Arithmetic mind hacking, part 1: addition

I have a bad memory for numbers. Really bad. It has improved since I started studying arithmetic strategies. I wish I started earlier, but we didn't have the internets when I was younger, o, also my social standing did not depend on my number-crunching abilities then.

Let's talk about addition. I think this is the easiest concept to absorb for most people.

You have one cookie, then you get another cookie from a loving spoiling parent/guardian, then you have how many cookies?

Zero; because before you considered the metaphysical abstract notion of numbers you already ate the cookies.

To crunch numbers quickly we need to get practical. Brutally practical, if it doesn't work for you, practice. If it still doesn't work for you, simplify, adapt, remould, evolve; stir and shake; rinse and repeat.

Say I have... 2512 cookies and I find 3467 cookies stored in a jar. How many cookies do I have in total?

First strategy proposal:

I round off the trickiest looking number, to me that would be 3467, upwards to 3500; that would be a difference of 33.

I add 3500 to 2500 and add 12 later.

3500 + 2500 = 6000

Then I take 33, I round that off to 40.

6000 - 40 = 5960

I took too much so I give back 7.

5960 + 7 = 5967

I almost forgot I suspended 12 from the game; so I gotta get it back.

5967 + 12 = 5979.

2nd strategy proposal:

That previous strategy took 4 steps. It could get simplified.

How about starting by subtracting 12 from the rounded up difference of 33?
Conceptually it's like this: I borrowed 33 to get a nice round number, but instead of paying back in full, I pay back some right now (12).

33 - 12 = 21 (I still owe)

So I add as we did previously.

3500 + 2500 = 6000

We pay back the 21 by subtracting.

6000 - 21 = 5979

The difference

The first is more explicit, but it requires more memory, because of the 12.

The 2nd requires a wee less memory for numbers but it requires some practice because it requires the use concepts of borrowing and repayment in the rounding-of-the-numbers phase; but the payoff is in the number of steps.

It's one of those memory vs. time trade-offs.

The third and final strategy proposal

Go into heuristic mode. Check whether 10 and 60 make a hundred, 2 and 7 make a ten. No?

Now just add those up

(10 + 60) + (2+7) = 79

3400 + 2500 = 6000


This one requires a heuristic, in contrast with the previous proposals, that checks if a sum of decimal numbers go over 9.

Final note

The previous strategies were overkill for this problem.

For instance 789 + 837 and the previous strategies would work out great with this example.

Round off the number which contains a combination which add up to more than 9.  The one closest to 9; which would be 789. We have a debt of 11; in other words, we borrowed 11.

800 + 837 = 1637
1637 - 11 = 1626

During addition, check for sums larger than nine. Round off or just add the numbers. It's quite simple really. Some people have the innate ability to figure out these strategies, but other people need a tiny push in the right direction.