From time to time there really are occasions when I need to know a mathematical formula, and it can sometimes be a pain to google when I don’t know what the term is. My goal in this is to make a thread I can search for when I need one, so- please add any formulas and tell how they apply. Thankee.

I’ve seen this called "The “Number of Handshakes” Formula but the first word problem I heard that used it involved pictures, so I’ll go with that.

There are eight siblings. They’ve had group shots and individual shots made, but now they want to have a series of pictures made in which each sibling will be pictured with exactly one sibling until ultimately each sibling will have a picture of himself/herself one-on-one with each other sibling (i.e. A will have 7 pictures, one showing him standing with B, then with C, with D, with E, with F, with G, with H, and with I, and B will have a picture made with A, C, D, E, F, G, H, and I, etc.). Each sibling will have 7 pictures of themself in all. How many pictures will need to be made (not including copies for each sibling to have a picture)?

The handshake version is “8 people are in a room. If every person shakes hands with every other person one time, how many handshakes will occur?” A surprising number of people will instantly answer “64”, incidentally.

Since I’m not sure how to write it the way I would in a word processor it may seem clumsy, but the formula for this one is:

In the below X is the number of pictures needed, N = the number of siblings.

X = half the sum of N (N - 1) (I know that’s clumsy looking)

## X = half the sum of 8 (7), or half of 56. There will need to be 28 pictures in order to have a shot of each sibling with each sibling.

**The Rule of 72**

Useful to know. The Rule of 72 tells you how long it will take money, if left alone, to double if the interest is compounded annually.

## If you invest $1,000 at 4% interest, it will be $2,000 in 18 years ( 72/4 = 18).

What are some other useful formulas (not theoretical or things used in quantum physics but things that have everyday life uses)?