Putting on a 24 hour show is always a crazy fun time. It is not a show that lasts 24 hours, but rather a show that is written, rehearsed, and teched all within 24 hours. Here are some guidelines on how to run a 24 hour show. Note that literally anything goes, and you are free to ignore anything in this document; this is meant mostly as a summary of what we have found works well.
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Director - the director directs the show (gasp!). They should expect to be rehearsing from 8am to 8pm on Day 2, and come to the kick-off meeting on Day 1. They're in charge of the actors during the day of rehearsing, and should cast the show at the start of rehearsals.
Techie - techies do tech (gasp!); however, usually there is little tech during 24 hour shows. Most often there is one "helper" who sits at a light switch to control lights and helps find props that the director needs. If someone wants to do more intense tech (e.g. some lighting design), they are free to! In that situation, communication about the level of tech should happen before the 24 hours begin.
Publicity - It is often helpful to have one person dedicated to publicizing the show. They should do the things described in the "Publicity" section below.
Kick-off Meeting
Everyone involved in the show is required to be at the kick-off meeting. At this meeting, you should announce the title (if you haven't already)! At this point the 24 hours have begun, so people are allowed to discuss the plot and characters of the play as desired. You should have everyone declare what they are doing for the show (act, write, tech, etc.), and you should chose a director. It's also helpful to gather actor information for the writers: what genders they're willing to kiss, what size role they're willing to play, and any special skills they have. Also be sure to collect the contact information of everyone there.
At the end of the meeting, let the writers begin. You can send the contact info as well as a live doc of the script being written to all involved in the play.
Publicity
It's really helpful if someone (or a couple people) takes on the role of publicity. This person makes a funny/simply/shitty poster and hangs them up as much as possible. There should also be at least 3 dorm-spam emails (at least in my opinion - one in the morning, afternoon, and about an hour before the show) sent out to get people to come. Programs should also be made if possible, listing the actors, writers, techies, and director.
Tech
Unless someone wants to do tech, it is very minimal. People find costumes in their wardrobes, their dorms, and the Ensemble Office. Props are acquired in a similar way. It isn't uncommon to have props sketchily made out of cardboard. For lights, we can have someone sit at a light switch. For sound, we can use a laptop, with speakers if they can be found. Basically, make it work and don't worry too much about it being professional-looking.
Final Show
You have the actors, the play, and the programs. All you need to do is add audience and have a fabulous time! Good luck :D