Mental calculations/tricks you've come up with


I just found this

“The Trachtenberg system is a system of rapid mental calculation. The system consists of a number of readily memorized operations that allow one to perform arithmetic computations very quickly. It was developed by the Russian Jewish engineer Jakow Trachtenberg in order to keep his mind occupied while being held in a Nazi concentration camp.”

When I was eight I came up with a really quick way of instantly multiplying any number by 99 in my head which is really similar. Didn’t write out the ‘formula’ at the time obvs but it was just

a x 99 = FIRST DIGITS: [a -1] SECOND DIGITS: [100-a]

e.g. 66 x 99 = 6534
89 x 99 = 8811

remember telling my teacher and she was like ‘oh you’re just multiplying by 100 and taking one very good’ and didn’t get what I was trying to explain at all.


or ones you’ve not come up with but are cool


this is neat


If you want to add up a sequence of numbers with an even number of elements, you just add the first and last number together and multiply by the number of elements divided by 2.

For example, all the numbers from 1 to 100 added up is 101*50=5050.

It works because if you keep adding pairs of numbers from either end of the sequence they always add up to the same number. So in this example 1+100, 2+99, 3+98, etc always add up to 101 and there are 50 pairs in the sequence.


yeah that’s cool


One I learned when I worked in accountancy (arguably the only thing I learned when I worked in accountancy) was that if a set of numbers don’t add up the way you expect, and the difference between what the total should be, and what the total actaully is, is divisible by 9, then it is likely to be a transposition error.

12 12
13 13
14 14
15 51
20 20
21 21
= =
95 131

Difference 131-95=36


So…times the number by 100 and then minus one times the number

Not sure we need a fancy way to remember that do we,


but it’s not really doing that… it means you can say the answer out loud as you are still calculating it


I’ve probably missed the point somewhere


obviously that is essentially what it is but its just a quicker way than multiplying by 100 and taking away lol not a big deal

please post some maths problems


This is a good pop Sci book about mathematicians. It has some cool number theory stuff in it as well.


Big fan of the 7 bridges of konigsberg


I think every kid does this at school.

It’s a classic.


I only came across it at college in IB maths. My school maths teacher was utterly incompetent though so probably


I think we did it when we were 11.


I don’t remember ever doing this

:trophy: I got best in school in the UK maths challenge :trophy:


I GOT THAT TOO (in primary school, got rubbish at maths after)


Can’t remember if it was best in school but I definitely got a Gold Award in the UK Maths Challenge. Not sure how impressive that actually is/was mind.


I remember it being a multiple choice thing where you get penalised for incorrect answers so if you just went for the ones you actually knew it was fairly easy to get gold


I’ve taught it to year 5/6s every year