As it turns out, the equation that will tell you for any size group of people

*n*how many possible relationship configurations (couples, triads, and so on) are possible within that group is pretty complicated. It took a lot of work and many sheets of paper, and the considerable brainpower of a couple people with degrees in mathematics, but the equation is:

This will tell you for any group of people

*n*how many possible relationship configurations exist in that group.

And the number goes up fast.

*Scary*fast. For

*n*=9, there are 502 possible relationship configurations in that group. The number of people in the Squiggle I belong to is 15; I haven't calculated the number of possible relationship configurations exist in such a group.

I think I'm going to make this formula into a T-shirt.

- Current Mood: geeky

## Comments

james_the_evil1janetmilessweheg

http://www.mathsrevision.net/alevel/pure/binomial.php

That was a formula taught to me at age 16 or 17; before I went to university. Ouch, over 2 decades ago. The mathematicians in your group should have known it without thinking!

tacitkiwitayroquaryn_dktacitnis the size of the group; k is the counter for the Riemann sum.quaryn_dkquaryn_dkblaisepascaltacitblaisepascalI get, by both closed form and summing the damn thing, 501 for n=9 instead of your 502, and I get 32768-15-2 = 32751 for n=15.

Of course, I recognised Pascal's Triangle instantly.

tacitn-case (that is, there should be 4 possibilities in a triad, the three dyads plus the triad itself). There are 502 possibilities forn=9, if you count the 9-some case as well. Didn't catch that last night; we need to add one to the result.We (well, not me, but the math geeks among us) recognized the solution once we closed in on it, but we took a very backward and circuitous route to get there.

pstscrptIn this case, though the denominator almst spells out "kink!", which I think outweighs it.