2024 is potentially a huge year for mental calculation. Right now, many people are working behind the scenes to organize the next international competitions—including the first international Memoriad since 2016. Announcements will be made once each competition has confirmed dates.
In the meantime, I’m introducing a special challenge for groups. Mental Calculation is often done solo. So, just for something different, we are doing an experiment that I believe has never been done before: to challenge a group to work together to complete a calculation that would be extremely difficult for anyone working solo.
Brief Instructions
A small group of about 4 people works together. Someone tells them a large multiplication, such as 2468 × 7531, without showing them the numbers at any point. The group then works together to calculate the multiplication mentally, and says the answer aloud, with the digits in the correct order.
This is extremely laborious for a single person to do, because we only have enough working memory to remember about 10 digits at once. This is a biological limitation. However, during some parts of this calculation, it is necessary to remember more than 10 digits simultaneously 🤯
But if multiple people work together, they will have enough working memory combined.
Challenge Rules
The group must contain at least 2 people. There is no maximum group size, but there is no benefit to having too many people. I recommend trying 2–4 people.
One other person (who is not in the group, and who doesn’t need to be skilled at calculation) reads aloud a multiplication of a pair of numbers, such as 2468 × 7531. The group can use any mental calculation method to do the multiplication. The group must then read out their answer in the usual way, e.g “eighteen million, five hundred and eighty-six thousand, five hundred and eight”.
- The question must be read out once only, with no repetition.
- No-one in the group may see the numbers in the question.
- No-one in the group may write anything down (such as the question, answer or any method). The group must also not use their bodies to communicate numbers amongst the group for any reason, for example by raising 3 fingers to represent the number 3.
- The group may talk to each other an unlimited amount during the calculation.
- The final answer must be read out in the correct answer. For example “eighteen million, five hundred and eighty-six thousand, five hundred and eight”, and not in the backwards order or any unnatural jumbled order.
- The answer may be read out by one or more members of the group. It might be easiest for one member to read some part of the answer, before other members continue the answer.
You can submit your entry/entries by a short video. Contact me by email (or with this form) for more details. A live performance on Zoom is also possible to verify the submission. Please also provide the following:
- The names of the members of the group.
- The country or city where the group is based.
- A short written description of the method that the group used.
There is no particular deadline, but if I have successful entries, I will announce the top groups in early 2024.
Hints for the Best Performance
- Unless you already an expert, I suggest to start with 3-digit by 3-digit multiplications.
- The criss-cross method is usually recommended for someone calculating written multiplications solo. But, for this challenge, we don’t know yet whether it’s the best method! Is there another good method that is convenient for a small group?
- If you don’t know other fast mental calculators in your area, can you find a way to solve this challenge with 1–2 friends who can help you remember the digits, while you do the calculation steps?
- Can your group do 4-digit multiplications? How fast can it be done? How about 5-digit or larger multiplications? Can you do several consecutive questions without any errors?
Have fun, and I look forward to seeing how far you take this!
Bonus Challenge
If you can think of a cool name for this type of multiplication challenge, please send me your suggestions!