Re: Some maths help in a ebook

Eric Jacobsen wrote:

...

And thanks, Jerry, for the [x5]^2 trick, I'd not seen that before.

You're welcome. My father taught it to me. ("Casting out" too.)

They also missed the "divisible by three" trick, where if the sum of
the digits is divisible by three, the number is divisible by three.
This works recursively, i.e., if the sum of the digits is a
multiple-digit number, sum those. Repeat as needed until you get to
a number small enough to be recognizable as divisible by three.

It's a subset of the divisibility check for 9, known to accountants as "casting out nines". Use it as an accuracy check on arithmetic operations. An operation on the moduli is equal to the modulus of the operation on the numbers, so it provides a quick check. To increase the probability of finding an error from 8/9 to 98/99, do it again by "casting out" 11s. N mod(11) is the units digit minus the tens digit plus the hundreds digit minus .... Checking for divisibility by 11 is that easy.

And does anybody else find the x11 and x12 tricks kind of pointless? I
think both cases are simple enough to just do in my head more easily
than remembering their somewhat-convoluted tricks.

Something akin to the x11 method is _how_ I do it in my head. The process is simpler than the printed explanation,

Jerry
--
Engineering is the art of making what you want from things you can get.
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