Division
- Cross-Division Method: how to divide by large numbers like 2843
Fractions
- Fraction Addition and Subtraction: Mathematics and algorithm
- Fraction Multiplication and Division: Mathematics and algorithm
Square Roots & Deep Roots
- Estimating Square Roots: fast method to get 3–5 digits of accuracy on inexact square roots.
- Estimating Deep Roots: fast method to get 2–3 digits of accuracy on inexact cube roots and deeper roots.
- Exact Square Roots
- Exact Cube Roots
Sums of Squares
- Online Training Tool: makes practice more efficient, as it checks your answer automatically. Sums of squares questions typically have multiple possible correct answers!
Surprise Tasks
- PDF with some Example Surprise Tasks for my 2025 workshop in Bielefeld. I recommend to try this under timed conditions (15–20 minutes) and then study it to see whether you can think of better techniques for some questions. Important: the Surprises in the real JMCWC competition are (of course) a surprise. They will mostly be quite different to these examples, and different every year.
Good luck—see you in Bielefeld! 🎉