This trick was taught to me by my
father when I was a kid. I don’t
know how it works, only that it
does. If someone here knows the
mechanism of how it works please
let me know. My father found this trick in a book
of letters by the Lubavitcher Rebbe
(Igros Kodesh vol. 8 page 266),
who in turn was quoting a 15th
century Talmudic work called the
Kol Bo. The Kol-Bo brings it as a trick
Yeshiva students used to in order
to amuse themselves (this was
before the days when cat gifs were
but a mouse-click away), as a way
“to find a person’s age through logic [without being told explicitly]
”, though the trick can work for any
number. Here’s how it goes: You ask someone to choose a
number between 1 and 100. You
then ask them to divide the
number into 3 and give you the
remainder (e.g. if the number was
10, 9 divides neatly into three and then the remainder is 1). You then
ask them to divide their original
number into 5 and give you the
remainder of that, and then do the
same with 7. You should now have 3 numbers,
the remainders of dividing the
original number into 3, 5 and 7;
let’s call them x3, x5 and x7
respectively. Multiply these
numbers as follows: x3 should be multiplied by 70, x5 by 21 and x7
by 15. Add them all up and if it
adds up to more than 100
(technically, 105) subtract 105 until
you get the right number. An example: Let’s take the number
32. x3 = (32 % 3) = 2
x5 = (32 % 5) = 2
x7 = (32 % 7) = 4 so now let’s multiply them: x3 * 70 = 140
x5 * 21 = 42
x7 * 15 = 60 Adding them up we get: 140 + 42 + 60 = 242 Subtracting 105 we get 137, still
more than 105, so we subtract 105
again and get 32, our original
number! This trick can work for numbers
larger than 100 as well but you
have to know in which group of
100 (technically 105) the original
number is in. In the case of larger
numbers you might have to ADD 105 instead of subtracting in order
to get to the right number. I wrote a small Ruby program to
run this trick (here: Igros Rubygem)
, and a blog post about it (here:
program[0] and program[0] 2.0). Again, if anyone knows how this
trick works please post in the
comments. Edit: thanks Gerwin Dox for
explaining in the comments and
Abhishek Khare for offering the
following explanation: Source: https://www.quora.com/ What-are-some-great-
mathematics-tricks-you-know-of

I just fainted