Hand Computation Tricks.

What are they?

Well, the physics ones are just knowing common formulas.

The doubling principle one though is about something called the rule of 70. If you divide 70 by your interest rate, that's the number of compounds you have to wait through for the principle to double. So if you have a 7 percent interest rate, you have to wait 10 years for your principle to double.

The 10 factorial is just memorizing 9!, since 1-6 factorial can all be done easily inside 15 seconds, and I have those all memorized anyway, so 7 and 8 are just a single easy division/multiplication problem, and you only have to move a decimal place to find 10 factorial 9 factorial. That puts 11 easily within reach when you add 10x+x to get 11x, and anything beyond that would just be silly.

Another fun one I don't quite remember right has to do with fibonacci like sequences. Supposedly there's a constant multiplicative ratio between terms 5 and 10. It holds for the fibonacci sequence itself, but I haven't found another one it works for yet, so I dunno.

I don't get the "hand tricks". Are you sure you don't mean "rules of thumb"?

I meant hand computation tricks, as in tricks to complete computations by hand, preferably inside 15 seconds.

The real terrible problems I need to drill myself on are the systems of 3 equations. Those feel nearly impossible to solve within any sort of time limit.

What, you never learned how to reduce to row echelon form with your thumbs?

I've just had a quick play with this and I think I've found one.


Here's the sequence :

1 - first term
1
2
3
5 - fifth term
8
13
21
34
55 - tenth term
89
144
233
377
610 - fifteenth term
987
1597
2584
4181
6765 - twentieth term
10946
17711
28657
46368
75025 - twentyfifth term

So what I have is this :

10th term = 5th term x 11
15th term = 10th term x 11 + 5th term
20th term = 15th term x 11 + 10th term
25th term = 20th term x 11 + 15th term
30th term = 25th term x 11 + 20th term

It works !


Cool.
That's the best maths thing I've ever done.
Not bad for a Sunday morning

My latest fun one:

Imagine 9 lines all parallel to eachother, and 10 lines all parallel to eachother in a different direction. How many parallelograms are defined by those lines.

The answer:

First off let me say that I'm mostly proud because I arrived at my answer in a minute or so(I had more than 15 seconds because it was in the written rather than oral round(you get about an hour for a set of 45-60 questions))
The answer is 1620, but the real fun/interesting part was the summations that I multiplied together to get there.

1620 = (sum 1 to 8) * (sum 1 to 9)