Playwriting and Math

One of the many amazing things to come out of the Freedom Art Retreat back in 2011 was that one day, somewhere in between swimming in Pea Porridge Pond, eating grilled corn, drinking cocktails, singing along to ukeleles, hiking mountains and making group projects, I asked the group a question that had been on my mind for a while.  Actually, no, I tried to ask the question, but it was a barely formed, half articulated, bizarre mumbling thing in the general tenor of a question.

It was something like:  “So guys, I’m working on this 8-character play, Mad Props, and it’s a lot of characters!  But I was wondering, if I have 8 characters in a play, how many, um, if I wanted to know, like, how many different scenes are possible, with you know, different characters in different configurations, um, how would I figure that out?”

Now I used to be a math person, back when being a math person meant basic multiplication and division.  So, essentially, elementary school was when I peaked.  But I’m still a person who likes to figure things out, even if it’s not something I know how to figure out. That’s where the amazing powers of friendship and collaboration come in handy.  Thanks to the help of my fellow retreatants, particularly Jason Weber, we figured out what my question was, and then he even came up with the answer in the form of an amazing excel spreadsheet that figures it out for you using formulas.  Formulas!  On a theatre-in-the-woods retreat!

The key was remembering a math concept called “combinations (without repetition)” – just coming up with the right concept took a little while.  Did I mention I was having problems articulating the question?

It turns out what I was asking for was the total number of possible scenes, depending on total number of characters in the play, using different combinations of characters.  So, for example, if there are 8 characters in a play, then the total number of 1-character scenes possible in that play is 8.  The total number of 8-character scenes possible is of course, 1.  The trick is figuring out all the combinations of 5-character scenes and 3-character scenes, etc.  In an 8 character play, there are a total of 255 unique combinations of different characters on stage.  The only thing is, the formulas only give you the number of combinations.  You would have to figure out yourself what each of the unique combinations are.

For example, here are the 28 unique combinations for 2-character scenes in an 8-character play: ab, ac, ad, ae, af, ag, ah, bc, bd, be, bf, bg, bh, cd, ce, cf, cg, ch, de, df, dg, dh, ef, eg, eh, fg ,fh, gh

Here is what the basic formula looks like in my fancy spreadsheet (thank you Jason Weber!!):

=FACT(B7)/(FACT(A10)*FACT(B7-A10))
with B7 containing the total number of characters and A10 containing the # of characters in a scene

Ah, math.  Sometimes you are so helpful.

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