I should be writing reviews for the last 3 shows I saw. What I’m doing instead is, once again, something no one asked for.

There are 122 different shows at the Toronto Fringe Festival this year, spread out across 13 days – 929 performances in total. I know it seems like Derrick Chua sees everything, but can he? (Hi, Derrick!) Mathematically speaking, I am here to solve the question that keeps you up at night.

The Question: What is the maximum # of unique shows you could (somewhat reasonably) see this year?

Assumptions:

• You will see each show exactly once.
• You reserved tickets in advance and nothing was sold out.
• All shows are of equal intrinsic value, and nothing is a “must-see.”
• You always take the fastest route (i.e. walk or drive). A chauffeur takes care of the driving and handles parking.
• I’m assuming average google maps traffic conditions, or that you’ll get out and run if it’s standstill traffic.
• No allowance for late starts or shows running long (though most have a bit of a buffer, so it shouldn’t matter too much).
• No fatigue or burnout, no scheduled breaks. You pack snacks and eat on the go.

Methodology: This was solved using integer linear programming. Each yes/no decision (attending a show or not) is turned into a variable that has to follow defined rules (e.g. no overlapping shows, no repeats, no fractional shows, etc.). I inputted the data into a solver, and refined the output manually. In short: I used a computer program to run every possible outcome, and then I checked its work.

Results: You can see 99 out of 122 productions (81%). Zoom in to read the full schedule:

As of this morning (July 6), Derrick has seen 33 shows, which puts him 11 behind the maximized schedule. Better luck next year, friend.