Memory/mental math demonstrations

Hey guys, so I’ve been thinking. What do y’all think are some good ways to demonstrate (i.e. show off) memory and mental math skills? Of course, I know that showing off is not necessarily the most useful or productive use of these techniques, but whatever :slight_smile:

Regardless, what are some feats, tricks, or other cool things to do with memory and mental math techniques, when you want to show people what it is these methods can do?

I await your answers!


The one I most commonly do is day-of-week calculations. They don’t require any writing (you can ask people to tell you e.g. their date of birth), are very quick (I’m answering in less than a second), tehy are easy to understand (no need to explain what a cube root is or whatever) and they are relevant to the audience (they can pick a significant date for them).

I’ve also done memorizing a bunch of binary numbers generated by the audience, which is great for audience participation.

Other things that can work well: multiplying together two numbers while having a conversation with someone; exact square roots and cube roots (easier than they look); and squaring numbers (less digits for the audience to keep track of in e.g. 456² compared to e.g. 456 × 123).

If you search on this forum, there are quite a few other threads with ideas, mostly focusing on memory but with some mental maths too. @metivier in particular is also experienced with demonstrations, such as names and faces.

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Wow, thanks so much! That’s a lot of interesting ideas…

I also think day of the week calculations are one of the best, but I’m not nearly as fast as you are. Would you mind describing your process (how you do the calculation. How much is memory, how much is calculation. And how do you do it to real people? Like, do you ask for the year first?)

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For calendar, I use the method on my website, here: How to Calculate Calendar Dates – World Mental Calculation (the advanced variation at the bottom)

For this, I have the 100 year codes memorized, the 5 century codes, 12 month codes, and quite a few of the 366 birthday codes (e.g. 9th September I know immediately is +4).

I train using some tools I built myself, plus the Memoriad training software for time trials, and sometimes with a metronome if I’m pushing to break a record.


I must thank you again for the information you provided, I will be sure to check out your website.

One question I have is this. I know there are multiple ways to do calendar calculation that are all essentially the same mechanism. The only difference is everything is shifted in on direction or another to make there be more months with a code of zero, is that correct?

Because I use of of the “lesser” methods, where the only month with a year code of zero is May. And I have already memorized all the year codes in this method. Would you suggest I keep this? Or switch to a different one?


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Wait a minute, if I’m correct, I would not have to relearn the year codes, as they—in your method—are the same as in mine. I would merely have to relearn the month and century codes and voila! My one qualm is that the 2000 century would not have a century code of zero, as it does in my method

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Also, did you pick September 9th as a random example? Because, according to reading I’ve done, that is the most common birthday. More people are born on September 9th than any other date.

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Може да накарате публиката да Ви кажат 10 едноцифрени числа от 2 до 9 ,които да умножавате последователно.Например:7×8=56×2=…×7=…× 9=… и т.н.Доста е впечатлявящо,зависи от аудиторията и целта ,която искате да постигнете.Моето момче спечели" България търси талант",като представи някои от изброените от Даниел Тиимс дисциплини +представяне на числа ,като сбор от квадратите на няколко числа.Успех!


You can get the audience to tell you 10 one-digit numbers from 2 to 9, which you can multiply in sequence. For example: 7 × 8 = 56 × 2 =… × 7 =… × 9 =…, etc. It’s quite impressive, it depends on the audience and the goal you want to achieve. My boy won “Bulgaria is looking for talent” by presenting some of the disciplines listed by Daniel Thiems + presentation of numbers, as a sum of the squares of several numbers. Good luck!


That’s convenient—although look again at the method because 2000s does have a code of zero. I believe this is the best for competition purposes, where the range is 1600–2099, so 40% of years have a century code of zero.

However, the year 2000 has century code of zero and a year code of 00 + floor(00/4) + 2 = 2

Whether you change your system is your choice—I switched my system in 2016, when my max was 25 dates, and with my new system I could get to 35 dates. (Then with further improvements, I could get to 59 officially and 65 unofficially). It wasn’t so difficult, because I hadn’t trained for a while, and made sure to learn the year codes thoroughly before attempting any practice!

I chose it because it’s today’s date! But interesting fact—it’s actually my sister’s birthday today, and I often use that date as an example when giving classes in mental calculation.


I’m working on calendar calculation a bit, it takes me about 5 seconds per date but I want to get faster. I’m considering putting in the work and memorising the 366 date+month combinations. But i feel like the main thing slowing me down is the year code, i have to convert the year to a person and then quickly check what room of my house they were in to get the code. Is this something that will just get better with practice?
Do you also think it would be worthwhile to memorize every possible result of addition to eliminate the modular devision?, so e.g. after getting a result of 27 i would immediately see saturday in my mind etc. to eliminate the half-second required to devide by 7 and take the remainder.


(1) In the long run you should stop relying on any memory palace technique for that—the retrieval is just too slow, as you already identified. Same with learning vocabulary for speaking languages: memory palace methods are very inefficient for that. They are optimized for fast memorization, not fast recall.

Now that you have them in your mind, use some sort of flashcard system (spaced repetition software, or I just used my own tool) to drill them, aiming for almost instant recall.

(2) Yep, that’s how I do it—in fact I do all of the addition mod 7… so when I see 5 + 5 + 5 I immediately write “1” for Monday.


Thanks for your information.
I can now calculate the day of the week but it takes me nearly 20 seconds. I’d like to do it as quick as possible.
I’ve read faster advanced algorithm, but I don’t understand. Could you please help me with this?

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Good job—the first step is to be able to complete the calculation, and then afterwards you can improve the speed!

Are you using the method on my website, or another method?

The “faster advanced algorithm” maonly involves learning the 100 year codes, so e.g. for any year ending in 21, like 2021 or 1821, you add on the code for 21, which you learn from memory. With this system, the code for 21 is 0, which is easy. For 64 the code is +5.

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I use the system from the link you’ve mentioned.
Century code -
16 +2
17 +0
18 +5
19 +3
Year code - divided by 4 ( and then plus ) ( and then divided by 7 ) - remainder
Month -

How can I make it faster?
It’s also suggested to group Month and Day - to get a number. That can be doable for me. What I struggle is in the year code - division, plus and division - takes me some time.

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Okay, very good!

To use the faster advanced algorithm, you need to do item #3 below, and for best results you should do #1 and #2 too:

  1. Change the century codes to the ones listed near the bottom of the article

  2. Always add +2 when calculating the year; e.g. 21 → 21 + [21/4] + 2 = 28 (which, when divided by 7 gives 0, so you can just use this +0 as the year contribution)

  3. Memorize the year contributions, rather than calculating them each time. So I memorized that 21 → +0 and 64 → +5, rather than doing 64 + [64/4] + 2 (and optionally dividing by 7).

This is the same system I used when getting an official 59 dates in one minute in 2018, and also what the current record-holder Yusnier Viera uses.

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I believe 2020 Dec 7 was a Monday, so your calculation with the new method is correct :slight_smile: I can’t guess your mistake with the old method though, but perhaps you omitted the +2 for December.

Also: this has kinda hijacked this thread—if you have further questions please feel free to private message me.